34 research outputs found
de Sitter limit of inflation and nonlinear perturbation theory
We study the fourth order action of the comoving curvature perturbation in an
inflationary universe in order to understand more systematically the de Sitter
limit in nonlinear cosmological perturbation theory. We derive the action of
the curvature perturbation to fourth order in the comoving gauge, and show that
it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter
limit, we then extrapolate to the n'th order action of the comoving curvature
perturbation and discuss the slow-roll order of the n-point correlation
function.Comment: 14 pages, 1 figure; typos corrected and discussion of tensor modes
adde
An Observational Test of Holographic Inflation
Observational consequences of inflationary cosmology in the holographic dual
of the Randall-Sundrum type II braneworld scenario, as motivated by the AdS/CFT
correspondence, are investigated. High energy corrections to the standard
four-dimensional Friedmann equation induce a corresponding modification to the
form of the single-field inflationary consistency equation based on Einstein
gravity. The degree of departure from the standard expression is determined by
the ratio, r, of the primordial tensor and scalar perturbation amplitudes and
the coefficient, c, of the conformal anomaly in the dual gauge theory. It is
found that a necessary condition for detecting such a correction with the next
generation of cosmic microwave background (CMB) polarization experiments is
that r >= 0.06. The bound is tightened to r > 0.3 for values of the central
charge that are compatible with known compactifications of type IIB string
theory as parametrized in terms of F-theory compactification on Calabi-Yau
four-folds. This is close to the present upper bounds inferred from combined
observations of the CMB anisotropy power spectrum and high redshift surveys. We
conclude that if such modifications to the inflationary consistency equation
are to be observable, the gravitational wave background should be detected in
the near future. A further consequence of the non-standard dynamics at high
energies is that the initial state of the universe is a quiescent singularity
with a finite density and pressure.Comment: 7 pages, 2 figures. Uses RevTeX4 LaTeX clas
Non-gaussianity from the inflationary trispectrum
We present an estimate for the non-linear parameter \tau_NL, which measures
the non-gaussianity imprinted in the trispectrum of the comoving curvature
perturbation, \zeta. Our estimate is valid throughout the inflationary era,
until the slow-roll approximation breaks down, and takes into account the
evolution of perturbations on superhorizon scales. We find that the
non-gaussianity is always small if the field values at the end of inflation are
negligible when compared to their values at horizon crossing. Under the same
assumption, we show that in Nflation-type scenarios, where the potential is a
sum of monomials, the non-gaussianity measured by \tau_NL is independent of the
couplings and initial conditions.Comment: 15 pages, uses iopart.sty. Replaced with version accepted by JCAP;
journal reference adde
Large slow-roll corrections to the bispectrum of noncanonical inflation
Nongaussian statistics are a powerful discriminant between inflationary
models, particularly those with noncanonical kinetic terms. Focusing on
theories where the Lagrangian is an arbitrary Lorentz-invariant function of a
scalar field and its first derivatives, we review and extend the calculation of
the observable three-point function. We compute the "next-order" slow-roll
corrections to the bispectrum in closed form, and obtain quantitative estimates
of their magnitude in DBI and power-law k-inflation. In the DBI case our
results enable us to estimate corrections from the shape of the potential and
the warp factor: these can be of order several tens of percent. We track the
possible sources of large logarithms which can spoil ordinary perturbation
theory, and use them to obtain a general formula for the scale dependence of
the bispectrum. Our result satisfies the next-order version of Maldacena's
consistency condition and an equivalent consistency condition for the scale
dependence. We identify a new bispectrum shape available at next-order, which
is similar to a shape encountered in Galileon models. If fNL is sufficiently
large this shape may be independently detectable.Comment: v1: 37 pages, plus tables, figures and appendices. v2: supersedes
version published in JCAP; some clarifications and more detailed comparison
with earlier literature. All results unchanged. v3:improvements to some
plots; text unchange
The inflationary trispectrum
We calculate the trispectrum of the primordial curvature perturbation
generated by an epoch of slow-roll inflation in the early universe, and
demonstrate that the non-gaussian signature imprinted at horizon crossing is
unobservably small, of order tau_NL < r/50, where r < 1 is the tensor-to-scalar
ratio. Therefore any primordial non-gaussianity observed in future microwave
background experiments is likely to have been synthesized by gravitational
effects on superhorizon scales. We discuss the application of Maldacena's
consistency condition to the trispectrum.Comment: 23 pages, 2 diagrams drawn with feynmp.sty, uses iopart.cls. v2,
replaced with version accepted by JCAP. Estimate of maximal tau_NL refined in
Section 5, resulting in smaller numerical value. Sign errors in Eq. (44) and
Eq. (48) corrected. Some minor notational change
Large Nongaussianity from Nonlocal Inflation
We study the possibility of obtaining large nongaussian signatures in the
Cosmic Microwave Background in a general class of single-field nonlocal
hill-top inflation models. We estimate the nonlinearity parameter f_{NL} which
characterizes nongaussianity in such models and show that large nongaussianity
is possible. For the recently proposed p-adic inflation model we find that
f_{NL} ~ 120 when the string coupling is order unity. We show that large
nongaussianity is also possible in a toy model with an action similar to those
which arise in string field theory.Comment: 27 pages, no figures. Added references and some clarifying remark
Generating the curvature perturbation at the end of inflation
The dominant contribution to the primordial curvature perturbation may be
generated at the end of inflation. Taking the end of inflation to be sudden,
formulas are presented for the spectrum, spectral tilt and non-gaussianity.
They are evaluated for a minimal extension of the original hybrid inflation
model.Comment: 5 pages. v3: as it will appear in JCA
Non-gaussianity from the bispectrum in general multiple field inflation
We study the non-gaussianity from the bispectrum in multi-field inflation
models with a general kinetic term. The models include the multi-field
K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special
cases. We find that, in general, the sound speeds for the adiabatic and entropy
perturbations are different and they can be smaller than 1. Then the
non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a
special case where both sound speeds are the same due to a special form of the
kinetic term. We derive the exact second and third order actions including
metric perturbations. In the small sound speed limit and at leading order in
the slow-roll expansion, we derive the three point function for the curvature
perturbation which depends on both adiabatic and entropy perturbations. The
contribution from the entropy perturbations has a different momentum dependence
if the sound speed for the entropy perturbations is different from the
adiabatic one, which provides a possibility to distinguish the multi-field
models from single field models. On the other hand, in the multi-field DBI
case, the contribution from the entropy perturbations has the same momentum
dependence as the pure adiabatic contributions and it only changes the
amplitude of the three point function. This could help to ease the constraints
on the DBI-inflation models.Comment: 16 pages, no figur
Non-Gaussian perturbations from multi-field inflation
We show how the primordial bispectrum of density perturbations from inflation
may be characterised in terms of manifestly gauge-invariant cosmological
perturbations at second order. The primordial metric perturbation, zeta,
describing the perturbed expansion of uniform-density hypersurfaces on large
scales is related to scalar field perturbations on unperturbed (spatially-flat)
hypersurfaces at first- and second-order. The bispectrum of the metric
perturbation is thus composed of (i) a local contribution due to the
second-order gauge-transformation, and (ii) the instrinsic bispectrum of the
field perturbations on spatially flat hypersurfaces. We generalise previous
results to allow for scale-dependence of the scalar field power spectra and
correlations that can develop between fields on super-Hubble scales.Comment: 11 pages, RevTex; minor changes to text; conclusions unchanged;
version to appear in JCA
Degeneracy of consistency equations in braneworld inflation
In a Randall-Sundrum type II inflationary scenario we compute perturbation
amplitudes and spectral indices up to next-to-lowest order in the slow-roll
parameters, starting from the well-known lowest-order result for a de Sitter
brane. Using two different prescriptions for the tensor amplitude, we show that
the braneworld consistency equations are not degenerate with respect to the
standard relations and we explore their observational consequences. It is then
shown that, while the degeneracy between high- and low-energy regimes can come
from suitable values of the cosmological observables, exact functional matching
between consistency expressions is plausibly discarded. This result is then
extended to the Gauss-Bonnet case.Comment: 16 pages, 3 figures. v3: major revision. Changed title, updated
references, rearranged material, new prescription for the tensor spectrum,
new figures, extended and more robust conclusion