35 research outputs found

### Strong scale dependent bispectrum in the Starobinsky model of inflation

We compute analytically the dominant contribution to the tree-level
bispectrum in the Starobinsky model of inflation. In this model, the potential
is vacuum energy dominated but contains a subdominant linear term which changes
the slope abruptly at a point. We show that on large scales compared with the
transition scale $k_0$ and in the equilateral limit the analogue of the
non-linearity parameter scales as $(k/k_0)^2$, that is its amplitude decays for
larger and larger scales until it becomes subdominant with respect to the usual
slow-roll suppressed corrections. On small scales we show that the
non-linearity parameter oscillates with angular frequency given by $3/k_0$ and
its amplitude grows linearly towards smaller scales and can be large depending
on the model parameters. We also compare our results with previous results in
the literature.Comment: 14 pages, 3 figure

### On the four-dimensional effective theories in brane-worlds

Models with extra dimensions have attracted much interest recently because
they may provide the solution for long standing problems in physics. One
interesting and very attractive idea is that our visible universe is confined
to a four-dimensional hypersurface in a higher-dimensional spacetime. This
membrane like universe was dubbed brane-world. The main goal of this thesis is
the study of the four-dimensional (4D) effective theories and their
observational consequences in the brane-world universe. After introducing the
brane-world idea with some detail we shall use the gradient expansion method to
obtain the 4D effective theories of gravity for several higher-dimensional
theories with different numbers of extra-dimensions. In the second half of the
thesis, after introducing the concept of brane-inflation we will focus on some
observational consequences of these low energy effective theories. In
particular, the last two chapters before the conclusion are devoted to the
study of non-Gaussianities in general models of inflation.Comment: 176 pages, 8 figures; PhD thesis, Institute of Cosmology and
Gravitation, University of Portsmout

### 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 $T_{\mathcal{RS}} \gg 1$
suppresses the tensor to scalar ratio $r \propto T_{\mathcal{RS}}^{-2}$ and the
amplitude of the bispectrum $f_{NL}^{equi} \propto T_{\mathcal{RS}}^{-2}$ 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 $\tau_{NL}^{equi} \propto T_{\mathcal{RS}}^2 f_{NL}^{equi 2}$ for a
given amplitude of the bispectrum.Comment: 22 pages, 10 figures, minor corrections, references are added,
published version in PR

### On the Trispectrum of Galileon Inflation

We present a detailed study of the trispectrum of the curvature perturbation
generated within a stable, well defined and predictive theory which comprises
an inflationary phase. In this model the usual shift symmetry is enhanced up to
the so-called Galileon symmetry. The appeal of this type of theories rests on
being unitary and stable under quantum corrections. Furthermore, in the
specific model under consideration here, these properties have been shown to
approximately hold in realistic scenarios which account for curved spacetime
and the coupling with gravity. In the literature, the analysis of the
bispectrum of the curvature perturbation for this theory revealed non-Gaussian
features which are shared by a number of inflationary models, including stable
ones. It is therefore both timely and useful to investigate further and turn to
observables such as the trispectrum. We find that, in a number of specific
momenta configurations, the trispectrum shape-functions present strikingly
different features as compared to, for example, the entire class of the
so-called $P(X,\phi)$ inflationary models.Comment: 39 pages, 14 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

### 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

### CMB statistical anisotropy from noncommutative gravitational waves

Primordial statistical anisotropy is a key indicator to investigate early
Universe models and has been probed by the cosmic microwave background (CMB)
anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated
from anisotropic gravitational waves, parametrised by $P_h({\bf k}) =
P_h^{(0)}(k) [ 1 + \sum_{LM} f_L(k) g_{LM} Y_{LM} (\hat{\bf k}) ]$, where
$P_h^{(0)}(k)$ is the usual scale-invariant power spectrum. Such anisotropic
tensor fluctuations may arise from an inflationary model with noncommutativity
of fields. It is verified that in this model, an isotropic component and a
quadrupole asymmetry with $f_0(k) = f_2(k) \propto k^{-2}$ are created and
hence highly red-tilted off-diagonal components arise in the CMB power spectra,
namely $\ell_2 = \ell_1 \pm 2$ in $TT$, $TE$, $EE$ and $BB$, and $\ell_2 =
\ell_1 \pm 1$ in $TB$ and $EB$. We find that B-mode polarisation is more
sensitive to such signals than temperature and E-mode polarisation due to the
smallness of large-scale cosmic variance and we can potentially measure $g_{00}
= 30$ and $g_{2M} = 58$ at 68% CL in a cosmic-variance-limited experiment. Such
a level of signal may be measured in a PRISM like experiment, while the
instrumental noise contaminates it in the $Planck$ experiment. These results
imply that it is impossible to measure the noncommutative parameter if it is
small enough for the perturbative treatment to be valid. Our formalism and
methodology for dealing with the CMB tensor statistical anisotropy are general
and straightforwardly applicable to other early Universe models.Comment: 13 pages, 2 figures, 1 table. Accepted for publication in JCA