230 research outputs found
A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll
We study multifield contributions to the scalar power spectrum in an ensemble
of six-field inflationary models obtained in string theory. We identify
examples in which inflation occurs by chance, near an approximate inflection
point, and we compute the primordial perturbations numerically, both exactly
and using an array of truncated models. The scalar mass spectrum and the number
of fluctuating fields are accurately described by a simple random matrix model.
During the approach to the inflection point, bending trajectories and
violations of slow roll are commonplace, and 'many-field' effects, in which
three or more fields influence the perturbations, are often important. However,
in a large fraction of models consistent with constraints on the tilt the
signatures of multifield evolution occur on unobservably large scales. Our
scenario is a concrete microphysical realization of quasi-single-field
inflation, with scalar masses of order , but the cubic and quartic couplings
are typically too small to produce detectable non-Gaussianity. We argue that
our results are characteristic of a broader class of models arising from
multifield potentials that are natural in the Wilsonian sense.Comment: 39 pages, 17 figures. References added. Matches version published in
JCA
On the redundancy of operators and the bispectrum in the most general second-order scalar-tensor theory
In this short note we explain how to use the linear equation of motions to
simplify the third-order action for the cosmological fluctuations. No field
redefinition is needed in this exact procedure which considerably limits the
range of independent cubic operators, and hence of possible shapes of the
primordial bispectrum. We demonstrate this in the context of the most general
single-field scalar-tensor theory with second-order equations of motion, whose
third-order action has been calculated recently in arXiv:1107.2642 and
1107.3917. In particular, we show that the three cubic operators initially
pointed out in these works as new compared to k-inflation can actually be
expressed in terms of standard k-inflationary operators.Comment: 9 pages. Wordings changed; matches version published in JCA
A general proof of the equivalence between the \delta N and covariant formalisms
Recently, the equivalence between the \delta N and covariant formalisms has
been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity
in their proof. They showed that the evolution equation of the curvature
covector in the covariant formalism on uniform energy density slicings
coincides with that of the curvature perturbation in the \delta N formalism
assuming the coincidence of uniform energy and uniform expansion (Hubble)
slicings, which is the case on superhorizon scales in Einstein gravity. In this
short note, we explicitly show the equivalence between the \delta N and
covariant formalisms without specifying the slicing condition and the
associated slicing coincidence, in other words, regardless of the gravity
theory.Comment: 7 pages,a reference added, to be published in EP
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
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
Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation
We study a cosmological scenario in which the DBI action governing the motion
of a D3-brane in a higher-dimensional spacetime is supplemented with an induced
gravity term. The latter reduces to the quartic Galileon Lagrangian when the
motion of the brane is non-relativistic and we show that it tends to violate
the null energy condition and to render cosmological fluctuations ghosts. There
nonetheless exists an interesting parameter space in which a stable phase of
quasi-exponential expansion can be achieved while the induced gravity leaves
non trivial imprints. We derive the exact second-order action governing the
dynamics of linear perturbations and we show that it can be simply understood
through a bimetric perspective. In the relativistic regime, we also calculate
the dominant contribution to the primordial bispectrum and demonstrate that
large non-Gaussianities of orthogonal shape can be generated, for the first
time in a concrete model. More generally, we find that the sign and the shape
of the bispectrum offer powerful diagnostics of the precise strength of the
induced gravity.Comment: 34 pages including 9 figures, plus appendices and bibliography.
Wordings changed and references added; matches version published in JCA
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
Combined local and equilateral non-Gaussianities from multifield DBI inflation
We study multifield aspects of Dirac-Born-Infeld (DBI) inflation. More
specifically, we consider an inflationary phase driven by the radial motion of
a D-brane in a conical throat and determine how the D-brane fluctuations in the
angular directions can be converted into curvature perturbations when the
tachyonic instability arises at the end of inflation. The simultaneous presence
of multiple fields and non-standard kinetic terms gives both local and
equilateral shapes for non-Gaussianities in the bispectrum. We also study the
trispectrum, pointing out that it acquires a particular momentum dependent
component whose amplitude is given by . We show that
this relation is valid in every multifield DBI model, in particular for any
brane trajectory, and thus constitutes an interesting observational signature
of such scenarios.Comment: 38 pages, 11 figures. Typos corrected; references added. This version
matches the one in press by JCA
Transport equations for the inflationary trispectrum
We use transport techniques to calculate the trispectrum produced in
multiple-field inflationary models with canonical kinetic terms. Our method
allows the time evolution of the local trispectrum parameters, tauNL and gNL,
to be tracked throughout the inflationary phase. We illustrate our approach
using examples. We give a simplified method to calculate the superhorizon part
of the relation between field fluctuations on spatially flat hypersurfaces and
the curvature perturbation on uniform density slices, and obtain its
third-order part for the first time. We clarify how the 'backwards' formalism
of Yokoyama et al. relates to our analysis and other recent work. We supply
explicit formulae which enable each inflationary observable to be computed in
any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published
in JCAP; typo fixed in Eq. (54
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