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