224 research outputs found
Local non-Gaussianity from rapidly varying sound speeds
We study the effect of non-trivial sound speeds on local-type non-Gaussianity
during multiple-field inflation. To this end, we consider a model of
multiple-field DBI and use the deltaN formalism to track the super-horizon
evolution of perturbations. By adopting a sum separable Hubble parameter we
derive analytic expressions for the relevant quantities in the two-field case,
valid beyond slow variation. We find that non-trivial sound speeds can, in
principle, curve the trajectory in such a way that significant local-type
non-Gaussianity is produced. Deviations from slow variation, such as rapidly
varying sound speeds, enhance this effect. To illustrate our results we
consider two-field inflation in the tip regions of two warped throats and find
large local-type non-Gaussianity produced towards the end of the inflationary
process.Comment: 30 pages, 7 figures; typos corrected, references added, accepted for
publication in JCA
Inflationary perturbation theory is geometrical optics in phase space
A pressing problem in comparing inflationary models with observation is the
accurate calculation of correlation functions. One approach is to evolve them
using ordinary differential equations ("transport equations"), analogous to the
Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this
approach to the complete set of momentum space correlation functions. A formal
solution can be obtained using raytracing techniques adapted from geometrical
optics. We reformulate inflationary perturbation theory in this language, and
show that raytracing reproduces the familiar "delta N" Taylor expansion. Our
method produces ordinary differential equations which allow the Taylor
coefficients to be computed efficiently. We use raytracing methods to express
the gauge transformation between field fluctuations and the curvature
perturbation, zeta, in geometrical terms. Using these results we give a compact
expression for the nonlinear gauge-transform part of fNL in terms of the
principal curvatures of uniform energy-density hypersurfaces in field space.Comment: 22 pages, plus bibliography and appendix. v2: minor changes, matches
version published in JCA
Inflationary signatures of single-field models beyond slow-roll
If the expansion of the early Universe was not close to de Sitter, the
statistical imprints of the primordial density perturbation on the cosmic
microwave background can be quite different from those derived in slow-roll
inflation. In this paper we study the inflationary signatures of all
single-field models which are free of ghost-like instabilities. We allow for a
rapid change of the Hubble parameter and the speed of sound of scalar
fluctuations, in a way that is compatible with a nearly scale-invariant
spectrum of perturbations, as supported by current cosmological observations.
Our results rely on the scale-invariant approximation, which is different from
the standard slow-roll approximation. We obtain the propagator of scalar
fluctuations and compute the bispectrum, keeping next-order corrections
proportional to the deviation of the spectral index from unity. These theories
offer an explicit example where the shape and scale-dependences of the
bispectrum are highly non-trivial whenever slow-roll is not a good
approximation.Comment: v1: 36 pages, including tables, appendices and references. v2:
abstract improved, references added, minor clarifications throughout the
text; matches version published in JCA
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
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