1,276 research outputs found
Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity
We provide the gauge-invariant expression for large-scale cosmic microwave
background temperature fluctuations at second-order in perturbation theory. It
enables to unambiguously define the nonlinearity parameter f_NL which is used
by experimental collaborations to pin down the level of Non-Gaussianity in the
temperature fluctuations. Furthermore, it contains a primordial term encoding
all the information about the Non-Gaussianity generated at primordial epochs
and about the mechanism which gave rise to cosmological perturbations, thus
neatly disentangling the primordial contribution to Non-Gaussianity from the
one caused by the post-inflationary evolution.Comment: 4 pages, LaTeX file. Revised to match the version to appear in Phys.
Rev. Let
The Maximal Amount of Gravitational Waves in the Curvaton Scenario
The curvaton scenario for the generation of the cosmological curvature
perturbation on large scales represents an alternative to the standard
slow-roll scenario of inflation in which the observed density perturbations are
due to fluctuations of the inflaton field itself. Its basic assumption is that
the initial curvature perturbation due to the inflaton field is negligible.
This is attained by lowering the energy scale of inflation, thereby highly
suppressing the amount of gravitational waves produced during inflation. We
compute the power-spectrum of the gravitational waves generated at second order
in perturbation theory by the curvaton (isocurvature) perturbations between the
end of inflation and the curvaton decay. An interesting property of this
contribution to the tensor perturbations is that it is directly proportional to
the amount of non-Gaussianity predicted within the curvaton scenario. We show
that the spectrum of gravitational waves may be in the range of future
gravitational wave detectors.Comment: 4 pages, laTeX; added a clarifying comment in the conclusions,
version matches publication in PRD, Rapid Communication
Testing Primordial Black Holes as Dark Matter through LISA
The idea that primordial black holes (PBHs) can comprise most of the dark
matter of the universe has recently reacquired a lot of momentum. Observational
constraints, however, rule out this possibility for most of the PBH masses,
with a notable exception around . These light PBHs may be
originated when a sizeable comoving curvature perturbation generated during
inflation re-enters the horizon during the radiation phase. During such a
stage, it is unavoidable that gravitational waves (GWs) are generated. Since
their source is quadratic in the curvature perturbations, these GWs are
generated fully non-Gaussian. Their frequency today is about the mHz, which is
exactly the range where the LISA mission has the maximum of its sensitivity.
This is certainly an impressive coincidence. We show that this scenario of PBHs
as dark matter can be tested by LISA by measuring the GW two-point correlator.
On the other hand, we show that the short observation time (as compared to the
age of the universe) and propagation effects of the GWs across the perturbed
universe from the production point to the LISA detector suppress the bispectrum
to an unobservable level. This suppression is completely general and not
specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio
Loop Representations for 2+1 Gravity on a Torus
We study the loop representation of the quantum theory for 2+1 dimensional
general relativity on a manifold, , where
is the torus, and compare it with the connection representation
for this system. In particular, we look at the loop transform in the part of
the phase space where the holonomies are boosts and study its kernel. This
kernel is dense in the connection representation and the transform is not
continuous with respect to the natural topologies, even in its domain of
definition. Nonetheless, loop representations isomorphic to the connection
representation corresponding to this part of the phase space can still be
constructed if due care is taken. We present this construction but note that
certain ambiguities remain; in particular, functions of loops cannot be
uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-
A simplified structure for the second order cosmological perturbation equations
Increasingly accurate observations of the cosmic microwave background and the
large scale distribution of galaxies necessitate the study of nonlinear
perturbations of Friedmann-Lemaitre cosmologies, whose equations are
notoriously complicated. In this paper we present a new derivation of the
governing equations for second order perturbations within the framework of the
metric-based approach that is minimal, as regards amount of calculation and
length of expressions, and flexible, as regards choice of gauge and
stress-energy tensor. Because of their generality and the simplicity of their
structure our equations provide a convenient starting point for determining the
behaviour of nonlinear perturbations of FL cosmologies with any given
stress-energy content, using either the Poisson gauge or the uniform curvature
gauge.Comment: 30 pages, no figures. Changed title to the one in published version
and some minor changes and addition
Second-Order Cosmological Perturbations from Inflation
We present the first computation of the cosmological perturbations generated during inflation up to second-order in deviations from the homogeneous background solution. Our results, which fully account for the inflaton self-interactions as well as for the second-order fluctuations of the background metric, provide the exact expression for the gauge-invariant curvature perturbation bispectrum produced during inflation in terms of the slow-roll parameters or, alternatively, in terms of the scalar spectral n_S and and the tensor to adiabatic scalar amplitude ratio r. The bispectrum represents a specific non-Gaussian signature of fluctuations generated by quantum oscillations during slow-roll inflation. Our findings indicate that -- for a broad class of single-field models of inflation -- the level of non-Gaussianity in the cosmic microwave background anisotropies is large enough to be detectable by present and forthcoming satellite missions such as MAP and Planck
The Effects of Gravitational Back-Reaction on Cosmological Perturbations
Because of the non-linearity of the Einstein equations, the cosmological
fluctuations which are generated during inflation on a wide range of
wavelengths do not evolve independently. In particular, to second order in
perturbation theory, the first order fluctuations back-react both on the
background geometry and on the perturbations themselves. I this paper, the
gravitational back-reaction of long wavelength (super-Hubble) scalar metric
fluctuations on the perturbations themselves is investigated for a large class
of inflationary models. Specifically, the equations describing the evolution of
long wavelength cosmological metric and matter perturbations in an inflationary
universe are solved to second order in both the amplitude of the perturbations
and in the slow roll expansion parameter. Assuming that the linear fluctuations
have random phases, we show that the fractional correction to the power
spectrum due to the leading infrared back-reaction terms does not change the
shape of the spectrum. The amplitude of the effect is suppressed by the product
of the inflationary slow-roll parameter and the amplitude of the linear power
spectrum. The non-gaussianity of the spectrum induced by back-reaction is
commented upon.Comment: 9 page
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