We study relativistic effects, arising from the light propagation in an
inhomogeneous universe. We particularly investigate the effects imprinted in a
cross-correlation function between galaxy positions and intrinsic galaxy shapes
(GI correlation). Considering the Doppler and gravitational redshift effects as
major relativistic effects, we present an analytical model of the GI
correlation function, from which we find that the relativistic effects induce
non-vanishing odd multipole anisotropies. Focusing particularly on the dipole
anisotropy, we show that the Doppler effect dominates at large scales, while
the gravitational redshift effect originated from the halo potential dominates
at the scales below $10$-$30\, {\rm Mpc}/h$, with the amplitude of the dipole
GI correlation being positive over all the scales. Also, we newly derive the
covariance matrix for the modelled GI dipole. Taking into account the full
covariance, we estimate the signal-to-noise ratio and show that the GI dipole
induced by the relativistic effects is detectable in future large-volume galaxy
surveys. We discuss how the measurement of dipole GI correlation could be
helpful to detect relativistic effects in combination with the conventional
galaxy-galaxy cross correlation.

DOI： 10.1093/mnras/stac3462

arXiv

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Other Link： http://arxiv.org/pdf/2207.03454v2

The local position invariance (LPI) is one of the three major pillars of
Einstein equivalence principle, ensuring the space-time independence on the
outcomes of local experiments. The LPI has been tested by measuring the
gravitational redshift effect in various depths of gravitational potentials. We
propose a new cosmological test of the LPI by observing the asymmetry in the
cross-correlation function between different types of galaxies, which
predominantly arises from the gravitational redshift effect induced by the
gravitational potential of halos at which the galaxies reside. We show that the
ongoing and upcoming galaxy surveys can give a fruitful constraint on the
LPI-violating parameter, $\alpha$, at distant universes (redshift
$z\sim0.1-1.8$) over the cosmological scales (separation $s\sim5-10\, {\rm
Mpc}/h$) that have not yet been explored, finding that the expected upper limit
on $\alpha$ can reach $0.03$.

DOI： 10.1093/mnras/stad2191

arXiv

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Other Link： http://arxiv.org/pdf/2112.07727v2

We explore the structure around shell-crossing time of cold dark matter
protohaloes seeded by two or three crossed sine waves of various relative
initial amplitudes, by comparing Lagrangian perturbation theory (LPT) up to
10th order to high-resolution cosmological simulations performed with the
public Vlasov code ColDICE. Accurate analyses of the density, the velocity, and
related quantities such as the vorticity are performed by exploiting the fact
that ColDICE can follow locally the phase-space sheet at the quadratic level.
To test LPT predictions beyond shell-crossing, we employ a ballistic
approximation, which assumes that the velocity field is frozen just after
shell-crossing. In the generic case, where the amplitudes of the sine waves are
all different, high-order LPT predictions match very well the exact solution,
even beyond collapse. As expected, convergence slows down when going from
quasi-1D dynamics where one wave dominates over the two others, to the
axial-symmetric configuration, where all the amplitudes of the waves are equal.
It is also noticed that LPT convergence is slower when considering velocity
related quantities. Additionally, the structure of the system at and beyond
collapse given by LPT and the simulations agrees very well with singularity
theory predictions, in particular with respect to the caustic and vorticity
patterns that develop beyond collapse. Again, this does not apply to
axial-symmetric configurations, that are still correct from the qualitative
point of view, but where multiple foldings of the phase-space sheet produce
very high density contrasts, hence a strong backreaction of the gravitational
force.

DOI： 10.1051/0004-6361/202142756

arXiv

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Other Link： http://arxiv.org/pdf/2111.08836v2

It has been recently recognized that the observational relativistic effects,
mainly arising from the light propagation in an inhomogeneous universe, induce
the dipole asymmetry in the cross-correlation function of galaxies. In
particular, the dipole asymmetry at small scales is shown to be dominated by
the gravitational redshift effects. In this paper, we exploit a simple
analytical description for the dipole asymmetry in the cross-correlation
function valid at quasi-linear regime. In contrast to the previous model, a new
prescription involves only one dimensional integrals, providing a faster way to
reproduce the results obtained by Saga et al. (2020). Using the analytical
model, we discuss the detectability of the dipole signal induced by the
gravitational redshift effect from upcoming galaxy surveys. The gravitational
redshift effect at small scales enhances the signal-to-noise ratio (S/N) of the
dipole, and in most of the cases considered, the S/N is found to reach a
maximum at $z\approx0.5$. We show that current and future surveys such as DESI
and SKA provide an idealistic data set, giving a large S/N of $10\sim 20$. Two
potential systematics arising from off-centered galaxies are also discussed
(transverse Doppler effect and diminution of the gravitational redshift
effect), and their impacts are found to be mitigated by a partial cancellation
between two competitive effects. Thus, the detection of the dipole signal at
small scales is directly linked to the gravitational redshift effect, and
should provide an alternative route to test gravity.

DOI： 10.1093/mnras/stac186

arXiv

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Other Link： http://arxiv.org/pdf/2109.06012v2

Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing Ltd  

Primordial magnetic field (PMF) is one of the feasible candidates to explain
observed large-scale magnetic fields, for example, intergalactic magnetic
fields. We present a new mechanism that brings us information about PMFs on
small scales based on the abundance of primordial black holes (PBHs). The
anisotropic stress of the PMFs can act as a source of the super-horizon
curvature perturbation in the early universe. If the amplitude of PMFs is
sufficiently large, the resultant density perturbation also has a large
amplitude, and thereby, the PBH abundance is enhanced. Since the anisotropic
stress of the PMFs is consist of the square of the magnetic fields, the
statistics of the density perturbation follows the non-Gaussian distribution.
Assuming Gaussian distributions and delta-function type power spectrum for
PMFs, based on a Monte-Carlo method, we obtain an approximate probability
density function of the density perturbation, and it is an important piece to
relate the amplitude of PMFs with the abundance of PBHs. Finally, we place the
strongest constraint on the amplitude of PMFs as a few hundred nano-Gauss on
$10^{2}\;{\rm Mpc}^{-1} \leq k\leq 10^{18}\;{\rm Mpc}^{-1}$ where the typical
cosmological observations never reach.

DOI： 10.1088/1475-7516/2020/05/039

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/2002.01286v2

The observed galaxy distribution via galaxy redshift surveys appears
distorted due to redshift-space distortions (RSD). While one dominant
contribution to RSD comes from the Doppler effect induced by the peculiar
velocity of galaxies, the relativistic effects, including the gravitational
redshift effect, are recently recognized to give small but important
contributions. Such contributions lead to an asymmetric galaxy clustering along
the line of sight, and produce non-vanishing odd multipoles when
cross-correlating between different biased objects. However, non-zero odd
multipoles are also generated by the Doppler effect beyond the distant-observer
approximation, known as the wide-angle effect, and at quasi-linear scales, the
interplay between wide-angle and relativistic effects becomes significant. In
this paper, based on the formalism developed by Taruya et al., we present a
quasi-linear model of the cross-correlation function taking a proper account of
both the wide-angle and gravitational redshift effects, as one of the major
relativistic effects. Our quasi-linear predictions of the dipole agree well
with simulations even at the scales below $20\,h^{-1}\,$Mpc, where
non-perturbative contributions from the halo potential play an important role,
flipping the sign of the dipole amplitude. When increasing the bias difference
and redshift, the scale where the sign flip happens is shifted to a larger
scale. We derive a simple approximate formula to quantitatively account for the
behaviors of the sign flip.

DOI： 10.1093/mnras/staa2232

arXiv

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Other Link： http://arxiv.org/pdf/2004.03772v2

Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

Spatially fluctuating primordial magnetic fields (PMFs) inhomogeneously
reheat the Universe when they dissipate deep inside the horizon before
recombination. Such an energy injection turns into an additional photon
temperature perturbation. We investigate secondary cosmic microwave background
(CMB) temperature anisotropies originated from this mechanism, which we call
{\it inhomogeneous magnetic reheating}. We find that it can bring us
information about non-linear coupling between PMFs and primordial curvature
perturbations parametrized by $b_{\rm NL}$, which should be important for
probing the generation mechanism of PMFs. In fact, by using current CMB
observations, we obtain an upper bound on the non-linear parameter as $\log
(b_{\rm NL} (B_{\lambda}/{\rm nG})^2) \lesssim {-36.5n_{B} - 94.0}$ with
$B_{\lambda}$ and $n_{\rm B}$ being a magnetic field amplitude smoothed over
$\lambda=1\; {\rm Mpc}$ scale and a spectral index of the PMF power spectrum,
respectively. Our constraints are far stronger than a previous forecast based
on the future CMB spectral distortion anisotropy measurements because
inhomogeneous magnetic reheating covers a much wider range of scales, i.e.,
$1\; {\rm Mpc}^{-1} \lesssim k\lesssim 10^{15}\; {\rm Mpc}^{-1}$.

DOI： 10.1093/mnras/stz2882

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1904.09121v2

Redshift-space distortions (RSD) in galaxy redshift surveys generally break
both the isotropy and homogeneity of galaxy distribution. While the former
aspect is particularly highlighted as a probe of growth of structure induced by
gravity, the latter aspect, often quoted as wide-angle RSD but ignored in most
of the cases, will become important and critical to account for as increasing
the statistical precision in next-generation surveys. However, the impact of
wide-angle RSD has been mostly studied using linear perturbation theory. In
this paper, employing the Zel'dovich approximation, i.e., first-order
Lagrangian perturbation theory for gravitational evolution of matter
fluctuations, we present a quasi-linear treatment of wide-angle RSD, and
compute the cross-correlation function. The present formalism consistently
reproduces linear theory results, and can be easily extended to incorporate
relativistic corrections (e.g., gravitational redshift).

DOI： 10.1093/mnras/stz3272

arXiv

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Other Link： http://arxiv.org/pdf/1908.03854v2

We present robust constraints on the stochastic gravitational waves (GWs) at
Mpc scales from the cosmic microwave background (CMB) data. CMB constraints on
GWs are usually characterized as the tensor-to-scalar ratio, assuming
specifically a power-law form of the primordial spectrum, and are obtained from
the angular spectra of CMB. Here, we relax the assumption of the power-law
form, and consider to what extent one can constrain a monochromatic GW at
shorter wavelengths. Previously, such a constraint has been derived at the
wavelengths larger than the resolution scale of the CMB measurements, typically
above $100$Mpc (below $10^{-16}$Hz in frequency). However, GWs whose wavelength
is much shorter than $100$Mpc can imprint a small but non-negligible signal on
CMB anisotropies at observed angular scales, $\ell<1000$. Here, using the CMB
temperature, polarization, and lensing data set, we obtain the best constraints
to date at $10^{-16}-10^{-14}$Hz of the GWs produced before the time of
decoupling, which are tighter than those derived from the astrometric
measurements and upper bounds on extra radiations. In the future, the
constraints on GWs at Mpc scales will be further improved by several orders of
magnitude with the precision $B$-mode measurement on large scales, $\ell<100$.

DOI： 10.1103/PhysRevD.100.021303

arXiv

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Other Link： http://arxiv.org/pdf/1904.02115v2

Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Primordial magnetic fields (PMFs) can source gravitational wave background
(GWB). In this paper, we investigate the possible constraints on small-scale
PMF considering the ongoing and forthcoming direct detection observations of
GWB. In contrast to the conventional cosmological probes, e.g., cosmic
microwave background anisotropies, which are useful to investigate large-scale
PMFs ($>1 {\rm Mpc}$), the direct detection experiments of GWB can explore
small-scale PMFs whose scales correspond to the observed frequencies of GWB. We
show that future ground-based or space-based interferometric gravitational wave
detectors give a strong constraint of about $10^{2} {\rm nG}$ on much smaller
scales of about $k\approx 10^{12} {\rm Mpc}^{-1}$. We also demonstrate that
pulsar timing arrays have a potential to strongly constrain PMFs. The current
limits on GWB from pulsar timing arrays can put the tight constraint on the
amplitude of the PMFs of about $30 {\rm nG}$ whose coherent length is of about
$k\approx 10^{6} {\rm Mpc}^{-1}$. The future experiments for the direct
detection of GWB by the Square Kilometre Array could give much tighter
constraints on the amplitude of PMFs about $5 {\rm nG}$ on $k\approx 10^{6}
{\rm Mpc}^{-1}$, on which scales, it is difficult to reach by using the
cosmological observations.

DOI： 10.1103/PhysRevD.98.083518

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1807.00561v2

We consider the growth of primordial dark matter halos seeded by three
crossed initial sine waves of various amplitudes. Using a Lagrangian treatment
of cosmological gravitational dynamics, we examine the convergence properties
of a high-order perturbative expansion in the vicinity of shell-crossing, by
comparing the analytical results with state-of-the-art high resolution
Vlasov-Poisson simulations. Based on a quantitative exploration of parameter
space, we study explicitly for the first time the convergence speed of the
perturbative series, and find, in agreement with intuition, that it slows down
when going from quasi one-dimensional initial conditions (one sine wave
dominating) to quasi triaxial symmetry (three sine waves with same amplitude).
In most cases, the system structure at collapse time is, as expected, very
similar to what is obtained with simple one-dimensional dynamics, except in the
quasi-triaxial regime, where the phase-space sheet presents a velocity spike.
In all cases, the perturbative series exhibits a generic convergence behavior
as fast as an exponential of a power-law of the order of the expansion,
allowing one to numerically extrapolate it to infinite order. The results of
such an extrapolation agree remarkably well with the simulations, even at
shell-crossing.

DOI： 10.1103/PhysRevLett.121.241302

arXiv

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Other Link： http://arxiv.org/pdf/1805.08787v2

The apparent distribution of large-scale structures in the universe is
sensitive to the velocity/potential of the sources as well as the potential
along the line-of-sight through the mapping from real space to redshift space
(redshift-space distortions, RSD). Since odd multipoles of the halo
cross-correlation function vanish when considering standard Doppler RSD, the
dipole is a sensitive probe of relativistic and wide-angle effects. We build a
catalogue of ten million haloes (Milky-Way size to galaxy-cluster size) from
the full-sky light-cone of a new "RayGalGroupSims" N-body simulation which
covers a volume of ($2.625~h^{-1}$Gpc)$^3$ with $4096^3$ particles. Using
ray-tracing techniques, we find the null geodesics connecting all the sources
to the observer. We then self-consistently derive all the relativistic
contributions (in the weak-field approximation) to RSD: Doppler, transverse
Doppler, gravitational, lensing and integrated Sachs-Wolfe. It allows us, for
the first time, to disentangle all contributions to the dipole from linear to
non-linear scales. At large scale, we recover the linear predictions dominated
by a contribution from the divergence of neighbouring line-of-sights. While the
linear theory remains a reasonable approximation of the velocity contribution
to the dipole at non-linear scales it fails to reproduce the potential
contribution below $30-60~h^{-1}$Mpc (depending on the halo mass). At scales
smaller than $\sim 10~h^{-1}$Mpc, the dipole is dominated by the asymmetry
caused by the gravitational redshift. The transition between the two regimes is
mass dependent as well. We also identify a new non-trivial contribution from
the non-linear coupling between potential and velocity terms.

DOI： 10.1093/mnras/sty3206

arXiv

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Other Link： http://arxiv.org/pdf/1803.04294v2

Language：English   Publishing type：Research paper (scientific journal)   Publisher：OXFORD UNIV PRESS  

We provide a new bound on the amplitude of primordial magnetic fields (PMFs)
by using a novel mechanism, named {\it magnetic reheating}. Before the epoch of
recombination, PMFs induce the fluid motions in a photon-baryon plasma through
the Lorentz force. Due to the viscosity in the plasma, such induced fluid
motions would be damped and this means the dissipation of PMFs. In the early
Universe with $z \gtrsim 2 \times 10^6$, cosmic microwave background (CMB)
photons are quickly thermalized with the dissipated energy and shift to a
different Planck distribution with a new temperature. In other words, the
energy injection due to the dissipation of PMFs changes the baryon-photon
number ratio during this era and we name such a process {\it magnetic
reheating}. By using the current results of the baryon-photon number ratio
obtained from the Big Bang nucleosynthesis and CMB observations, we put a
strongest constraint on the amplitude of PMFs on small scales which we can not
access through CMB anisotropy and CMB distortions, $B_{0} \lesssim 1.0 \;
\mu{\rm G}$ at the scales $10^{4} \; h{\rm Mpc}^{-1} < k < 10^{8} \; h{\rm
Mpc}^{-1}$. Moreover, when the spectrum of PMFs is given by the power-law, the
magnetic reheating puts a quite strong constraint in the case of the
blue-tilted spectrum, for example, $B_0 \lesssim 10^{-17} \;{\rm nG}$,
$10^{-23} \;{\rm nG}$, and $10^{-29} \;{\rm nG}$ at 1~comoving Mpc for
$n_{B}=1.0$, $2.0$, and $3.0$, respectively. This constraint would give an
impact on generation mechanisms of PMFs in the early Universe.

DOI： 10.1093/mnrasl/slx195

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1708.08225v2

Cosmological defects result from cosmological phase transitions in the early
Universe and the dynamics reflects their symmetry-breaking mechanisms. These
cosmological defects may be probed through weak lensing effects because they
interact with ordinary matters only through the gravitational force. In this
paper, we investigate global textures by using weak lensing curl and B modes.
Non-topological textures are modeled by the non-linear sigma model (NLSM), and
induce not only the scalar perturbation but also vector and tensor
perturbations in the primordial plasma due to the nonlinearity in the
anisotropic stress of scalar fields. We show angular power spectra of curl and
B modes from both vector and tensor modes based on the NLSM. Furthermore, we
give the analytic estimations for curl and B mode power spectra. The amplitude
of weak lensing signals depends on a combined parameter $\epsilon^{2}_{v} =
N^{-1}\left( v/m_{\rm pl} \right)^{4}$ where $N$ and $v$ are the number of the
scalar fields and the vacuum expectation value, respectively. We discuss the
detectability of the curl and B modes with several observation specifications.
In the case of the CMB lensing observation without including the instrumental
noise, we can reach $\epsilon_{v} \approx 2.7\times 10^{-6}$. This constraint
is about 10 times stronger than the current one determined from the Planck. For
the cosmic shear observation, we find that the signal-to-noise ratio depends on
the mean redshift and the observing number of galaxies as $\propto z^{0.7}_{\rm
m}$ and $\propto N^{0.2}_{\rm g}$, respectively. In the study of textures using
cosmic shear observations, the mean redshift would be one of the key design
parameters.

DOI： 10.1103/PhysRevD.95.123524

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1612.04006v2

The second-order vector mode is inevitably induced from the coupling of
first-order scalar modes in cosmological perturbation theory and might hinder a
possible detection of primordial gravitational waves from inflation through
21cm lensing observations. Here, we investigate the weak lensing signal in 21cm
photons emitted by neutral hydrogen atoms in the dark ages induced by the
second-order vector mode by decomposing the deflection angle of the 21cm
lensing signal into the gradient and curl modes. The curl mode is a good tracer
of the cosmological vector and tensor modes since the scalar mode does not
induce the curl one. By comparing angular power spectra of the 21cm lensing
curl mode induced by the second-order vector mode and primordial gravitational
waves whose amplitude is parametrized by the tensor-to-scalar ratio $r$, we
find that the 21cm curl mode from the second-order vector mode dominates over
that from primordial gravitational waves on almost all scales if $r \lesssim
10^{-5}$. If we use the multipoles of the power spectrum up to $\ell_{\rm max}
= 10^{5}$ and $10^{6}$ in reconstructing the curl mode from 21cm temperature
maps, the signal-to-noise ratios of the 21cm curl mode from the second-order
vector mode achieve ${\rm S/N} \approx 0.46$ and $73$, respectively.
Observation of 21cm radiation is, in principle, a powerful tool to explore not
only the tensor mode but also the cosmological vector mode.

DOI： 10.1103/PhysRevD.94.063523

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1607.03973v2

The vector mode of cosmological perturbation theory imprints characteristic
signals on the weak lensing signals such as curl- and B-modes which are never
imprinted by the scalar mode. However, the vector mode is neglected in the
standard first-order cosmological perturbation theory since it only has a
decaying mode. This situation changes if the cosmological perturbation theory
is expanded up to second order. The second-order vector and tensor modes are
inevitably induced by the product of the first-order scalar modes. We study the
effect of the second-order vector mode on the weak lensing curl- and B-modes.
We find that the curl-mode induced by the second-order vector mode is
comparable to that induced by the primordial gravitational waves with the
tensor-to-scalar ratio $r = 0.1$ at $\ell \approx 200$. In this case, the
curl-mode induced by the second-order vector mode dominates at $\ell > 200$.
Furthermore, the B-mode cosmic shear induced by the second-order vector mode
dominates on almost all scales. However, we find that the observational
signatures of the second-order vector and tensor modes cannot exceed the
expected noise of ongoing and upcoming weak lensing measurements. We conclude
that the curl- and B-modes induced by the second-order vector and tensor modes
are unlikely to be detected in future experiments.

DOI： 10.1103/PhysRevD.92.063533

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1505.02774v2

If vector type perturbations are present in the primordial plasma before
recombination, the generation of magnetic fields is known to be inevitable
through the Harrison mechanism. In the context of the standard cosmological
perturbation theory, non-linear couplings of first-order scalar perturbations
create second-order vector perturbations, which generate magnetic fields. Here
we reinvestigate the generation of magnetic fields at second-order in
cosmological perturbations on the basis of our previous study, and extend it by
newly taking into account the time evolution of purely second-order vector
perturbations with a newly developed second-order Boltzmann code. We confirm
that the amplitude of magnetic fields from the product-terms of the first-order
scalar modes is consistent with the result in our previous study. However, we
find, both numerically and analytically, that the magnetic fields from the
purely second-order vector perturbations partially cancel out the magnetic
fields from one of the product-terms of the first-order scalar modes, in the
tight coupling regime in the radiation dominated era. Therefore, the amplitude
of the magnetic fields on small scales, $k \gtrsim 10~h{\rm Mpc}^{-1}$, is
smaller than the previous estimates. The amplitude of the generated magnetic
fields at cosmological recombination is about $B_{\rm rec} =5.0\times
10^{-24}~{\rm Gauss}$ on $k = 5.0 \times 10^{-1}~h{\rm Mpc}^{-1}$. Finally, we
discuss the reason of the discrepancies that exist in estimates of the
amplitude of magnetic fields among other authors.

DOI： 10.1103/PhysRevD.91.123510

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1504.03790v2

Gravitational waves (GWs) are inevitably induced at second-order in
cosmological perturbations through non-linear couplings with first order scalar
perturbations, whose existence is well established by recent cosmological
observations. So far, the evolution and the spectrum of the secondary induced
GWs have been derived by taking into account the sources of GWs only from the
product of first order scalar perturbations. Here we newly investigate the
effects of purely second-order anisotropic stresses of photons and neutrinos on
the evolution of GWs, which have been omitted in the literature. We present a
full treatment of the Einstein-Boltzmann system to calculate the spectrum of
GWs with anisotropic stress based on the formalism of the cosmological
perturbation theory. We find that photon anisotropic stress amplifies the
amplitude of GWs by about $150 %$ whereas neutrino anisotropic stress suppress
that of GWs by about $30 %$ on small scales $k\gtrsim 1.0 h{\rm Mpc}^{-1}$
compared to the case without anisotropic stress. The second order anisotropic
stress does not affect GWs with wavenumbers $k\lesssim 1.0 h{\rm Mpc}^{-1}$.
The result is in marked contrast with the case at linear order, where the
effect of anisotropic stress is damping in amplitude of GWs.

DOI： 10.1103/PhysRevD.91.024030

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1412.1081v2

The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may
be the smoking gun of not only the primordial tensor mode but also of the
primordial vector mode. If there exist nonzero vector-mode metric perturbations
in the early Universe, they are known to be supported by anisotropic stress
fluctuations of free-streaming particles such as neutrinos, and to create
characteristic signatures on both the CMB temperature, E-mode, and B-mode
polarization anisotropies. We place constraints on the properties of the
primordial vector mode characterized by the vector-to-scalar ratio $r_{v}$ and
the spectral index $n_{v}$ of the vector-shear power spectrum, from the {\it
Planck} and BICEP2 B-mode data. We find that, for scale-invariant initial
spectra, the $\Lambda$CDM model including the vector mode fits the data better
than the model including the tensor mode. The difference in $\chi^{2}$ between
the vector and tensor models is $\Delta\chi^{2} = 3.294$, because, on large
scales the vector mode generates smaller temperature fluctuations than the
tensor mode, which is preferred for the data. In contrast, the tensor mode can
fit the data set equally well if we allow a significantly blue-tilted spectrum.
We find that the best-fitting tensor mode has a large blue tilt and leads to an
indistinct reionization bump on larger angular scales. The slightly red-tilted
vector mode supported by the current data set can also create ${\cal
O}(10^{-22})$-Gauss magnetic fields at cosmological recombination. Our
constraints should motivate research that considers models of the early
Universe that involve the vector mode.

DOI： 10.1088/1475-7516/2014/10/004

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1405.4810v2

We investigate parity-violating signatures of temperature and polarization
bispectra of the cosmic microwave background (CMB) in an inflationary model
where a rolling pseudoscalar produces large equilateral tensor non-Gaussianity.
By a concrete computation based on full-sky formalism, it is shown that
resultant CMB bispectra have nonzero signals in both parity-even $(\ell_1 +
\ell_2 + \ell_3 = {\rm even})$ and parity-odd $(\ell_1 + \ell_2 + \ell_3 = {\rm
odd})$ spaces, and are almost uncorrelated with usual scalar-mode equilateral
bispectra. These characteristic signatures and polarization information help to
detect such tensor non-Gaussianity. Use of both temperature and E-mode
bispectra potentially improves of $400\%$ the detectability with respect to an
analysis with temperature bispectrum alone. Considering B-mode bispectrum, the
signal-to-noise ratio may be able to increase by 3 orders of magnitude. We
present the $1\sigma$ uncertainties of a parameter depending on a coupling
constant and a rolling condition for the pseudoscalar expected in the ${\it
Planck}$ and the proposed PRISM experiments.

DOI： 10.1088/1475-7516/2013/11/051

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arXiv

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Other Link： http://arxiv.org/pdf/1308.6769v2

Recently the lower bounds of the intergalactic magnetic fields $10^{-16} \sim
10^{-20}$ Gauss are set by gamma-ray observations while it is unlikely to
generate such large scale magnetic fields through astrophysical processes. It
is known that large scale magnetic fields could be generated if there exist
cosmological vector mode perturbations in the primordial plasma. The vector
mode, however, has only a decaying solution in General Relativity if the plasma
consists of perfect fluids. In order to investigate a possible mechanism of
magnetogenesis in the primordial plasma, here we consider cosmological
perturbations in the Einstein-Aether gravity model, in which the aether field
can act as a new source of vector metric perturbations and thus of magnetic
fields. We estimate the angular power spectra of temperature and B-mode
polarization of the Cosmic Microwave Background (CMB) Anisotropies in this
model and put a rough constraint on the aether field parameters from latest
observations. We then estimate the power spectrum of associated magnetic fields
around the recombination epoch within this limit. It is found that the spectrum
has a characteristic peak at $k=0.1 h{\rm Mpc^{-1 } }$, and at that scale the
amplitude can be as large as $B\sim 10^{-22}$ Gauss where the upper bound comes
from CMB temperature anisotropies. The magnetic fields with this amplitude can
be seeds of large scale magnetic fields observed today if the sufficient dynamo
mechanism takes place. Analytic interpretation for the power spectra is also
given.

DOI： 10.1103/PhysRevD.87.104025

Web of Science

Scopus

arXiv

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Other Link： http://arxiv.org/pdf/1302.4189v2

We study temperature and polarization anisotropies of the cosmic microwave
background (CMB) radiation sourced from primordial cross-bispectra between
metric perturbations and vector fields, which are generated from the inflation
model where an inflaton and a vector field are coupled. In case the vector
field survives after the reheating, both the primordial scalar and tensor
fluctuations can be enhanced by the anisotropic stress composed of the vector
fields during radiation dominated era. We show that through this enhancement
the primordial cross-bispectra generate not only CMB bispectra but also CMB
power spectra. In general, we can expect such cross-bispectra produce the
non-trivial mode-coupling signals between the scalar and tensor fluctuations.
However, we explicitly show that such mode-coupling signals do not appear in
CMB power spectra. Through the numerical analysis of the CMB scalar-mode power
spectra, we find that although signals from these cross-bispectra are smaller
than primary non-electromagnetic ones, these have some characteristic features
such as negative auto-correlations of the temperature and polarization modes,
respectively. On the other hand, signals from tensor modes are almost
comparable to primary non-electromagnetic ones and hence the shape of observed
$B$-mode spectrum may deviate from the prediction in the non-electromagnetic
case. The above imprints may help us to judge the existence of the coupling
between the scalar and vector fields in the early Universe.

DOI： 10.1088/1475-7516/2012/11/046

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Other Link： http://arxiv.org/pdf/1209.3384v2