No Arabic abstract
Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite past and quantum scale symmetry is realized. The cosmological evolution is dominantly described by the slow increase of a scalar field which sets the scale of all masses. We construct the primordial flat frame for standard models of inflation as Starobinsky inflation or chaotic inflation. In particular, we discuss the evolution of inhomogeneous solutions in the neighborhood of the homogeneous isotropic background solution and their relation to the observable primordial fluctuation spectrum. If the propagators for the graviton and scalar field remain regular, our observed inhomogeneous Universe can be extrapolated back to the infinite past in physical time. In this case there is no physical big-bang singularity -- the latter reflects only a singular choice of ``field coordinates. Independently of the issue of singularity the primordial flat frame offers a new view on the physical properties of the inflationary universe.
We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter $c_s$ during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, provided the sound-speed parameter is confined in a rather narrow range of values, $0.003 < c_s < 0.01$.
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency range with assumption that the phase transition between two consecutive regimes to be abrupt during evolution of the Universe. The suppression of energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of energy spectrum of the primordial gravitational waves, we study an existence of the early phase transition during inflation for the space-condensate inflation model.
We investigate the scalar and the tensor perturbations of the $varphi^2$ inflation model in the strong-gravity limit of Eddington-inspired Born-Infeld (EiBI) theory. In order to consider the strong EiBI-gravity effect, we take the value of $kappa$ large, where $kappa$ is the EiBI theory parameter. The energy density of the Universe at the early stage is very high, and the Universe is in a strong-gravity regime. Therefore, the perturbation feature is not altered from what was investigated earlier. At the attractor inflationary stage, however, the feature is changed in the strong EiBI-gravity limit. The correction to the scalar perturbation in this limit comes mainly via the background matter field, while that to the tensor perturbation comes directly from the gravity ($kappa$) effect. The change in the value of the scalar spectrum is little compared with that in the weak EiBI-gravity limit, or in GR. The form of the tensor spectrum is the same with that in the weak limit, but the value of the spectrum can be suppressed down to zero in the strong limit. Therefore, the resulting tensor-to-scalar ratio can also be suppressed in the same way, which makes $varphi^2$ model in EiBI theory viable.
In the present paper, we study the inflationary phenomenology of a $k$-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term $omega X^gamma$ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation $ddotxi=Hdotxi$ for the scalar coupling function $xi (phi)$. As a result, the scalar functions of the theory are revealed to be interconnected and by assuming a specific form for one of them, specifies immediately the other. Here, we shall assume that the scalar potential is directly derivable from the equations of motion, once the Gauss-Bonnet coupling is appropriately chosen, but obviously the opposite is feasible as well. As a result, each term entering the equations of motion, can be written in terms of the scalar field and a relatively tractable phenomenology is produced. For quadratic kinetic terms, the resulting scalar potential is quite elegant functionally. Different exponents, which lead to either a more perplexed solution for the scalar potential, are still a possibility which was not further studied. We also discuss in brief the non-Gaussianities issue under the slow-roll and constant-roll conditions holding true, and we demonstrate that the predicted amount of non-Gaussianities is significantly enhanced in comparison to the $k$-inflation free Einstein-Gauss-Bonnet theory.
The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $eta_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.