1,607 research outputs found
Primordial Black Holes from Inflation and non-Gaussianity
Primordial black holes may owe their origin to the small-scale enhancement of
the comoving curvature perturbation generated during inflation. Their mass
fraction at formation is markedly sensitive to possible non-Gaussianities in
such large, but rare fluctuations. We discuss a path-integral formulation which
provides the exact mass fraction of primordial black holes at formation in the
presence of non-Gaussianity. Through a couple of classes of models, one based
on single-field inflation and the other on spectator fields, we show that
restricting to a Gaussian statistics may lead to severe inaccuracies in the
estimate of the mass fraction as well as on the clustering properties of the
primordial black holes.Comment: 21 pages, 2 figures, v2: matching published versio
Large-scale bias in the Universe: bispectrum method
Evidence that the Universe may be close to the critical density, required for
its expansion eventually to be halted, comes principally from dynamical studies
of large-scale structure. These studies either use the observed peculiar
velocity field of galaxies directly, or indirectly by quantifying its
anisotropic effect on galaxy clustering in redshift surveys. A potential
difficulty with both such approaches is that the density parameter
is obtained only in the combination , if linear
perturbation theory is used. The determination of the density parameter
is therefore compromised by the lack of a good measurement of the
bias parameter , which relates the clustering of sample galaxies to the
clustering of mass.
In this paper, we develop an idea of Fry (1994), using second-order
perturbation theory to investigate how to measure the bias parameter on large
scales. The use of higher-order statistics allows the degeneracy between
and to be lifted, and an unambiguous determination of
then becomes possible. We apply a likelihood approach to the bispectrum, the
three-point function in Fourier space. This paper is the first step in turning
the idea into a practical proposition for redshift surveys, and is principally
concerned with noise properties of the bispectrum, which are non-trivial. The
calculation of the required bispectrum covariances involves the six-point
function, including many noise terms, for which we have developed a generating
functional approach which will be of value in calculating high-order statistics
in general.Comment: 12 pages, latex, 7 postscript figures included. Accepted by MNRAS.
(Minor numerical typesetting errors corrected: results unchanged
The nonlinear redshift-space power spectrum of galaxies
We study the power spectrum of galaxies in redshift space, with third order
perturbation theory to include corrections that are absent in linear theory. We
assume a local bias for the galaxies: i.e. the galaxy density is sampled from
some local function of the underlying mass distribution. We find that the
effect of the nonlinear bias in real space is to introduce two new features:
first, there is a contribution to the power which is constant with wavenumber,
whose nature we reveal as essentially a shot-noise term. In principle this
contribution can mask the primordial power spectrum, and could limit the
accuracy with which the latter might be measured on very large scales.
Secondly, the effect of second- and third-order bias is to modify the effective
bias (defined as the square root of the ratio of galaxy power spectrum to
matter power spectrum). The effective bias is almost scale-independent over a
wide range of scales. These general conclusions also hold in redshift space. In
addition, we have investigated the distortion of the power spectrum by peculiar
velocities, which may be used to constrain the density of the Universe. We look
at the quadrupole-to-monopole ratio, and find that higher-order terms can mimic
linear theory bias, but the bias implied is neither the linear bias, nor the
effective bias referred to above. We test the theory with biased N-body
simulations, and find excellent agreement in both real and redshift space,
providing the local biasing is applied on a scale whose fractional r.m.s.
density fluctuations are .Comment: 13 pages, 7 figures. Accepted by MNRA
Influence of Super-Horizon Scales on Cosmological Observables Generated during Inflation
Using the techniques of out-of-equilibrium field theory, we study the
influence on the properties of cosmological perturbations generated during
inflation on observable scales coming from fluctuations corresponding today to
scales much bigger than the present Hubble radius. We write the effective
action for the coarse-grained inflaton perturbations integrating out the
sub-horizon modes, which manifest themselves as a colored noise and lead to
memory effects. Using the simple model of a scalar field with cubic
self-interactions evolving in a fixed de Sitter background, we evaluate the
two- and three-point correlation function on observable scales. Our basic
procedure shows that perturbations do preserve some memory of the
super-horizon-scale dynamics, in the form of scale-dependent imprints in the
statistical moments. In particular, we find a blue tilt of the power-spectrum
on large scales, in agreement with the recent results of the WMAP collaboration
which show a suppression of the lower multipoles in the Cosmic Microwave
Background anisotropies, and a substantial enhancement of the intrinsic
non-Gaussianity on large scalesComment: 19 pages, 5 figures. One reference adde
Super Heavy Dark Matter in light of BICEP2, Planck and Ultra High Energy Cosmic Rays Observations
The announcement by BICEP2 of the detection of B-mode polarization consistent
with primordial gravitational waves with a tensor-to-scalar ratio,
, challenged predictions from most inflationary models
of a lower value for . More recent results by Planck on polarized dust
emission show that the observed tensor modes signal is compatible with pure
foreground emission. A more significant constraint on was then obtained by
a joint analysis of Planck, BICEP2 and Keck Array data showing an upper limit
to the tensor to scalar ratio , excluding the case with low
statistical significance. Forthcoming measurements by BICEP3, the Keck Array,
and other CMB polarization experiments, open the possibility for making the
fundamental measurement of . Here we discuss how sets the scale for
models where the dark matter is created at the inflationary epoch, the
generically called super-heavy dark matter models. We also consider the
constraints on such scenarios given by recent data from ultrahigh energy cosmic
ray observatories which set the limit on super-heavy dark matter particles
lifetime. We discuss how super-heavy dark matter can be discovered by a precise
measurement of combined with future observations of ultra high energy
cosmic rays.Comment: 17 pages, 14 eps figures, accepted for publication in JCA
Comments on Backreaction and Cosmic Acceleration
In this brief WEB note we comment on recent papers related to our paper "On
Acceleration Without Dark Energy".Comment: 5 pages WEB not
The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
We analyze the temperature three--point correlation function and the skewness
of the Cosmic Microwave Background (CMB), providing general relations in terms
of multipole coefficients. We then focus on applications to large angular scale
anisotropies, such as those measured by the {\em COBE} DMR, calculating the
contribution to these quantities from primordial, inflation generated, scalar
perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic
inflation we are able to provide a {\it universal} expression for the ensemble
averaged three--point function and for the corresponding skewness, which
accounts for all primordial second--order effects. These general expressions
would moreover apply to any situation where the bispectrum of the primordial
gravitational potential has a {\em hierarchical} form. Our results are then
specialized to a number of relevant models: power--law inflation driven by an
exponential potential, chaotic inflation with a quartic and quadratic potential
and a particular case of hybrid inflation. In all these cases non--Gaussian
effects are small: as an example, the {\em mean} skewness is much smaller than
the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation
field.Comment: 18 pages; LaTeX; 4 PostScript figures included at the end of the
file; SISSA REF.193/93/A and DFPD 93/A/8
Non-Gaussianity from Inflation: Theory and Observations
This is a review of models of inflation and of their predictions for the
primordial non-Gaussianity in the density perturbations which are thought to be
at the origin of structures in the Universe. Non-Gaussianity emerges as a key
observable to discriminate among competing scenarios for the generation of
cosmological perturbations and is one of the primary targets of present and
future Cosmic Microwave Background satellite missions. We give a detailed
presentation of the state-of-the-art of the subject of non-Gaussianity, both
from the theoretical and the observational point of view, and provide all the
tools necessary to compute at second order in perturbation theory the level of
non-Gaussianity in any model of cosmological perturbations. We discuss the new
wave of models of inflation, which are firmly rooted in modern particle physics
theory and predict a significant amount of non-Gaussianity. The review is
addressed to both astrophysicists and particle physicists and contains useful
tables which summarize the theoretical and observational results regarding
non-Gaussianity.Comment: LaTeX file: 218 pages, 19 figures. Replaced to match the accepted
version in Physics Reports. A high-resolution version of Fig. 2 can be
downloaded from: http://www.pd.infn.it/~liguori/Non_Gaussianity
Second-order matter perturbations in a LambdaCDM cosmology and non-Gaussianity
We obtain exact expressions for the effect of primordial non-Gaussianity on
the matter density perturbation up to second order in a LambdaCDM cosmology,
fully accounting for the general relativistic corrections arising on scales
comparable with the Hubble radius. We present our results both in the Poisson
gauge and in the comoving and synchronous gauge, which are relevant for
comparison to different cosmological observables.Comment: 15 pages. LaTeX file. Invited article for CQG issue on non-linear
cosmolog
CMB temperature anisotropies from third order gravitational perturbations
In this paper we present a complete computation of the Cosmic Microwave
Background (CMB) anisotropies up to third order from gravitational
perturbations accounting for scalar, vector and tensor perturbations. We then
specify our results to the large scale limit, providing the evolution of the
gravitational potentials in a flat universe filled with matter and cosmological
constant which characterizes the Integrated Sachs-Wolfe effect. As a byproduct
in the large scale approximation we are able to give non-perturbative solutions
for the photon geodesic equations. Our results are the first step to provide a
complete theoretical prediction for cubic non-linearities which are
particularly relevant for characterizing the level of non-Gaussianity in the
CMB through the detection of the four-point angular connected correlation
function (trispectrum). For this purpose we also allow for generic initial
conditions due to primordial non-Gaussianity.Comment: 19 pages, LateX file; typos corrected; some corrections made and
several consistency checks performed regarding Eqs.(2.18); (2.28)-(2.29) and
Eqs.(3.8)-(3.24) and Eq.(4.2). Version accepted for publication in JCA
- …