29 research outputs found
Trispectrum estimator in equilateral type non-Gaussian models
We investigate an estimator to measure the primordial trispectrum in
equilateral type non-Gaussian models such as k-inflation, single field DBI
inflation and multi-field DBI inflation models from Cosmic Microwave Background
(CMB) anisotropies. The shape of the trispectrum whose amplitude is not
constrained by the bispectrum in the context of effective theory of inflation
and k-inflation is known to admit a separable form of the estimator for CMB
anisotropies. We show that this shape is correlated with the full
quantum trispectrum in single field DBI inflation, while it is
correlated with the one in multi-field DBI inflation when curvature
perturbation is originated from purely entropic contribution. This suggests
that , the amplitude of this particular shape, provides a
reasonable measure of the non-Gaussianity from the trispectrum in equilateral
non-Gaussian models. We relate model parameters such as the sound speed,
and the transfer coefficient from entropy perturbations to the curvature
perturbation, with , which enables us
to constrain model parameters in these models once is
measured in WMAP and Planck.Comment: 19 pages, 4 figures. Accepted for publication in JCA
On the full quantum trispectrum in multi-field DBI inflation
We compute the leading order connected four-point function of the primordial
curvature perturbation coming from the four-point function of the fields in
multi-field DBI inflation models. We confirm that the consistency relations in
the squeezed limit and in the counter-collinear limit hold as in single field
models thanks to special properties of the DBI action. We also study the
momentum dependence of the trispectra coming from the adiabatic, mixed and
purely entropic contributions separately and we find that they have different
momentum dependence. This means that if the amount of the transfer from the
entropy perturbations to the curvature perturbation is significantly large, the
trispectrum can distinguish multi-field DBI inflation models from single field
DBI inflation models. A large amount of transfer
suppresses the tensor to scalar ratio and the
amplitude of the bispectrum and
so it can ease the severe observational constraints on the DBI inflation model
based on string theory. On the other hand, it enhances the amplitude of the
trispectrum for a
given amplitude of the bispectrum.Comment: 22 pages, 10 figures, minor corrections, references are added,
published version in PR
Primordial non-Gaussianity from the DBI Galileons
We study primordial fluctuations generated during inflation in a class of
models motivated by the DBI Galileons, which are extensions of the DBI action
that yield second order field equations. This class of models generalises the
DBI Galileons in a similar way with K-inflation. We calculate the primordial
non-Gaussianity from the bispectrum of the curvature perturbations at leading
order in the slow-varying approximations. We show that the estimator for the
equilateral-type non-Gaussianity, , can be applied to
measure the amplitude of the primordial bispectrum even in the presence of the
Galileon-like term although it gives a slightly different momentum dependence
from K-inflation models. For the DBI Galileons, we find and large primordial non-Gaussianities can be
obtained when is much smaller than 1 as in the usual DBI inflation. In
G-inflation models, where a de Sitter solution is obtained without any
potentials, the non-linear parameter is given by where is the tensor to scalar ratio, giving a stringent
constraint on the model.Comment: 10 pages, 1 figure. Accepted for publication in PR
On the full trispectrum in single field DBI-inflation
We compute the tree-level connected four-point function of the primordial
curvature perturbation for a fairly general minimally coupled single field
inflationary model, where the inflaton's Lagrangian is a general function of
the scalar field and its first derivatives. This model includes K-inflation and
DBI-inflation as particular cases. We show that, at the leading order in the
slow-roll expansion and in the small sound speed limit, there are two important
tree-level diagrams for the trispectrum. One is a diagram where a scalar mode
is exchanged and the other is a diagram where the interaction occurs at a
point, i.e. a contact interaction diagram. The scalar exchange contribution is
comparable to the contact interaction contribution. For the DBI-inflation
model, in the so-called equilateral configuration, the scalar exchange
trispectrum is maximized when the angles between the four momentum vectors are
equal and in this case the amplitude of the trispectrum from the scalar
exchange is one order of magnitude higher than the contact interaction
trispectrum.Comment: 16 pages, 6 figure
Lorentz boost and non-Gaussianity in multi-field DBI-inflation
We show that higher-order actions for cosmological perturbations in the
multi-field DBI-inflation model are obtained by a Lorentz boost from the rest
frame of the brane to the frame where the brane is moving. We confirm that this
simple method provides the same third- and fourth- order actions at leading
order in slow-roll and in the small sound speed limit as those obtained by the
usual ADM formalism. As an application, we compute the leading order connected
four-point function of the primordial curvature perturbation coming from the
intrinsic fourth-order contact interaction in the multi-field DBI-inflation
model. At the third order, the interaction Hamiltonian arises purely by the
boost from the second-order action in the rest frame of the brane. The boost
acts on the adiabatic and entropy modes in the same way thus there exists a
symmetry between the adiabatic and entropy modes. But at fourth order this
symmetry is broken due to the intrinsic fourth-order action in the rest frame
and the difference between the Lagrangian and the interaction Hamiltonian.
Therefore, contrary to the three-point function, the momentum dependence of the
purely adiabatic component and the components including the entropic
contributions are different in the four-point function. This suggests that the
trispectrum can distinguish the multi-field DBI-inflation model from the single
field DBI-inflation model.Comment: 11 pages, no figures, v2:references added. Accepted for publication
in PR
Trispectrum estimation in various models of equilateral type non-Gaussianity
We calculate the shape correlations between trispectra in various equilateral
non-Gaussian models, including DBI inflation, ghost inflation and Lifshitz
scalars, using the full trispectrum as well as the reduced trispectum. We find
that most theoretical models are distinguishable from the shapes of primordial
trispectra except for several exceptions where it is difficult to discriminate
between the models, such as single field DBI inflation and a Lifshitz scalar
model. We introduce an estimator for the amplitude of the trispectrum, and relate it to model parameters in various models. Using
constraints on from WMAP5, we give constraints on the
model parameters.Comment: 16 pages, 3 figures; (v2) minor revisions, reference added; (v3)
typos in Tables correcte
Non-Gaussianities in multi-field DBI inflation with a waterfall phase transition
We study multi-field DBI inflation models with a waterfall phase transition.
This transition happens for a D3 brane moving in the warped conifold if there
is an instability along angular directions. The transition converts the angular
perturbations into the curvature perturbation. Thanks to this conversion,
multi-field models can evade the stringent constraints that strongly disfavour
single field ultra-violet DBI inflation models in string theory. We explicitly
demonstrate that our model satisfies current observational constraints on the
spectral index and equilateral non-Gaussianity as well as the bound on the
tensor to scalar ratio imposed in string theory models. In addition we show
that large local type non-Gaussianity is generated together with equilateral
non-Gaussianity in this model.Comment: 18 pages, 6 figure
Slow-roll corrections to inflaton fluctuations on a brane
Quantum fluctuations of an inflaton field, slow-rolling during inflation are
coupled to metric fluctuations. In conventional four dimensional cosmology one
can calculate the effect of scalar metric perturbations as slow-roll
corrections to the evolution of a massless free field in de Sitter spacetime.
This gives the well-known first-order corrections to the field perturbations
after horizon-exit. If inflaton fluctuations on a four dimensional brane
embedded in a five dimensional bulk spacetime are studied to first-order in
slow-roll then we recover the usual conserved curvature perturbation on
super-horizon scales. But on small scales, at high energies, we find that the
coupling to the bulk metric perturbations cannot be neglected, leading to a
modified amplitude of vacuum oscillations on small scales. This is a large
effect which casts doubt on the reliability of the usual calculation of
inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure
Slow-roll corrections to inflaton fluctuations on a brane
Quantum fluctuations of an inflaton field, slow-rolling during inflation are
coupled to metric fluctuations. In conventional four dimensional cosmology one
can calculate the effect of scalar metric perturbations as slow-roll
corrections to the evolution of a massless free field in de Sitter spacetime.
This gives the well-known first-order corrections to the field perturbations
after horizon-exit. If inflaton fluctuations on a four dimensional brane
embedded in a five dimensional bulk spacetime are studied to first-order in
slow-roll then we recover the usual conserved curvature perturbation on
super-horizon scales. But on small scales, at high energies, we find that the
coupling to the bulk metric perturbations cannot be neglected, leading to a
modified amplitude of vacuum oscillations on small scales. This is a large
effect which casts doubt on the reliability of the usual calculation of
inflaton fluctuations on the brane neglecting their gravitational coupling.Comment: 18 pages, 4 figure