55 research outputs found
Nonlinear perturbations of cosmological scalar fields
We present a covariant formalism to study nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential equations governing the evolution of these two covectors, as well as the evolution equation for the covector associated to the curvature perturbation. The form of these equations is very close to the analogous equations obtained in the linear theory but our equations are fully nonlinear and exact. As an application of our formalism, we expand these equations at second order in the perturbations. On large scales, we obtain a closed system of coupled scalar equations giving the evolution of the second-order adiabatic and entropy perturbations in terms of the first-order perturbations. These equations in general contain a nonlocal term which, however, rapidly decays in an expanding universe
Non-linear isocurvature perturbations and non-Gaussianities
We study non-linear primordial adiabatic and isocurvature perturbations and
their non-Gaussianity. After giving a general formulation in the context of an
extended delta N-formalism, we analyse in detail two illustrative examples. The
first is a mixed curvaton-inflaton scenario in which fluctuations of both the
inflaton and a curvaton (a light isocurvature field during inflation)
contribute to the primordial density perturbation. The second example is that
of double inflation involving two decoupled massive scalar fields during
inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum
of primordial isocurvature perturbations may be large and comparable to the
bispectrum of adiabatic curvature perturbations.Comment: 24 pages, typos corrected, references adde
From heaviness to lightness during inflation
We study the quantum fluctuations of scalar fields with a variable effective
mass during an inflationary phase. We consider the situation where the
effective mass depends on a background scalar field, which evolves during
inflation from being frozen into a damped oscillatory phase when the Hubble
parameter decreases below its mass. We find power spectra with suppressed
amplitude on large scales, similar to the standard massless spectrum on small
scales, and affected by modulations on intermediate scales. We stress the
analogies and differences with the parametric resonance in the preheating
scenario. We also discuss some potentially observable consequences when the
scalar field behaves like a curvaton.Comment: 23 pages; 8 figures; published versio
Evolution of fNL to the adiabatic limit
We study inflationary perturbations in multiple-field models, for which zeta
typically evolves until all isocurvature modes decay--the "adiabatic limit". We
use numerical methods to explore the sensitivity of the nonlinear parameter fNL
to the process by which this limit is achieved, finding an appreciable
dependence on model-specific data such as the time at which slow-roll breaks
down or the timescale of reheating. In models with a sum-separable potential
where the isocurvature modes decay before the end of the slow-roll phase we
give an analytic criterion for the asymptotic value of fNL to be large. Other
examples can be constructed using a waterfall field to terminate inflation
while fNL is transiently large, caused by descent from a ridge or convergence
into a valley. We show that these two types of evolution are distinguished by
the sign of the bispectrum, and give approximate expressions for the peak fNL.Comment: v1: 25 pages, plus Appendix and bibliography, 6 figures. v2: minor
edits to match published version 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
Lectures on inflation and cosmological perturbations
The purpose of these lectures is to give a pedagogical introduction to
inflation and the production of primordial perturbations, as well as a review
of some of the latest developments in this domain. After a short introduction,
we review the main principles of the Hot Big Bang model, as well as its
limitations. This motivates the study of cosmological inflation induced by a
slow-rolling scalar field. We then turn to the analysis of cosmological
perturbations, and explain how the vacuum quantum fluctuations are amplified
during an inflationary phase. The next step consists in relating the
perturbations generated during inflation to the perturbations of the
cosmological fluid in the radiation dominated phase. The final part of these
lectures gives a review of more general models of inflation, involving multiple
fields or non standard kinetic terms. Although more complicated, these models
are usually motivated by high energy physics and they can lead to specific
signatures that are not expected in the simplest models of inflation. After
introducing a very general formalism to describe perturbations in multi-field
models with arbitrary kinetic terms, several interesting cases are presented.
We also stress the role of entropy perturbations in the context of multi-field
models. Finally, we discuss in detail the non-Gaussianities of the primordial
perturbations and some models that could produce a detectable level of
non-Gaussianities.Comment: 56 pages, 5 figures; Lectures given at the Second TRR33 Winter School
on cosmology, Passo del Tonale (Italy), December 200
The Effective Field Theory of Multifield Inflation
We generalize the Effective Field Theory of Inflation to include additional
light scalar degrees of freedom that are in their vacuum at the time the modes
of interest are crossing the horizon. In order to make the scalars light in a
natural way we consider the case where they are the Goldstone bosons of a
global symmetry group or are partially protected by an approximate
supersymmetry. We write the most general Lagrangian that couples the scalar
mode associated to the breaking of time translation during inflation to the
additional light scalar fields. This Lagrangian is constrained by
diffeomorphism invariance and the additional symmetries that keep the new
scalars light. This Lagrangian describes the fluctuations around the time of
horizon crossing and it is supplemented with a general parameterization
describing how the additional fluctuating fields can affect cosmological
perturbations. We find that multifield inflation can reproduce the
non-Gaussianities that can be generated in single field inflation but can also
give rise to new kinds of non-Gaussianities. We find several new three-point
function shapes. We show that in multifield inflation it is possible to
naturally suppress the three-point function making the four-point function the
leading source of detectable non-Gaussianities. We find that under certain
circumstances, i.e. if specific shapes of non-Gaussianities are detected in the
data, one could distinguish between single and multifield inflation and
sometimes even among the various mechanisms that kept the additional fields
light.Comment: 62 pages, 1 figure; v2: JHEP published version, minor corrections,
comments and references adde
Nonlinear superhorizon perturbations of non-canonical scalar field
We develop a theory of non-linear cosmological perturbations at superhorizon
scales for a scalar field with a Lagrangian of the form , where
and is the scalar field. We
employ the ADM formalism and the spatial gradient expansion approach to obtain
general solutions valid up to the second order in the gradient expansion. This
formulation can be applied to, for example, DBI inflation models to investigate
superhorizon evolution of non-Gaussianities. With slight modification, we also
obtain general solutions valid up to the same order for a perfect fluid with a
general equation of state .Comment: 14 page
Scale dependence of in N-flation
Adopting the horizon-crossing approximation, we derive the spectral index of
in general N-flation model. Axion N-flation model is taken as a
typical model for generating a large which characterizes the size of
local form bispectrum. We find that its tilt is negligibly small
when all inflatons have the same potential, but a negative detectable
can be achieved in the axion N-flation with different decay
constants for different inflatons. The measurement of can be used
to support or falsify the axion N-flation in the near future.Comment: 15 pages, 2 figures; a subsection with detectable scale dependence of
f_NL added; more discussions added and version accepted for publication in
JCA
Local non-Gaussianity from inflation
The non-Gaussian distribution of primordial perturbations has the potential
to reveal the physical processes at work in the very early Universe. Local
models provide a well-defined class of non-Gaussian distributions that arise
naturally from the non-linear evolution of density perturbations on
super-Hubble scales starting from Gaussian field fluctuations during inflation.
I describe the delta-N formalism used to calculate the primordial density
perturbation on large scales and then review several models for the origin of
local primordial non-Gaussianity, including the cuvaton, modulated reheating
and ekpyrotic scenarios. I include an appendix with a table of sign conventions
used in specific papers.Comment: 21 pages, 1 figure, invited review to appear in Classical and Quantum
Gravity special issue on non-linear and non-Gaussian cosmological
perturbation
- …