The value of the tensor-to-scalar ratio r in the region allowed by the latest Planck 2015 measurements can be associated to a large variety of inflationary models. We discuss here the potential of future Cosmic Microwave Background cosmological observations in disentangling among the possible theoretical scenarios allowed by our analyses of current Planck temperature and polarization data. Rather than focusing only on r, we focus as well on the running of the primordial power spectrum, αs and the running thereof, βs. If future cosmological measurements, as those from the COrE mission, confirm the current best-fit value for βs 10 −2 as the preferred one, it will be possible to rule-out the most favoured inflationary models. I. MOTIVATIONSThe smoking-gun of inflation [1][2][3] is the detection of a stochastic background of gravitational waves. Such primordial signature is characterized by its amplitude, parametrized via the tensor-to-scalar ratio r. Recent analyses from Planck 2015 [4] have presented the tightest bounds to date on r using temperature and polarization measurements. Albeit current Planck constraints are perfectly compatible with a vanishing tensor-to-scalar ratio, yet there is still enough room for other theoretical possibilities besides the Starobinsky R 2 -gravity scenario, which emerges as the best-fit model. Looking forward to the next generation of CMB observations, and depending on the value of r that Nature has chosen, one can envision two distinct possibilities: (a) either r turns out to be way too small to be measured by the next generation of CMB observations, or (b) the value of r is large enough to be detected. However, in this latter case, the measured tensor-to-scalar ratio will typically correspond to several inflationary models. Given that measuring r (if r < f ew × 10 −4 ) might be extremely difficult [5,6], and disentangling between the various models that lie in the same regions in the canonical (n s , r) plane might not be straightforward either, we explore here the possibility of extending the analysis to other (complementary) inflationary observables.For the scalar power spectrum of the primordial perturbations, we consider, as additional observables, the running α s and the running of the running β s . For the primordial tensor power spectrum, we consider its running n t . The aim of this paper is to assess the potential of future CMB observations in falsifying inflation (or unraveling the fundamental model among the most favoured candidates after Planck 2015 data) by looking to these three additional observables. For illustration, we will consider some well-motivated models that are compatible with current data. The structure of the paper is as follows. Section II deals with the basic definitions of the different cosmological observables and their current constraints. Section III describes the theoretical predictions from the most favoured inflationary scenarios after Planck 2015 CMB temperature and polarization measurements. In Section IV we perform Markov Chain Monte Carlo...

We examine the impact of a non-minimal coupling of the inflaton to the Ricci scalar, 1 2 ξRφ 2 , on the inflationary predictions. Such a non-minimal coupling is expected to be present in the inflaton Lagrangian on fairly general grounds. As a case study, we focus on the simplest inflationary model governed by the potential V ∝ φ 2 , using the latest combined 2015 analysis of Planck and BICEP2/Keck Array. We find that the presence of a coupling ξ is favoured at a significance of 99% CL, assuming that nature has chosen the potential V ∝ φ 2 to generate the primordial perturbations and a number of e-foldings N = 60. Within the context of the same scenario, we find that the value of ξ is different from zero at the 2σ level. When considering the cross-correlation polarization spectra from BICEP2/Keck Array and Planck, a value of r = 0.038 +0.039 −0.030 is predicted in this particular non-minimally coupled scenario. Future cosmological observations may therefore test these values of r and verify or falsify the non-minimally coupled model explored here. PACS numbers: 98.70.Vc, 98.80.Cq, 98.80.Bp

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.Comment: Revtex, 8 pages, 4 figures. References updated. Matches published version in PR