Abstract: We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t -> (t) over tilde (t), or equivalently under field redefinition of the inflaton phi -> (phi) over tilde(phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k(L) in the squeezed limit k(L) -> 0 compared to the local shape.

Abstract: Context. The existence of a maximum correlation angle (theta(max) & 60 greater than or similar to degrees) in the two-point angular temperature correlations of cosmic microwave background (CMB) radiation, measured by WMAP and Planck, stands in sharp contrast to the prediction of standard inflationary cosmology, in which the correlations should extend across the full sky (i.e., 180 degrees). The introduction of a hard lower cuto ff (k(min)) in the primordial power spectrum, however, leads naturally to the existence of theta(max). Among other cosmological anomalies detected in these data, an apparent dominance of odd-over-even parity multipoles has been seen in the angular power spectrum of the CMB. This feature, however, may simply be due to observational contamination in certain regions of the sky. Aims. In attempting to provide a more detailed assessment of whether this odd-over-even asymmetry is intrinsic to the CMB, we therefore proceed in this paper, first, to examine whether this odd-even parity imbalance also manifests itself in the angular correlation function and, second, to examine in detail the interplay between the presence of theta(max) and this observed anomaly. Methods. We employed several parity statistics and recalculated the angular correlation function for di fferent values of the cuto ff kmin in order to optimize the fit to the di fferent Planck 2018 data. Results. We find a phenomenological connection between these features in the data, concluding that both must be considered together in order to optimize the theoretical fit to the Planck 2018 data. Conclusions. This outcome is independent of whether the parity imbalance is intrinsic to the CMB, but if it is, the odd-over-even asymmetry would clearly point to the emergence of new physics.

Abstract: We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.