338 research outputs found
Stochastic growth of quantum fluctuations during slow-roll inflation
We compute the growth of the mean square of quantum fluctuations of test
fields with small effective mass during a slowly changing, nearly de Sitter
stage which took place in different inflationary models. We consider a
minimally coupled scalar with a small mass, a modulus with an effective mass (with as the Hubble parameter) and a massless non-minimally
coupled scalar in the test field approximation and compare the growth of their
relative mean square with the one of gauge-invariant inflaton fluctuations. We
find that in most of the single field inflationary models the mean square gauge
invariant inflaton fluctuation grows {\em faster} than any test field with a
non-negative effective mass. Hybrid inflationary models can be an exception:
the mean square of a test field can dominate over the gauge invariant inflaton
fluctuation one on suitably choosing parameters. We also compute the stochastic
growth of quantum fluctuation of a second field, relaxing the assumption of its
zero homogeneous value, in a generic inflationary model; as a main result, we
obtain that the equation of motion of a gauge invariant variable associated,
order by order, with a generic quantum scalar fluctuation during inflation can
be obtained only if we use the number of e-folds as the time variable in the
corresponding Langevin and Fokker-Planck equations for the stochastic approach.
We employ this approach to derive some bounds in the case of a model with two
massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the
version to be published in Phys. Rev.
Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
High-precision constraints on primordial non-Gaussianity (PNG) will
significantly improve our understanding of the physics of the early universe.
Among all the subtleties in using large scale structure observables to
constrain PNG, accounting for relativistic corrections to the clustering
statistics is particularly important for the upcoming galaxy surveys covering
progressively larger fraction of the sky. We focus on relativistic projection
effects due to the fact that we observe the galaxies through the light that
reaches the telescope on perturbed geodesics. These projection effects can give
rise to an effective that can be misinterpreted as the primordial
non-Gaussianity signal and hence is a systematic to be carefully computed and
accounted for in modelling of the bispectrum. We develop the technique to
properly account for relativistic effects in terms of purely observable
quantities, namely angles and redshifts. We give some examples by applying this
approach to a subset of the contributions to the tree-level bispectrum of the
observed galaxy number counts calculated within perturbation theory and
estimate the corresponding non-Gaussianity parameter, , for the
local, equilateral and orthogonal shapes. For the local shape, we also compute
the local non-Gaussianity resulting from terms obtained using the consistency
relation for observed number counts. Our goal here is not to give a precise
estimate of for each shape but rather we aim to provide a scheme
to compute the non-Gaussian contamination due to relativistic projection
effects. For the terms considered in this work, we obtain contamination of
.Comment: 31 pages, 6 figures, Typos corrected to match the published version
in JCA
Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
We prove that the stochastic and standard field-theoretical approaches
produce exactly the same results for the amount of light massive scalar field
fluctuations generated during inflation in the leading order of the slow-roll
approximation. This is true both in the case for which this field is a test one
and inflation is driven by another field, and the case for which the field
plays the role of inflaton itself. In the latter case, in order to calculate
the average of the mean square of the gauge-invariant inflaton fluctuation, the
logarithm of the scale factor has to be used as the time variable in the
Fokker-Planck equation in the stochastic approach. The implications of particle
production during inflation for the second stage of inflation and for the
moduli problem are also discussed. The case of a massless self-interacting test
scalar field in a de Sitter background with a zero initial renormalized mean
square is also considered in order to show how the stochastic approach can
easily produce results corresponding to diagrams with an arbitrary number of
scalar field loops in the field-theoretical approach (explicit results up to 4
loops inclusive are presented).Comment: Discussion expanded, references added, conclusions unchanged, matches
the version to be published in Phys. Rev.
Second Order Gauge-Invariant Perturbations during Inflation
The evolution of gauge invariant second-order scalar perturbations in a
general single field inflationary scenario are presented. Different second
order gauge invariant expressions for the curvature are considered. We evaluate
perturbatively one of these second order curvature fluctuations and a second
order gauge invariant scalar field fluctuation during the slow-roll stage of a
massive chaotic inflationary scenario, taking into account the deviation from a
pure de Sitter evolution and considering only the contribution of super-Hubble
perturbations in mode-mode coupling. The spectra resulting from their
contribution to the second order quantum correlation function are nearly
scale-invariant, with additional logarithmic corrections to the first order
spectrum. For all scales of interest the amplitude of these spectra depend on
the total number of e-folds. We find, on comparing first and second order
perturbation results, an upper limit to the total number of e-folds beyond
which the two orders are comparable.Comment: 17 pages, 6 figures. Final version to appear in Phys. Rev.
Place Field Repetition and Purely Local Remapping in a Multicompartment Environment
Hippocampal place cells support spatial memory using sensory information from the environment and self-motion information to localize their firing fields. Currently, there is disagreement about whether CA1 place cells can use pure self-motion information to disambiguate different compartments in environments containing multiple visually identical compartments. Some studies report that place cells can disambiguate different compartments, while others report that they do not. Furthermore, while numerous studies have examined remapping, there has been little examination of remapping in different subregions of a single environment. Is remapping purely local or do place fields in neighboring, unaffected, regions detect the change? We recorded place cells as rats foraged across a 4-compartment environment and report 3 new findings. First, we find that, unlike studies in which rats foraged in 2 compartments, place fields showed a high degree of spatial repetition with a slight degree of rate-based discrimination. Second, this repetition does not diminish with extended experience. Third, remapping was found to be purely local for both geometric change and contextual change. Our results reveal the limited capacity of the path integrator to drive pattern separation in hippocampal representations, and suggest that doorways may play a privileged role in segmenting the neural representation of space
On Adiabatic Renormalization of Inflationary Perturbations
We discuss the impact of adiabatic renormalization on the power spectrum of
scalar and tensor perturbations from inflation. We show that adiabatic
regularization is ambiguous as it leads to very different results, for
different adiabatic subtraction schemes, both in the range v\equiv k/(aH)
\gsim 0.1 and in the infrared regime. All these schemes agree in the far
ultraviolet, . Therefore, we argue that in the far infrared regime,
, the adiabatic expansion is no longer valid, and the unrenormalized
spectra are the physical, measurable quantities. These findings cast some doubt
on the validity of the adiabatic subtraction at horizon exit, , to
determine the perturbation spectra from inflation which has recently advocated
in the literature.Comment: 7 pages, 3 figures, revtex. New version with more results and
modified plot
Light-cone averaging in cosmology: formalism and applications
We present a general gauge invariant formalism for defining cosmological
averages that are relevant for observations based on light-like signals. Such
averages involve either null hypersurfaces corresponding to a family of past
light-cones or compact surfaces given by their intersection with timelike
hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of
these light-cone averages are given. After introducing some adapted "geodesic
light-cone" coordinates, we give explicit expressions for averaging the
redshift to luminosity-distance relation and the so-called "redshift drift" in
a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected.
Version accepted for publication in JCA
Back-reaction of Cosmological Fluctuations during Power-Law Inflation
We study the renormalized energy-momentum tensor of cosmological scalar
fluctuations during the slow-rollover regime for power-law inflation and find
that it is characterized by a negative energy density at the leading order,
with the same time behaviour as the background energy. The average expansion
rate appears decreased by the back-reaction of the effective energy of
cosmological fluctuations, but this value is comparable with the energy of
background only if inflation starts at a Planckian energy. We also find that,
for this particular model, the first and second order inflaton fluctuations are
decoupled and satisfy the same equation of motion. To conclude, the fourth
order adiabatic expansion for the inflaton scalar field is evaluated for a
general potential V(\phi).Comment: 9 pages, no figures, revtex. Some changes made, comments and
references added, conclusions unchanged, version accepted for pubblication in
Phys. Rev.
Effect of lensing non-Gaussianity on the CMB power spectra
Observed CMB anisotropies are lensed, and the lensed power spectra can be calculated accurately assuming the lensing deflections are Gaussian. However, the lensing deflections are actually slightly non-Gaussian due to both non-linear large-scale structure growth and post-Born corrections. We calculate the leading correction to the lensed CMB power spectra from the non-Gaussianity, which is determined by the lensing bispectrum. The lowest-order result gives ∼0.3% corrections to the BB and EE polarization spectra on small-scales, however we show that the effect on EE is reduced by about a factor of two by higher-order Gaussian lensing smoothing, rendering the total effect safely negligible for the foreseeable future. We give a simple analytic model for the signal expected from skewness of the large-scale lensing field; the effect is similar to a net demagnification and hence a small change in acoustic scale (and therefore out of phase with the dominant lensing smoothing that predominantly affects the peaks and troughs of the power spectrum)
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