In this work, we analyze two possible alternative and model-independent approaches to describe the inflationary period. The first one assumes a general equation of state during inflation due to Mukhanov, while the second one is based on the slow-roll
hierarchy suggested by Hoffman and Turner. We find that, remarkably, the two approaches are equivalent from the observational viewpoint, as they single out the same areas in the parameter space, and agree with the inflationary attractors where successful inflation occurs. Rephrased in terms of the familiar picture of a slowly rolling, canonically normalized scalar field, the resulting inflaton excursions in these two approaches are almost identical. Furthermore, once the Galactic dust polarization data from Planck are included in the numerical fits, inflaton excursions can safely take sub-Planckian values.
Effective field theory is a powerful organizing principle that allows to describe physics below a certain scale model-independently. Above that energy scale, identified with the cutoff, the EFT description breaks down and new physics is expected to a
ppear, as confirmed in many familiar examples in quantum field theory. In this work, we examine the validity of effective field theory methods applied to inflation. We address the issue of whether Planck-suppressed non-renormalizable interactions are suppressed enough to be safely neglected when computing inflationary predictions. We focus on non-derivative non-renormalizable operators and estimate the cutoff that should suppress them using two independent approaches: (i) the usual unitarity and perturbativity argument, (ii) by computing the UV-divergent part of the inflaton entropy, known to scale as the square of the UV-cutoff. We find that in the absence of gravity (decoupling limit) the cutoff appears to depends linearly on the total inflaton excursion. On the other hand, once gravity is restored, the cutoff is brought back to the Planck scale. These results suggest that inflationary scenarios with super-Planckian excursion are not natural from the EFT viewpoint.
Tensor modes in the cosmic microwave background are one of the most robust signatures of inflation. We derive theoretical bounds on the tensor fraction, as a generalization of the well-known Lyth bound. Under reasonable assumptions, the new bounds ar
e at least two orders of magnitude stronger than the original one. We comment on a previously derived generalization, the so-called Efstathiou-Mack relationship. We also derive a new absolute upper bound on tensors using de Sitter entropy bounds.
