The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling to gravity arising in beyond-generalized Proca theories, the speed of gravitational waves ct on the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological background can be equal to that of light c under a certain condition. By using this condition alone, we show that the speed of gravitational waves in the vicinity of static and spherically symmetric black holes is also equivalent to c for the propagation of odd-parity perturbations along both radial and angular directions. As a by-product, the black holes arising in our beyond-generalized Proca theories are plagued by neither ghost nor Laplacian instabilities against odd-parity perturbations. We show the existence of both exact and numerical black hole solutions endowed with vector hairs induced by the quartic-order coupling.

The Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories up to quartic order are the general scheme of scalar-tensor theories allowing the possibility for realizing the tensor propagation speed ct equivalent to 1 on the isotropic cosmological background. We propose a dark energy model in which the late-time cosmic acceleration occurs by a simple k-essence Lagrangian analogous to the ghost condensate with cubic and quartic Galileons in the framework of GLPV theories. We show that a wide variety of the variation of the dark energy equation of state wDE including the entry to the region wDE&lt
-1 can be realized without violating conditions for the absence of ghosts and Laplacian instabilities. The approach to the tracker equation of state wDE=-2 during the matter era, which is disfavored by observational data, can be avoided by the existence of a quadratic k-essence Lagrangian X2. We study the evolution of nonrelativistic matter perturbations for the model ct2=1 and show that the two quantities μ and Σ, which are related to the Newtonian and weak lensing gravitational potentials respectively, are practically equivalent to each other, such that μ≃Σ&gt
1. For the case in which the deviation of wDE from -1 is significant at a later cosmological epoch, the values of μ and Σ tend to be larger at low redshifts. We also find that our dark energy model can be consistent with the bounds on the deviation parameter αH from Horndeski theories arising from the modification of gravitational law inside massive objects.

In U(1) gauge-invariant scalar–vector–tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ→ϕ+c, we show the existence of new hairy BH solutions where a cubic-order scalar–vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

We study relativistic star solutions in second-order generalized Proca theories characterized by a U(1)-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

We study the evolution of gravitational waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass mg that depends either on the inflaton field φ or on its time derivative φ, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's R2 inflation model with a φ-dependent mg, and the second is a low energy-scale inflation model with a φ-dependent mg. We compute the energy density spectrum ΩGW(k) today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both cosmic microwave background and DECi-hertz Interferometer Gravitational wave Observatory, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential V(φ)=M2φ2/2 around φ≈Mpl (where Mpl is the reduced Planck mass), we find that the peak position of ΩGW(k) induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.

We present a family of exact black-hole solutions on a static spherically symmetric background in second-order generalized Proca theories with derivative vector-field interactions coupled to gravity. We also derive nonexact solutions in power-law coupling models including vector Galileons and numerically show the existence of regular black holes with a primary hair associated with the longitudinal propagation. The intrinsic vector-field derivative interactions generally give rise to a secondary hair induced by nontrivial field profiles. The deviation from General Relativity is most significant around the horizon and hence there is a golden opportunity for probing the Proca hair by the measurements of gravitational waves (GWs) in the regime of strong gravity.

In the context of generalized Proca theories, we derive the profile of a vector field A(mu) whose squared A(mu)A(mu) is coupled to the trace T of matter on a static and spherically symmetric background. The cubic Galileon self-interaction leads to the suppression of a longitudinal vector component due to the operation of the Vainshtein mechanism. For quartic and sixth-order derivative interactions, the solutions consistent with those in the continuous limit of small derivative couplings correspond to the branch with the vanishing longitudinal mode. We compute the corrections to gravitational potentials outside a compact body induced by the vector field in the presence of cubic, quartic, and sixth-order derivative couplings, and show that the models can be consistent with local gravity constraints under mild bounds on the temporal vector component. The quintic vector Galileon does not allow regular solutions of the longitudinal mode for a rapidly decreasing matter density outside the body.

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordstrom (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.

In a model of the late-time cosmic acceleration within the framework of generalized Proca theories, there exists a de Sitter attractor preceded by the dark energy equation of state w(DE) = -1 -s, where s is a positive constant. We run the Markov-chain-Monte Carlo code to confront the model with the observational data of the cosmic microwave background (CMB), baryon acoustic oscillations, supernovae type Ia, and local measurements of the Hubble expansion rate for the background cosmological solutions and obtain the bound s = 0.254(-0.097)(+0.118) at 95% confidence level (C.L.). Existence of the additional parameter s to those in the Lambda-cold-dark-matter (Lambda CDM) model allows to reduce tensions of the Hubble constant H-0 between the CMB and the low-redshift measurements. Including the cosmic growth data of redshift-space distortions in the galaxy power spectrum and taking into account no-ghost and stability conditions of cosmological perturbations, we find that the bound on s is shifted to s = 0.16(-0.08)(+0.08) (95% C.L.) and hence the model with s > 0 is still favored over Lambda CDM model. Apart from the quantities s, H-0 and the today's matter density parameter Omega(m0), the constraints on other model parameters associated with perturbations are less stringent, reflecting the fact that there are different sets of parameters that give rise to a similar cosmic expansion and growth history.

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than -1. The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the Lambda CDM model.

A non-Abelian SU(2) gauge field with a nonminimal Horndeski coupling to gravity gives rise to a de Sitter solution followed by a graceful exit to a radiation-dominated epoch. In this Horndeski-Yang-Mills (HYM) theory we derive the second-order action for tensor perturbations on the homogeneous and isotropic quasi-de Sitter background. We find that the presence of the Horndeski nonminimal coupling to the gauge field inevitably introduces ghost instabilities in the tensor sector during inflation. Moreover, we also find Laplacian instabilities for the tensor perturbations deep inside the Hubble radius during inflation. Thus, we conclude that the HYM theory does not provide a consistent inflationary framework due to the presence of ghosts and Laplacian instabilities.

In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) scalar-tensor theories, which are outside the domain of second-order Horndeski theories, it is known that there exists a solid angle deficit singularity in the case where the parameter alpha(H) characterizing the deviation from Horndeski theories approaches a nonvanishing constant at the center of a spherically symmetric body. Meanwhile, it was recently shown that second-order generalized Proca theories with a massive vector field A(mu) can be consistently extended to beyond-generalized Proca theories, which recover shift-symmetric GLPV theories in the scalar limit A(mu) -> del(mu)chi In beyond-generalized Proca theories up to quartic-order Lagrangians, we show that solid angle deficit singularities are generally absent due to the existence of a temporal vector component. We also derive the vector-field profiles around a compact object and show that the success of the Vainshtein mechanism operated by vector Galileons is not prevented by new interactions in beyond generalized Proca theories.

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Sigma and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Sigma/H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Sigma/H decreases with the decrease of v. As long as the conditions |Sigma| << H and v (2 <<) phi(2) are satisfied around the onset of late-time cosmic acceleration, where phi is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point ( Sigma = 0 = v) in accordance with the cosmic no-hair conjecture. In the presence of v and Sigma the early evolution of the dark energy equation of state wDE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w(DE)((iso)) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Sigma always decreases in time.

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories. (C) 2016 The Authors. Published by Elsevier B.V.

We use FIRAS and PLANCK 2015 data to place observational bounds on inflationary in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBS). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaltre-RobertsonWalker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling G(eff) with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. Wc find that the existence of intrinsic vector modes allows a possibility for reducing G(eff). in fact, within the parameter space, G(eff) can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter eta and the evolution of the growth rate f sigma(8) are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the ACDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.

We measure the redshift-space correlation function from a spectroscopic sample of 2783 emission line galaxies from the FastSound survey. The survey, which uses the Subaru Telescope and covers a redshift range of 1.19 < z < 1.55, is the first cosmological study at such high redshifts. We detect clear anisotropy due to redshift-space distortions (RSD) both in the correlation function as a function of separations parallel and perpendicular to the line of sight and its quadrupole moment. RSD has been extensively used to test general relativity on cosmological scales at z < 1. Adopting a Lambda CDM cosmology with the fixed expansion history and no velocity dispersion (sigma(v) = 0), and using the RSD measurements on scales above 8 h(-1) Mpc, we obtain the first constraint on the growth rate at the redshift, f(z)sigma(8)(z) = 0.482 +/- 0.116 at z similar to 1.4 after marginalizing over the galaxy bias parameter b(z)sigma(8)(z). This corresponds to 4.2 sigma detection of RSD. Our constraint is consistent with the prediction of general relativity f sigma(8) similar to 0.392 within the 1 sigma confidence level. When we allow sv to vary and marginalize over it, the growth rate constraint becomes f sigma(8) = 0.494(-0.120)(+0.126). We also demonstrate that by combining with the low-z constraints on f sigma(8), high-z galaxy surveys like the FastSound can be useful to distinguish modified gravity models without relying on CMB anisotropy experiments.

For a massive vector field with derivative self-interactions, the breaking of the gauge invariance allows the propagation of a longitudinal mode in addition to the two transverse modes. We consider generalized Proca theories with second-order equations of motion in a curved space-time and study how the longitudinal scalar mode of the vector field gravitates on a spherically symmetric background. We show explicitly that cubic-order self-interactions lead to the suppression of the longitudinal mode through the Vainshtein mechanism. Provided that the dimensionless coupling of the interaction is not negligible, this screening mechanism is sufficiently efficient to give rise to tiny corrections to gravitational potentials consistent with solar-system tests of gravity. We also study the quartic interactions with the presence of nonminimal derivative coupling with the Ricci scalar and find the existence of solutions where the longitudinal mode completely vanishes. Finally, we discuss the case in which the effect of the quartic interactions dominates over the cubic one and show that local gravity constraints can be satisfied under a mild bound on the parameters of the theory.

In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the conical singularity arises at the center of a spherically symmetric body (r = 0) in the case where the parameter alpha(H4) characterizing the deviation from the Horndeski Lagrangian L-4 approaches a non-zero constant as r -> 0. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian does not modify the divergent property of the Ricci scalar R induced by the non-zero alpha(H4). Provided that alpha(H4) = 0, curvature scalar quantities can remain finite at r = 0 even in the presence of L-5 beyond the Horndeski domain. For the theories in which the scalar field phi is directly coupled to R we also obtain spherically symmetric solutions inside/outside the body to study whether the fifth force mediated by phi can be screened by non-linear field self-interactions. We find that there is one specific model of GLPV theories in which the effect of L5 vanishes in the equations of motion. We also show that, depending on the sign of a L-5-dependent term in the field equation, the model can be compatible with solar-system constraints under the Vainshtein mechanism or it is plagued by the problem of a divergence of the field derivative in high-density regions.

We propose a dark energy model where a scalar field phi has nonlinear self-interactions in the presence of a dilatonic coupling with the Ricci scalar. This belongs to a subclass of theories beyond Horndeski, which accommodates covariant Galileons and Brans-Dicke theories as specific cases. We derive conditions under which the scalar sound speed squared c(s)(2) is positive from the radiation era to today. Since c(s)(2) remains smaller than the order of 1, the deviation from Horndeski theories does not cause heavy oscillations of gaugeinvariant gravitational potentials. In this case, the evolution of matter perturbations at low redshifts is similar to that in the coupled dark energy scenario with an enhanced gravitational interaction. On the spherically symmetric background with a matter source, the existence of field self-interactions suppresses the propagation of the fifth force inside a Vainshtein radius. We estimate an allowed parameter space in which the model can be compatible with Solar System constraints while satisfying conditions for the cosmological viability of background and perturbations.

In a class of Gleyzes-Langlois-Piazza-Vernizzi theories, we derive both vacuum and interior Schwarzs-child solutions under the condition that the derivatives of a scalar field phi with respect to the radius r vanish. If the parameter alpha(H) characterizing the deviation from Horndeski theories approaches a nonzero constant at the center of a spherically symmetric body, we find that the conical singularity arises at r = 0 with the Ricci scalar given by R = -2 alpha(H)/r(2). This originates from violation of the geometrical structure of four-dimensional curvature quantities. The conical singularity can disappear for the models in which the parameter alpha(H) vanishes in the limit that r -> 0. We propose explicit models without the conical singularity by properly designing the classical Lagrangian in such a way that the main contribution to alpha(H) comes from the field derivative phi'(r) around r = 0. We show that the extension of covariant Galileons with a diatonic coupling allows for the recovery of general relativistic behavior inside a so-called Vainshtein radius. In this case, both the propagation of a fifth force and the deviation from Horndeski theories are suppressed outside a compact body in such a way that the model is compatible with local gravity experiments inside the solar system.

The disformal transformation of metric g(mu nu) -> Omega(2) (phi)g(mu nu) + Gamma(phi, X)partial derivative(mu)phi partial derivative(nu)phi, where phi is a scalar field with the kinetic energy X = partial derivative(mu)phi partial derivative(mu)phi/2, preserves the Lagrangian structure of Gleyzes-Langlois-Piazza-Vernizzi theories (which is the minimum extension of Horndeski theories). In the presence of matter, this transformation gives rise to a kinetic-type coupling between the scalar field phi and matter. We consider the Einstein frame in which the second-order action of tensor perturbations on the isotropic cosmological background is of the same form as that in General Relativity and study the role of couplings at the levels of both background and linear perturbations. We show that the effective gravitational potential felt by matter perturbations in the Einstein frame can be conveniently expressed in terms of the sum of a General Relativistic contribution and couplings induced by the modification of gravity. For the theories in which the transformed action belongs to a class of Horndeski theories, there is no anisotropic stress between two gravitational potentials in the Einstein frame due to a gravitational demixing. We propose a concrete dark energy model encompassing Brans-Dicke theories as well as theories with the tensor propagation speed c(t) different from 1. We clarify the correspondence between physical quantities in the Jordan/Einstein frames and study the evolution of gravitational potentials and matter perturbations from the matter-dominated epoch to today in both analytic and numerical approaches.

We study the possibility of realizing a growth rate of matter density perturbations lower than that in general relativity. Using the approach of the effective field theory of modified gravity encompassing theories beyond Horndeski, we derive the effective gravitational coupling G(eff) and the gravitational slip parameter eta for perturbations deep inside the Hubble radius. In Horndeski theories we derive a necessary condition for achieving weak gravity associated with tensor perturbations, but this is not a sufficient condition due to the presence of a scalar-matter interaction that always enhances G(eff). Beyond the Horndeski domain it is possible to realize G(eff) smaller than Newton's gravitational constant G, while the scalar and tensor perturbations satisfy no-ghost and stability conditions. We present a concrete dark energy scenario with varying c(t) and numerically study the evolution of perturbations to confront the model with the observations of redshift-space distortions and weak lensing.

We show that the universal alpha-attractor models of inflation can be realized by including an auxiliary vector field A(mu) for the Starobinsky model with the Lagrangian f(R) = R + R-2/(6M(2)). If the same procedure is applied to general modified f(R) theories in which the Ricci scalar R is replaced by R + A(mu)A(mu) + beta del(mu)A(mu) with constant beta, we obtain the Brans-Dicke theory with a scalar potential and the BransDicke parameter omega(BD) = beta(2)/4. We also place observational constraints on inflationary models based on auxiliary vector modified f(R) theories from the latest Planck measurements of the cosmic microwave background anisotropies in both temperature and polarization. In the modified Starobinsky model, we find that the parameter beta is constrained to be beta < 25 (68% confidence level) from the bounds of the scalar spectral index and the tensor-to-scalar ratio.

In the approach of the effective field theory of modified gravity, we derive the equations of motion for linear perturbations in the presence of a barotropic perfect fluid on the flat isotropic cosmological background. In a simple version of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, which is the minimum extension of Horndeski theories, we show that a slight deviation of the tensor propagation speed squared c(t)(2) from 1 generally leads to the large modification to the propagation speed squared c(s)(2) of a scalar degree of freedom phi. This problem persists whenever the kinetic energy rho(X) of the field phi is much smaller than the background energy density rho(m), which is the case for most of dark energy models in the asymptotic past. Since the scaling solution characterized by the constant ratio rho(X)/rho(m) is one way out for avoiding such a problem, we study the evolution of perturbations for a scaling dark energy model in the framework of GLPV theories in the Jordan frame. Provided the oscillating mode of scalar perturbations is fine-tuned so that it is initially suppressed, the anisotropic parameter eta = -Phi/Psi between the two gravitational potentials Psi and Phi significantly deviates from 1 for c(t)(2) away from 1. For other general initial conditions, the deviation of c(t)(2) from 1 gives rise to the large oscillation of Psi with the frequency related to c(s)(2). In both cases, the model can leave distinct imprints for the observations of CMB and weak lensing.

In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter background. We also show that the leading-order spectrum in concrete modified gravitational theories can be mapped on to that in General Relativity under a disformal transformation. Our general formula will be useful to constrain inflationary models from the future precise measurement of the B-mode polarization in the cosmic microwave background.

It is known that Horndeski theories can be transformed to a,sub-class of Gleyzes-Langlois-Piazza-Vernizzi (MTV) theories under the disformal transformation of the metric g(mu v) -> Omega(2)(phi)g(mu v) + Gamma(phi, X)del(mu)phi del(v)phi, where Omega is a function of a scalar field phi and Gamma is another function depending on both phi and X - g(mu v)del(mu)phi del(v)phi. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the Hat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories (mcompassing florndeski and GLPV theories, we obtain the secondorder actions of scalar/tensor perturbations and present the relations for physical quantities betAveen the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

In second-order scalar-tensor theories we study how the Vainshtein mechanism works in a spherically symmetric background with a matter source. In the presence of the field coupling with the Ricci scalar we generally derive the Vainshtein radius within which the General Relativistic behavior is recovered even for the coupling constant of the order of unity. Our analysis covers the models such as the extended Galileon and Brans-Dicke theories with a dilatonic field self-interaction. We show that, if these models are responsible for the cosmic acceleration today, the corrections to gravitational potentials are generally small enough to be compatible with local gravity constraints.

A Galileon-like nonlinear self-interaction (∂φ)2 □φ generally leads to a enhanced friction during inflation, by which even steep potentials for the standard inflation can drive cosmic acceleration. However if the Galileon term is dominant by the end of inflation, this can affect the field oscillation during reheating and the scalar propagation speed squared c2 s can be negative, which leads to the instability of small-scale perturbations. For chaotic inflation and natural inflation we clarify the parameter space in which the field oscillates coherently during reheating. Moreover we place observational constraints of the scalar spectral index ns and the tensor-to-scalar ratio r.

We discriminate between theoretical models of dark energy from recent observations. We place constraints on dark energy models from the background cosmology by using the data of supernovae Ia, cosmic microwave background, and baryon acoustic oscillations. We further show that the recent measurement of the peculiar velocity of galaxies is powerful to constrain modified gravity models.

We consider perturbations of a static and spherically symmetric background endowed with a metric tensor and a scalar field in the framework of the effective field theory of modified gravity. We employ the previously developed 2 + 1 + 1 canonical formalism of a double Arnowitt-Deser-Misner (ADM) decomposition of space-time, which singles out both time and radial directions. Our building block is a general gravitational action that depends on scalar quantities constructed from the 2 + 1 + 1 canonical variables and the lapse. Variation of the action up to first order in perturbations gives rise to three independent background equations of motion, as expected from spherical symmetry. The dynamical equations of linear perturbations follow from the second-order Lagrangian after a suitable gauge fixing. We derive conditions for the avoidance of ghosts and Laplacian instabilities for the odd-type perturbations. We show that our results not only incorporate those derived in the most general scalar-tensor theories with second-order equations of motion (the Horndeski theories) but they can be applied to more generic theories beyond Horndeski.

In this paper, we review the effective field theory of modified gravity in which the Lagrangian involves three-dimensional geometric quantities appearing in the 3+1 decomposition of spacetime. On the flat isotropic cosmological background, we expand a general action up to second-order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories -including Horndeski theory/its recent generalizations and the projectable/nonprojectable versions of Horava-Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Horava-Lifshitz gravity already derived in the literature.

The prospects for direct measurements of inflationary gravitational waves by next generation interferometric detectors inferred from the possible detection of B-mode polarization of the cosmic microwave background are studied. We compute the spectra of the gravitational wave background and the signal-to-noise ratios by two interferometric detectors (DECIGO and BBO) for large-field inflationary models in which the tensor-to-scalar ratio is greater than the order of 0.01. If the reheating temperature T-RH of chaotic inflation with the quadratic potential is high (T-RH > 7.9 x 10(6) GeV for upgraded DECIGO and T-RH > 1.8 x 10(6) GeV for BBO), it will be possible to reach the sensitivity of the gravitational background in future experiments at 3 sigma confidence level. The direct detection is also possible for natural inflation with the potential V(phi) = A(4) [1 - cos(phi/f)], provided that f > 4.2M(pl) (upgraded DECIGO) and f > 3.6M(pl) (BBO) with T-RH higher than 10(8) GeV. The quartic potential V(phi) = lambda phi(4)/4 with a nonminimal coupling xi between the inflaton field phi and the Ricci scalar R gives rise to a detectable level of gravitational waves vertical bar xi vertical bar for smaller than the order of 0.01, irrespective of the reheating temperature.

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lemaitre-Robertson-Walker background. In addition to a dark energy field chi associated with the gravitational sector, we take into account multiple scalar fields phi(I) (I = 1, 2, ... , N - 1) characterized by the Lagrangians P-(I) (X-I) with X-I = partial derivative(mu)phi(I)partial derivative(mu)phi(I). These additional scalar fields can model the perfect fluids of radiation and nonrelativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce nontrivial modifications to all the propagation speeds of N scalar fields, but the modifications to those for the matter fields phi(I) are generally suppressed relative to that for the dark energy field chi. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square c(s1)(2) associated with the field chi becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

The observational evidence of dark energy is one of the most serious problems in modern cosmology. From the joint constraints on the dark energy equation of state using the recent data of SN Ia, CMB and BAO, there is a possibility that the gravitational law may be modified from General Relativity at large distances. We review a number of theoretical models of modified gravity which can account for the cosmic acceleration, while recovering the General Relativistic behavior in the solar system. We also discuss the growth of structures in modified gravity models in order to confront them with the observations of galaxy clusterings and weak lensing.

Nonlocal massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state w(DE) smaller than -1 in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to nonrelativistic matter associated with galaxy clusterings is close to Newton's gravitational constant G for a mass scale m slightly smaller than today's Hubble parameter H-0. Taking into account the background expansion history as well as the evolution of matter perturbations delta(m), we test for these models with Type Ia Supernovae (SnIa) from Union 2.1, the cosmic microwave background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of delta(m). Using a higher value of H-0 derived from its direct measurement (H-0 greater than or similar to 70 km s(-1) Mpc(-1)) the data strongly support the nonlocal massive gravity model (-1.1 less than or similar to w(DE) less than or similar to -1.04 in the past) over the ACDM model (w(DE) = -1), whereas for a lower prior (67 km s(-1) Mpc(-1) less than or similar to H-0 less than or similar to 70 km s(-1) Mpc(-1)) the two models are statistically comparable.

The general k-essence Lagrangian for the existence of cosmological scaling solutions is derived in the presence of multiple scalar fields coupled to a barotropic perfect fluid. In addition to the scaling fixed point associated with the dynamics during the radiation and matter eras, we also obtain a scalar-field dominated solution relevant to dark energy and discuss the stability of them in the two-field setup. We apply our general results to a model of two canonical fields with coupled exponential potentials arising in string theory. Depending on model parameters and initial conditions, we show that the scaling matter-dominated epochs followed by an attractor with cosmic acceleration can be realized with/without the couplings to scalar fields. The different types of scaling solutions can be distinguished from each other by the evolution of the dark energy equation of state from high redshifts to today.

In this paper, inflationary cosmology is reviewed, paying particular attention to its observational signatures associated with large-scale density perturbations generated from quantum fluctuations. In the most general scalar-tensor theories with second-order equations of motion, we derive the scalar spectral index n(s), the tensor-to-scalar ratio r, and the nonlinear estimator f(NL) of primordial non-Gaussianities to confront models with observations of cosmic microwave background (CMB) temperature anisotropies. Our analysis includes models such as potential-driven slow-roll inflation, k-inflation, Starobinsky inflation, and Higgs inflation with non-minimal/derivative/Galileon couplings. We constrain a host of inflationary models by using the Planck data combined with other measurements to find models most favored observationally in the current literature. We also study anisotropic inflation based on a scalar coupling with a vector (or two-form) field and discuss its observational signatures appearing in the two-point and three-point correlation functions of scalar and tensor perturbations.

We place observational likelihood constraints on braneworld and non-commutative inflation for a number of inflaton potentials, using Planck, WMAP polarization and BAO data. Both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models. At more than 95% confidence level, the monomial potential V (phi) proportional to phi(p) is ruled out for p >= 2 in the Randall-Sundrum (RS) braneworld cosmology and, for p > 0, also in the high-curvature limit of the Gauss-Bonnet (GB) braneworld and in the infrared limit of non-commutative inflation, due to a large scalar spectral index. Some parameter values for natural inflation, small-varying inflaton models and Starobinsky inflation are allowed in all scenarios, although some tuning is required for natural inflation in a non-commutative spacetime.

We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy field into the gravitational sector, for which we adopt a generic Lagrangian depending on three- dimensional geometrical scalar quantities arising in the Arnowitt- DeserMisner decomposition. We add to this dark energy- associated gravitational sector a scalar field. and its kinetic energy X as dark matter variables. Compared to the single- field case, we find that there are additional conditions to obey in order to keep the equations of motion for linear cosmological perturbations at second order. For such a second- order multifield theory, we derive conditions under which ghosts and Laplacian instabilities of the scalar and tensor perturbations are absent. We apply our general results to models with dark energy emerging in the framework of the Horndeski theory and dark matter described by a k- essence Lagrangian Pd.; X_. We derive the effective coupling between such an imperfect- fluid dark matter and the gravitational sector under the quasistatic approximation on subhorizon scales. By considering the purely kinetic Lagrangian PdX_ as a particular case, the formalism is verified to reproduce the gravitational coupling of a perfect- fluid dark matter.

We review the role of fundamental spin-0 bosons as bosonic coherent motion (BCM) in the Universe. The fundamental spin-0 bosons have the potential to account for the baryon number generation, cold dark matter (CDM) via BCM, inflation, and dark energy. Among these, we pay particular attention to the CDM possibility because it can be experimentally tested with the current experimental techniques. We also comment on the panoply of the other roles of spin-0 bosons–such as those for cosmic accelerations at early and late times.

The recent Planck data of cosmic microwave background temperature anisotropies support the Starobinsky theory in which the quadratic Ricci scalar drives cosmic inflation. We build up a multidimensional quantum consisted ultraviolet completion of the model in a phenomenological "bottom-up approach." We present the maximal class of theories compatible with unitarity and (super-)renormalizability or finiteness which reduces to the Starobinsky theory in the low-energy limit. The outcome is a maximal extension of the Krasnikov-Tomboulis-Modesto theory including an extra scalar degree of freedom besides the graviton field. The original theory was afterwards independently discovered by Biswas-Gerwick-Koivisto-Mazumdar starting from first principles. We explicitly show power counting super-renormalizability or finiteness (in odd dimensions) and unitarity (no ghosts) of the theory. Any further extension of the theory is nonunitary, confirming the existence of at most one single extra degree of freedom, the scalaron. A mechanism to achieve the Starobinsky theory in string (field) theory is also investigated at the end of the paper.

We present a general covariant action for massive gravity merging together a class of "non-polynomial" and super-renormalizable or finite theories of gravity with the non-local theory of gravity recently proposed by Jaccard, Maggiore and Mitsou (Phys. Rev. D 88 (2013) 044033). Our diffeomorphism invariant action gives rise to the equations of motion appearing in non-local massive gravity plus quadratic curvature terms. Not only the massive graviton propagator reduces smoothly to the massless one without a vDVZ discontinuity, but also our finite theory of gravity is unitary at tree level around the Minkowski background. We also show that, as long as the graviton mass m is much smaller the today's Hubble parameter H-0, a late-time cosmic acceleration can be realized without a dark energy component due to the growth of a scalar degree of freedom. In the presence of the cosmological constant Lambda, the dominance of the non-local mass term leads to a kind of "degravitation" for Lambda at the late cosmological epoch. (C) 2013 Elsevier B.V. All rights reserved.

Quintessence is a canonical scalar field introduced to explain the late-time cosmic acceleration. The cosmological dynamics of quintessence is reviewed, paying particular attention to the evolution of the dark energy equation of state w. For the field potentials having tracking and thawing properties, the evolution of w can be known analytically in terms of a few model parameters. Using the analytic expression of w, we constrain quintessence models from the observations of supernovae type Ia, cosmic microwave background and baryon acoustic oscillations. The tracking freezing models are hardly distinguishable from the Lambda-cold-dark-matter model, whereas in thawing models the today's field equation of state is constrained to be w(0) < -0.7 (95% CL). We also derive an analytic formula for the growth rate of matter density perturbations in dynamical dark energy models, which allows a possibility of putting further bounds on w from the measurement of redshift-space distortions in the galaxy power spectrum. Finally, we review particle physics models of quintessence-such as those motivated by supersymmetric theories. The field potentials of thawing models based on a pseudo-Nambu-Goldstone boson or extended supergravity theories have a nice property that a tiny mass of quintessence can be protected against radiative corrections.

We study how the Vainshtein mechanism operates in the most general scalartensor theories with second-order equations of motion. The field equations of motion, which can be also applicable to most of other screening scenarios proposed in literature, are generally derived in a spherically symmetric space-time with a matter source. In the presence of a field coupling to the Ricci scalar, we clarify conditions under which the Vainshtein mechanism is at work in a weak gravitational background. We also obtain the solutions of the field equation inside a spherically symmetric body and show how they can be connected to exterior solutions that accommodate the Vainshtein mechanism. We apply our general results to a number of concrete models such as the covariant/extended Galileons and the DBI Galileons with Gauss-Bonnet and other terms. In these models the fifth force can be suppressed to be compatible with solar-system constraints, provided that non-linear field kinetic terms coupled to the Einstein tensor do not dominate,. over other non-linear field self-interactions.

We study an inflationary scenario with a two-form field to which an inflaton couples nontrivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the nonlinear estimators f(NL) and tau(NL) are correlated with the amplitude g(*) of the statistical anisotropy in the power spectrum. Unlike the vector models, both f(NL) and tau(NL) vanish in the squeezed limit. However, the estimator f(NL) can reach the order of 10 in the equilateral and enfolded limits. These results are consistent with the latest bounds on f(NL) constrained by Planck. DOI: 10.1103/PhysRevD.87.083520

For two types of quintessence models having thawing and tracking properties, there exist analytic solutions for the dark energy equation of state w expressed in terms of several free parameters. We put observational bounds on the parameters in such scenarios by using the recent type Ia supernovae, cosmic microwave background, and baryon acoustic oscillations data. The observational constraints are quite different depending on whether or not the recent baryon acoustic oscillations data from BOSS are taken into account. With the BOSS data the upper bounds of today's values of w (= w(0)) in thawing models is very close to -1, whereas without this data the values of w(0) away from -1 can still be allowed. The tracker equation of state w((0)) during the matter era is constrained to be w((0)) < -0.949 at 95% C. L. even without the BOSS data, so that the tracker models with w away from -1 are severely disfavored. We also study observational constraints on scaling models in which w starts to evolve from 0 in the deep matter era and show that the transition to the equation of state close to w = -1 needs to occur at an early cosmological epoch. In the three classes of quintessence models studied in this paper, the past evolution of the Hubble parameters in the best-fit models shows only less than a 2.5% difference compared to Lambda CDM. DOI: 10.1103/PhysRevD.87.083505

In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G(eff) associated with the growth rate of matter perturbations as well as the effective gravitational potential Phi(eff) relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f (R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background. (C) 2011 Elsevier B.V. All rights reserved.

We demonstrate that there exists an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f(R,phi,X), where R is the Ricci scalar and X is the kinetic energy of a scalar field phi. This comes from a suitable definition of an energy momentum tensor of the "dark" component obeying the local energy conservation law in the Jordan frame. It is shown that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of the horizon entropy (S) over cap S in non-equilibrium thermodynamics as well as an entropy production term.

We try to address quantitatively the question whether a new mass is needed to fit current supernovae data. For this purpose, we consider an infra-red modification of gravity that does not contain any new mass scale but systematic subleading corrections proportional to the curvature. The modifications are of the same type as the one recently derived by enforcing the "Ultra Strong Equivalence Principle" (USEP) upon a Friedmann-Lemaitre-Robertson-Walker universe in the presence of a scalar field. The distance between two comoving observers is altered by these corrections and the observations at high redshift are affected at any time during the cosmic evolution. While the specific values of the parameters predicted by USEP are ruled out, there are regions of parameter space that fit Snla data very well. This allows an interesting possibility to explain the apparent cosmic acceleration today without introducing either a dark energy component or a new mass scale. (C) 2010 Elsevier B.V. All rights reserved.

We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f (R, phi, X), where R is the Ricci scalar and x is the kinetic energy of a scalar field phi. This comes from a suitable definition of an energy-momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy S corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area A in units of gravitational constant G, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, S globally increases with time, as it happens for viable f (R) inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of both the horizon entropy (S) over cap in non-equilibrium thermodynamics and an entropy production term. (C) 2010 Elsevier B.V. All rights reserved.

We study the effect of modified gravity on weak lensing in a class of scalar-tensor theory that includes f(R) gravity as a special case. These models are designed to satisfy local gravity constraints by having a large scalar-field Mass in a region of high curvature. Matter density perturbations in these models are enhanced at small redshifts because of the presence of a coupling Q that characterizes the strength between dark energy and non-relativistic matter. We compute a convergence power spectrum of weak lensing numerically and show that the spectral index and the amplitude of the spectrum in the linear regime can be significantly modified compared to the Lambda CDM model for large values of vertical bar Q vertical bar Of the Order Of unity. Thus weak lensing provides a powerful tool to constrain such large coupling scalar-tensor models including f(R) gravity. (c) 2008 Elsevier B.V. All rights reserved.

In a recent paper, 1 we have shown that f(R) = R + mu R-n modified gravity dark energy models are not cosmologically viable because during the matter era that precedes the accelerated stage the cosmic expansion is given by a similar to t(1/2) rather than a similar to t(2/3), where a is a scale factor and t is the cosmic time. A recent work by Capozziello et al.(2) criticized our results presenting some apparent counter-examples to our claim in f(R) = mu R-n models. We show here that those particular R-n models can produce an expansion as a similar to t(2/3) but this does not connect to a late-time acceleration. Hence, though acceptable f(R) dark energy models might exist, the R-n models presented in Capozziello et al. are not cosmologically viable, confirming our previous results in Ref. 1.

We study cosmologies based on low-energy effective string theory with higher-order string corrections to a tree-level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The theory of inflation with single and multiple fields is reviewed paying particular attention to the dynamics of adiabatic and entropy/isocurvature perturbations which provide the primary means of testing inflationary models. The theory and phenomenology of reheating and preheating after inflation is reviewed providing a unified discussion of both the gravitational and nongravitational features of multifield inflation. In addition inflation in theories with extra dimensions and models such as the curvaton scenario and modulated reheating which provide alternative ways of generating large-scale density perturbations are covered. Finally interesting observational implications are discussed that can result from adiabatic-isocurvature correlations and non-Gaussianity. © 2006 The American Physical Society.

Cosmological scaling solutions are particularly important in solving the coincidence problem of dark energy. We derive the equations of sub-Hubble linear matter perturbations for a general scalar-field Lagrangian-including quintessence, tachyon, dilatonic ghost condensate and k-essence-and solve them analytically for scaling solutions. We find that matter perturbations are always damped if a phantom field is coupled to dark matter and identify the cases in which the gravitational potential is constant. This provides an interesting possibility to place stringent observational constraints on scaling dark energy models. (c) 2005 Elsevier B.V. All rights reserved.

We study the cosmological evolution based on a D-dimensional action in low-energy effective string theory in the presence of second-order curvature corrections and a modulus scalar field (a dilaton or compactification modulus). A barotropic perfect fluid coupled to the scalar field is also allowed. Phase space analysis and the stability of asymptotic solutions are performed for a number of models which include (i) a fixed scalar field, (ii) a linear dilaton in the string frame, and (iii) a logarithmic modulus in the Einstein frame. We confront analytical solutions with observational constraints for the deceleration parameter and show that Gauss-Bonnet gravity alone (i.e., with no matter fields) may not explain the current acceleration of the universe. We also study the future evolution of the universe using the Gauss-Bonnet parametrization and find that big rip singularities can be avoided even in the presence of a phantom fluid because of the balance between the fluid and curvature corrections. A non-minimal coupling between the fluid and the modulus field also opens up the interesting possibility of avoiding a big rip regardless of the details of the fluid equation of state.

We study the dynamics of reheating in which an inflaton field couples two flavor fermions through Yukawa-couplings. When two fermions have a mixing term with a constant coupling, we show that the Mikheyev-Smirnov-Wolfenstein (MSW)-type resonance emerges due to a time-dependent background in addition to the standard fermion creation via parametric resonance. This MSW resonance not only alters the number densities of fermions generated by a preheating process but also can lead to the larger energy transfer from the inflaton to fermions. Our mechanism can provide additional source terms for the creation of superheavy fermions which may be relevant for the leptogenesis scenario. (C) 2003 Elsevier B.V. All rights reserved.

We study density perturbations in several cosmological models motivated by string theory. The evolution and the spectra of curvature perturbations R are analyzed in the ekpyrotic scenario and nonsingular string cosmologies. We find that these string-inspired models generally exhibit blue spectra in contrast to standard slow-roll inflationary scenarios. We also clarify the parameter range where R is enhanced on superhorizon scales. (C) 2002 Elsevier Science B.V. All rights reserved.