We consider the inflationary universe with a spectator scalar field coupled
to a $U(1)$ gauge field and calculate curvature perturbation and gravitational
waves (GWs). We find that the sourced GWs can be larger than the one from
vacuum fluctuation and they are statistically anisotropic as well as linearly
polarized. The GW power spectrum acquires higher multipole moments as
$\mathcal{P}_h \propto (1-\cos^2\theta+\cos^4\theta-\cos^6\theta)$ irrespective
of the model parameters.

Anisotropic inflation is an interesting model with an U(1) gauge field and it
predicts the statistical anisotropy of the curvature perturbation characterized
by a parameter $g_*$. However, we find that the background gauge field does not
follow the classical attractor solution due to the stochastic effect. We
develop the stochastic formalism of a vector field and solve Langevin and
Fokker-Planck equations. It is shown that this model is excluded by the CMB
constraint $g_*\le 10^{-2}$ with a high probability about $99.999\%$.

A detection of B-mode polarization of the Cosmic Microwave Background (CMB)
anisotropies would confirm the presence of a primordial gravitational wave
background (GWB). In the inflation paradigm this would be an unprecedented
probe of the energy scale of inflation as it is directly proportional to the
power spectrum of the GWB. However, similar tensor perturbations can be
produced by the matter fields present during inflation, breaking this simple
relationship. It is therefore important to be able to distinguish between
different generation mechanisms of the GWB. In this paper, we analyse the
detectability of a new axion-SU(2) gauge field model using its chiral,
scale-dependent tensor spectrum. We forecast the detectability of the resulting
CMB TB and EB cross-correlations by the LiteBIRD satellite, considering the
effects of residual foregrounds, gravitational lensing, and for the first time
assess the ability of such an experiment to jointly detect primordial TB and EB
spectra and self-calibrate its polarimeter. We find that LiteBIRD will be able
to detect the chiral signal for $r_*>0.03$ with $r_*$ denoting the
tensor-to-scalar ratio at the peak scale, and that the maximum signal-to-noise
for $r_*<0.07$ is $\sim 2$. We go on to consider an advanced stage of a
LISA-like mission, and find that such experiments would complement CMB
observations by providing sensitivity to GWB chirality on scales inaccessible
to the CMB. We conclude that in order to use the CMB to distinguish this model
from a conventional vacuum fluctuation model two-point statistics provide some
power, but to achieve high statistical significance we would require higher
order statistics which take advantage of the model's non-Gaussianity. On the
other hand, in the case of a spectrum peaked at very small scales, inaccessible
to the CMB, a highly significant detection could be made using space-based
laser interferometers.

We show that an inflation model in which a spectator axion field is coupled
to an SU(2) gauge field produces a large three-point function (bispectrum) of
primordial gravitational waves, $B_{h}$, on the scales relevant to the cosmic
microwave background experiments. The amplitude of the bispectrum at the
equilateral configuration is characterized by
$B_{h}/P_h^2=\mathcal{O}(10)\times \Omega_A^{-1}$, where $\Omega_A$ is a
fraction of the energy density in the gauge field and $P_h$ is the power
spectrum of gravitational waves produced by the gauge field.

We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB
scale can be generated even during extremely low energy inflation which
saturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source of
the gravitational waves is not quantum fluctuations of graviton but those of
$SU(2)$ gauge fields, energetically supported by coupled axion fields. The
curvature perturbation, the backreaction effect and the validity of
perturbative treatment are carefully checked. Our result indicates that
measuring $r$ alone does not immediately fix the inflationary energy scale.

Most of the upcoming cosmological information will come from analyzing the
clustering of the Large Scale Structures (LSS) of the universe through LSS or
CMB observations. It is therefore essential to be able to understand their
behavior with exquisite precision. The Effective Field Theory of Large Scale
Structures (EFTofLSS) provides a consistent framework to make predictions for
LSS observables in the mildly non-linear regime. In this paper we focus on
biased tracers. We argue that in calculations at a given order in the dark
matter perturbations, highly biased tracers will underperform because of their
larger higher derivative biases. A natural prediction of the EFTofLSS is
therefore that by simply adding higher derivative biases, all tracers should
perform comparably well. We implement this prediction for the halo-halo and the
halo-matter power spectra at one loop, and the halo-halo-halo,
halo-halo-matter, and halo-matter-matter bispectra at tree-level, and compare
with simulations. We find good agreement with the prediction: for all tracers,
we are able to match the bispectra up to $k\simeq0.17\,h/$Mpc at $z=0$ and the
power spectra to a higher wavenumber.

Inspired by the chromo-natural inflation model of Adshead&Wyman, we reshape
its scalar content to relax the tension with current observational bounds.
Besides an inflaton, the setup includes a spectator sector in which an axion
and SU(2) gauge fields are coupled via a Chern-Simons-type term. The result is
a viable theory endowed with an alternative production mechanism for
gravitational waves during inflation. The gravitational wave signal sourced by
the spectator fields can be much larger than the contribution from standard
vacuum fluctuations, it is distinguishable from the latter on the basis of its
chirality and, depending on the theory parameters values, also its tilt. This
production process breaks the well-known relation between the tensor-to-scalar
ratio and the energy scale of inflation. As a result, even if the Hubble rate
is itself too small for the vacuum to generate a tensor amplitude detectable by
upcoming experiments, this model still supports observable gravitational waves.

Spectator field models such as the curvaton scenario and the modulated
reheating are attractive scenarios for the generation of the cosmic curvature
perturbation, as the constraints on inflation models are relaxed. In this
paper, we discuss the effect of Hubble induced masses on the dynamics of
spectator fields after inflation. We pay particular attention to the Hubble
induced mass by the kinetic energy of an oscillating inflaton, which is
generically unsuppressed but often overlooked. In the curvaton scenario, the
Hubble induced mass relaxes the constraint on the property of the inflaton and
the curvaton, such as the reheating temperature and the inflation scale. We
comment on the implication of our discussion for baryogenesis in the curvaton
scenario. In the modulated reheating, the predictions of models e.g. the
non-gaussianity can be considerably altered. Furthermore, we propose a new
model of the modulated reheating utilizing the Hubble induced mass which
realizes a wide range of the local non-gaussianity parameter.

We explore Schwinger effect of spin 1/2 charged particles with static
electric field in 1+3 dimensional de Sitter spacetime. We analytically
calculate the vacuum expectation value of the spinor current which is induced
by the produced particles in the electric field. The renormalization is
performed with the adiabatic subtraction scheme. We find that the current
becomes negative, namely it flows in the direction opposite to the electric
field, if the electric field is weaker than a certain threshold value depending
on the fermion mass, which is also known to happen in the case of scalar
charged particles in 1+3 de Sitter spacetime. Contrary to the scalar case,
however, the IR hyperconductivity is absent in the spinor case.

Recent blazar observations provide growing evidence for the presence of
magnetic fields in the extragalactic regions. While a natural speculation is to
associate the production to inflationary physics, it has been known that
magnetogenesis solely from inflation is quite challenging. We therefore study a
model in which a non-inflaton field $\chi$ coupled to the electromagnetic field
through its kinetic term, $-I^2(\chi) F^2 /4$, continues to move after
inflation until the completion of reheating. This leads to a post-inflationary
amplification of the electromagnetic field. We compute all the relevant
contributions to the curvature perturbation, including gravitational
interactions, and impose the constraints from the CMB scalar fluctuations on
the strength of magnetic fields. We, for the first time, explicitly verify both
the backreaction and CMB constraints in a simple yet successful magnetogenesis
scenario without invoking a dedicated low-scale inflationary model in the
weak-coupling regime of the kinetic coupling model.

Helical hypermagnetic fields in the primordial Universe can produce the
observed amount of baryon asymmetry through the chiral anomaly without any
ingredients beyond the standard model of particle physics. While they generate
no $B-L$ asymmetry, the generated baryon asymmetry survives the spharelon
washout effect, because the generating process remains active until the
electroweak phase transition. Solving the Boltzmann equation numerically and
finding an attractor solution, we show that the baryon asymmetry of our
Universe can be explained, if the present large-scale magnetic fields indicated
by the blazar observations have a negative helicity and existed in the early
Universe before the electroweak phase transition. We also derive the upper
bound on the strength of the helical magnetic field, which is tighter than the
cosmic microwave background constraint, to avoid the overproduction of baryon
asymmetry.

We investigate the cosmological background evolution and perturbations in a
general class of spatially covariant theories of gravity, which propagates two
tensor modes and one scalar mode. We show that the structure of the theory is
preserved under the disformal transformation. We also evaluate the primordial
spectra for both the gravitational waves and the curvature perturbation, which
are invariant under the disformal transformation. Due to the existence of
higher spatial derivatives, the quadratic Lagrangian for the tensor modes
itself cannot be transformed to the form in the Einstein frame. Nevertheless,
there exists a one-parameter family of frames in which the spectrum of the
gravitational waves takes the standard form in the Einstein frame.

There has been a growing evidence for the existence of magnetic fields in the
extra-galactic regions, while the attempt to associate their origin with the
inflationary epoch alone has been found extremely challenging. We therefore
take into account the consistent post-inflationary evolution of the magnetic
fields that are originated from vacuum fluctuations during inflation. In the
model of our interest, the electromagnetic (EM) field is coupled to a
pseudo-scalar inflaton $\phi$ through the characteristic term $\phi F\tilde F$,
breaking the conformal invariance. This interaction dynamically breaks the
parity and enables a continuous production of only one of the polarization
states of the EM field through tachyonic instability. The produced magnetic
fields are thus helical. We find that the dominant contribution to the observed
magnetic fields in this model comes from the modes that leave the horizon near
the end of inflation, further enhanced by the tachyonic instability right after
the end of inflation. The EM field is subsequently amplified by parametric
resonance during the period of inflaton oscillation. Once the thermal plasma is
formed (reheating), the produced helical magnetic fields undergo a turbulent
process called inverse cascade, which shifts their peak correlation scales from
smaller to larger scales. We consistently take all these effects into account
within the regime where the perturbation of $\phi$ is negligible and obtain
$B_{\rm eff} \sim 10^{-19}$G, indicating the necessity of additional mechanisms
to accommodate the observations.

We consider the possibility of enhancing the inflationary tensor mode by
introducing a spectator scalar field with a small sound speed which induces
gravitational waves as a second order effect. We analytically obtain the power
spectra of gravitational waves and curvature perturbation induced by the
spectator scalar field. We found that the small sound speed amplifies the
curvature perturbation much more than the tensor mode and the current
observational constraint forces the induced gravitational waves to be
negligible compared with those from the vacuum fluctuation during inflation.

We propose a novel technique to probe the beyond standard model (BSM) of
particle physics. The mass spectrum of unknown BSM particles can be scanned by
observing gravitational waves (GWs) emitted by Hawking radiation of black
holes. This is because information on the radiation of the BSM particles is
imprinted in the spectrum of the GWs. We fully calculate the GW spectrum from
evaporating black holes taking into account the greybody factor. As an
observationally interesting application, we consider primordial black holes
which evaporate in the very early universe. In that case, since the frequencies
of GWs are substantially redshifted, the GWs emitted with the BSM energy scales
become accessible by observations.

In our previous paper, we have proposed a new algorithm to calculate the
power spectrum of the curvature perturbations generated in inflationary
universe with use of the stochastic approach. Since this algorithm does not
need the perturbative expansion with respect to the inflaton fields on
super-horizon scale, it works even in highly stochastic cases. For example,
when the curvature perturbations are very large or the non-Gaussianities of the
curvature perturbations are sizable, the perturbative expansion may break down
but our algorithm enables to calculate the curvature perturbations. We apply it
to two well-known inflation models, chaotic and hybrid inflation, in this
paper. Especially for hybrid inflation, while the potential is very flat around
the critical point and the standard perturbative computation is problematic, we
successfully calculate the curvature perturbations.

We comprehensively explore the quadratic curvaton models in the chaotic
inflation. In the light of the BICEP2 result $r \approx 0.2$, all model
parameters and relevant observables are computed. It is found the curvaton
field value is constrained into a narrow range, $\sigma_* =
\mathcal{O}(10^{-2}$-$10^{-1})$ and the running of the spectral index is $n_s'
\gtrsim -10^{-3}$. We show that if the curvaton is added, the models are
heavily degenerated on the $n_s$ - $r$ plane. However, introducing a new plane,
the degeneracy can be resolved. To distinguish the curvaton models, precise
measurements of not only $r$ but also $n_s'$ and the tensor tilt $n_T$ are
required.

We investigate the Euclidean vacuum mode functions of a massive vector field
in a spatially open chart of de Sitter spacetime. In the one-bubble open
inflationary scenario that naturally predicts a negative spatial curvature
after a quantum tunneling, it is known that a light scalar field has the
so-called supercurvature mode, i.e. an additional discrete mode which describes
fluctuations over scales larger than the spatial curvature scale. If such
supercurvature modes exist for a vector field with a sufficiently light mass,
then they would decay slower and easily survive the inflationary era. However,
the existence of supercurvature mode strongly depends on details of the system.
To clarify whether a massive vector field has supercurvature modes, we consider
a U(1) gauge field with gauge and conformal invariances spontaneously broken
through the Higgs mechanism, and present explicit expressions for the Euclidean
vacuum mode functions. We find that, for any values of the vector field mass,
there is no supercurvature mode. In the massless limit, the absence of
supercurvature modes in the scalar sector stems from the gauge symmetry.

Recently, there are several reports that the cosmic magnetic fields on Mpc
scale in void region is larger than $\sim 10^{-15}$G with an uncertainty of a
few orders from the current blazar observations. On the other hand, in
inflationary magnetogenesis models, additional primordial curvature
perturbations are inevitably produced from iso-curvature perturbations due to
generated electromagnetic fields. We explore such induced curvature
perturbations in a model independent way and obtained a severe upper bound for
the energy scale of inflation from the observed cosmic magnetic fields and the
observed amplitude of the curvature perturbation, as $\rho_{\rm inf}^{1/4} <
30{\rm GeV} \times (B_{\rm obs}/10^{-15}{\rm G})^{-1}$ where $B_{\rm obs}$ is
the strength of the magnetic field at present. Therefore, without a dedicated
low energy inflation model or an additional amplification of magnetic fields
after inflation, inflationary magnetogenesis on Mpc scale is generally
incompatible with CMB observations.

Since magnetic fields in galaxies, galactic clusters and even void regions
are observed, theoretical attempts to explain their origin are strongly
motivated. It is interesting to consider that inflation is responsible for the
origin of the magnetic fields as well as the density perturbation. However, it
is known that inflationary magnetogenesis suffers from several problems. We
explore these problems by using a specific model, namely the kinetic coupling
model, and show how the model is constrained. Model independent arguments are
also discussed.

We investigate the consistency of a scenario in which the baryon asymmetry,
dark matters, as well as the cosmic density perturbation are generated
simultaneously through the evaporation of primordial black holes (PBHs). This
scenario can explain the coincidence of the dark matter and the baryon density
of the universe, and is free from the isocurvature perturbation problem. We
show that this scenario predicts the masses of PBHs, right-handed neutrinos and
dark matters, the Hubble scale during inflation, the non-gaussianity and the
running of the spectral index. We also discuss the testability of the scenario
by detecting high frequency gravitational waves from PBHs.

We propose a new approach for calculating the curvature perturbations
produced during inflation in the stochastic formalism. In our formalism, the
fluctuations of the e-foldings are directly calculated without perturbatively
expanding the inflaton field and they are connected to the curvature
perturbations by the $\delta N$ formalism. The result automatically includes
the contributions of the higher order perturbations because we solve the
equation of motion non-perturbatively. In this paper, we analytically prove
that our result (the power spectrum and the nonlinearity parameter) is
consistent with the standard result in single field slow-roll inflation. We
also describe the algorithm for numerical calculations of the curvature
perturbations in more general inflation models.

We present a novel mechanism to generate the cosmic perturbation from
evaporation of primordial black holes. A mass of a field is fluctuated if it is
given by a vacuum expectation value of a light scalar field because of the
quantum fluctuation during inflation. The fluctuated mass causes variations of
the evaporation time of the primordial black holes. Therefore provided the
primordial black holes dominate the universe when they evaporate, primordial
cosmic perturbations are generated. We find that the amplitude of the large
scale curvature perturbation generated in this scenario can be consistent with
the observed value. Interestingly, our mechanism works even if all fields which
are responsible for inflation and the generation of the cosmic perturbation are
decoupled from the visible sector except for the gravitational interaction. An
implication to the running spectral index is also discussed.

We compute the power spectrum P_\zeta, and non-linear parameters f_nl and
\tau_nl of the curvature perturbation induced during inflation by the
electromagnetic fields in the kinetic coupling model (IFF model). By using the
observational result of P_\zeta, f_nl and \tau_nl reported by the Planck
collaboration, we study the constraint on the model comprehensively.
Interestingly, if the single slow-rolling inflaton is responsible for the
observed P_\zeta, the constraint from \tau_nl is most stringent. We also find a
general relationship between f_nl and \tau_nl generated in this model. Even if
f_nl \sim O(1), a detectable \tau_nl can be produced.

Recently observational lower bounds on the strength of cosmic magnetic fields
were reported, based on gamma-ray flux from distant blazars. If inflation is
responsible for the generation of such magnetic fields then the inflation
energy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl}
times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesis
models, where B_{obs} is the observed strength of cosmic magnetic fields. The
tensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times
(B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strength B_{obs} \geq
10^{-15}G is confirmed and if any signatures of gravitational waves from
inflation are detected in the near future, then our result indicates some
tensions between inflationary magnetogenesis and observations.