593 research outputs found
Quantum Stress Tensor Fluctuations of a Conformal Field and Inflationary Cosmology
We discuss the additional perturbation introduced during inflation by quantum
stress tensor fluctuations of a conformally invariant field such as the photon.
We consider both a kinematical model, which deals only with the expansion
fluctuations of geodesics, and a dynamical model which treats the coupling of
the stress tensor fluctuations to a scalar inflaton. In neither model do we
find any growth at late times, in accordance with a theorem due to Weinberg.
What we find instead is a correction which becomes larger the earlier one
starts inflation. This correction is non-Gaussian and highly scale dependent,
so the absence of such effects from the observed power spectra may imply a
constraint on the total duration of inflation. We discuss different views about
the validity of perturbation theory at very early times during which currently
observable modes are transplanckian.Comment: 31 pages, 1 figure, uses LaTeX2epsilo
Inflation without Slow Roll
We draw attention to the possibility that inflation (i.e. accelerated
expansion) might continue after the end of slow roll, during a period of fast
oscillations of the inflaton field \phi . This phenomenon takes place when a
mild non-convexity inequality is satisfied by the potential V(\phi). The
presence of such a period of \phi-oscillation-driven inflation can
substantially modify reheating scenarios.
In some models the effect of these fast oscillations might be imprinted on
the primordial perturbation spectrum at cosmological scales.Comment: 9 pages, Revtex, psfig, 1 figure, minor modifications, references
adde
The Entropy of the Gravitational Field
We derive a formula for the nonequilibrium entropy of a classical stochastic
field in terms of correlation functions of this field. The formalism is then
applied to define the entropy of gravitational perturbations (both
gravitational waves and density fluctuations). We calculate this entropy in a
specific cosmological model (the inflationary Universe) and find that on scales
of interest in cosmology the entropy in both density perturbations and
gravitational waves exceeds the entropy of statistical fluctuations of the
microwave background. The nonequilibrium entropy discussed here is a measure of
loss of information about the system. We discuss the origin of the entropy in
our cosmological models and compare the definition of entropy in terms of
correlation functions with the microcanonical definition in quantum statistical
mechanics.Comment: 40 pages, uses REVTE
Density Perturbations in the Ekpyrotic Scenario
We study the generation of density perturbations in the ekpyrotic scenario
for the early universe, including gravitational backreaction. We expose
interesting subtleties that apply to both inflationary and ekpyrotic models.
Our analysis includes a detailed proposal of how the perturbations generated in
a contracting phase may be matched across a `bounce' to those in an expanding
hot big bang phase. For the physical conditions relevant to the ekpyrotic
scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum
of energy density perturbations. We find that the perturbation amplitude is
typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file.
Minor typographical and numerical errors corrected, discussion added. This
version to appear in Physical Review
Gravity Waves Signatures from Anisotropic pre-Inflation
We show that expanding or contracting Kasner universes are unstable due to
the amplification of gravitational waves (GW). As an application of this
general relativity effect, we consider a pre-inflationary anisotropic geometry
characterized by a Kasner-like expansion, which is driven dynamically towards
inflation by a scalar field. We investigate the evolution of linear metric
fluctuations around this background, and calculate the amplification of the
long-wavelength GW of a certain polarization during the anisotropic expansion
(this effect is absent for another GW polarization, and for scalar
fluctuations). These GW are superimposed to the usual tensor modes of quantum
origin from inflation, and are potentially observable if the total number of
inflationary e-folds exceeds the minimum required to homogenize the observable
universe only by a small margin. Their contribution to the temperature
anisotropy angular power spectrum decreases with the multipole l as l^(-p),
where p depends on the slope of the initial GW power-spectrum. Constraints on
the long-wavelength GW can be translated into limits on the total duration of
inflation and the initial GW amplitude. The instability of classical GW (and
zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or
contraction) may have other interesting applications. In particular, if GW
become non-linear, they can significantly alter the geometry before the onset
of inflation
Cosmological density perturbations from conformal scalar field: infrared properties and statistical anisotropy
We consider a scenario in which primordial scalar perturbations are generated
when complex conformal scalar field rolls down its negative quartic potential.
Initially, these are the perturbations of the phase of this field; they are
converted into the adiabatic perturbations at a later stage. A potentially
dangerous feature of this scenario is the existence of perturbations in the
radial field direction, which have red power spectrum. We show, however, that
to the linear order in the small parameter - the quartic self-coupling - the
infrared effects are completely harmless, as they can be absorbed into field
redefinition. We then evaluate the statistical anisotropy inherent in the model
due to the existence of the long-ranged radial perturbations. To the linear
order in the quartic self-coupling the statistical anisotropy is free of the
infrared effects. The latter show up at the quadratic order in the
self-coupling and result in the mild (logarithmic) enhancement of the
corresponding contribution to the statistical anisotropy. The resulting
statistical anisotropy is a combination of a larger term which, however, decays
as momentum increases, and a smaller term which is independent of momentum.Comment: 19 pages, 2 figures. Journal version, typos corrected, subsection
adde
The Trans-Planckian Problem of Inflationary Cosmology
In most current models of inflation based on a weakly self-coupled scalar
matter field minimally coupled to gravity, the period of inflation lasts so
long that, at the beginning of the inflationary period, the physical
wavelengths of comoving scales which correspond to the present large-scale
structure of the Universe were smaller than the Planck length. Thus, the usual
computations of the spectrum of fluctuations in these models involve
extrapolating low energy physics (both in the matter and gravitational sector)
into regions where this physics is not applicable. In this paper we demonstrate
that the usual predictions of inflation for the spectrum of cosmological
fluctuations do indeed depend on the hidden assumptions about super-Planck
scale physics. We introduce a class of modified dispersion relations to mimic
possible effects of super-Planck scale physics, and show that in some cases
important deviations from the usual predictions of inflation are obtained. Some
implications of this result for the unification of fundamental physics and
early Universe cosmology are discussed.Comment: 16 pages, 2 figures. One important correction in the Corley/Jacobson
case with b_m>0 and some misprints corrected. Version published in PR
Inflation and de Sitter Thermodynamics
We consider the quasi-de Sitter geometry of the inflationary universe. We
calculate the energy flux of the slowly rolling background scalar field through
the quasi-de Sitter apparent horizon and set it equal to the change of the
entropy (1/4 of the area) multiplied by the temperature, dE=TdS. Remarkably,
this thermodynamic law reproduces the Friedmann equation for the rolling scalar
field. The flux of the slowly rolling field through the horizon of the quasi-de
Sitter geometry is similar to the accretion of a rolling scalar field onto a
black hole, which we also analyze. Next we add inflaton fluctuations which
generate scalar metric perturbations. Metric perturbations result in a
variation of the area entropy. Again, the equation dE=TdS with fluctuations
reproduces the linearized Einstein equations. In this picture as long as the
Einstein equations hold, holography does not put limits on the quantum field
theory during inflation. Due to the accumulating metric perturbations, the
horizon area during inflation randomly wiggles with dispersion increasing with
time. We discuss this in connection with the stochastic decsription of
inflation. We also address the issue of the instability of inflaton
fluctuations in the ``hot tin can'' picture of de Sitter horizon.Comment: 19 pages, 5 figure
Revising the observable consequences of slow-roll inflation
We study the generation of primordial perturbations in a (single-field)
slow-roll inflationary universe. In momentum space, these (Gaussian)
perturbations are characterized by a zero mean and a non-zero variance
. However, in position space the variance diverges in the
ultraviolet. The requirement of a finite variance in position space forces one
to regularize . This can (and should) be achieved by proper
renormalization in an expanding universe in a unique way. This affects the
predicted scalar and tensorial power spectra (evaluated when the modes acquire
classical properties) for wavelengths that today are at observable scales. As a
consequence, the imprint of slow-roll inflation on the CMB anisotropies is
significantly altered. We find a non-trivial change in the consistency
condition that relates the tensor-to-scalar ratio to the spectral indices.
For instance, an exact scale-invariant tensorial power spectrum, , is
now compatible with a non-zero ratio , which is forbidden
by the standard prediction (). The influence of relic gravitational
waves on the CMB may soon come within the range of planned measurements,
offering a non-trivial test of the new predictions.Comment: 24 page
Trans-Planckian Physics from a Nonlinear Dispersion Relation
We study a particular nonlinear dispersion relation -- a
series expansion in the physical wavenumber -- for modeling first-order
corrections in the equation of motion of a test scalar field in a de Sitter
spacetime from trans-Planckian physics in cosmology. Using both a numerical
approach and a semianalytical one, we show that the WKB approximation
previously adopted in the literature should be used with caution, since it
holds only when the comoving wavenumber . We determine the amplitude
and behavior of the corrections on the power spectrum for this test field.
Furthermore, we consider also a more realistic model of inflation, the
power-law model, using only a numerical approach to determine the corrections
on the power spectrum.Comment: 11 pages, 10 figures. Some changes made, comments and references
added, a figure added, typos corrected, conclusions unchanged, version
accepted for pubblication in Phys. Rev.
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