Abstract: The simple m(2)phi(2) potential as an inflationary model is coming under increasing tension with limits on the tensor-to-scalar ratio r and measurements of the scalar spectral index n(s). Cubic Galileon interactions in the context of the Horndeski action can potentially reconcile the observables. However, we show that this cannot be achieved with only a constant Galileon mass scale because the interactions turn off too slowly, leading also to gradient instabilities after inflation ends. Allowing for a more rapid transition can reconcile the observables but moderately breaks the slow-roll approximation leading to a relatively large and negative running of the tilt alpha(s) that can be of order n(s) – 1. We show that the observables on CMB and large scale structure scales can be predicted accurately using the optimized slow-roll approach instead of the traditional slow-roll expansion. Upper limits on vertical bar alpha(s)vertical bar place a lower bound of r greater than or similar to 0.005 and, conversely, a given r places a lower bound on vertical bar alpha(s)vertical bar, both of which are potentially observable with next generation CMB and large scale structure surveys.

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.