In this paper, we investigate a scenario of variable gravity and apply it to the unified description of inflation and late-time cosmic acceleration dubbed quintessential inflation. The scalar field called ``cosmon,'' which in this model unifies both the concepts, reduces to the inflaton at early epochs. We calculate the slow-roll parameters, the Hubble parameter at the end of inflation, the reheating temperature, and the tensor-to-scalar ratio, and we demonstrate the agreement of the model with observations and the Planck data. As for the postinflationary dynamics, the cosmon tracks the background before it exits the scaling regime at late times. The scenario gives rise to the correct epoch sequence of standard cosmology, namely, radiative regime, matter phase, and dark energy. We show that the long kinetic regime after inflation gives rise to enhancement of the relic gravity wave amplitude, resulting in violation of the nucleosynthesis constraint at the commencement of the radiative regime in the case of an inefficient reheating mechanism, such as gravitational particle production. Instant preheating is implemented to successfully circumvent the problem. As a generic feature, the scenario gives rise to a blue spectrum for gravity waves on scales smaller than the comoving horizon scale at the commencement of the radiative regime.

We investigate two classes of models of quintessential inflation, based upon canonical as well as noncanonical scalar fields. In particular, introducing potentials steeper than the standard exponential, we construct models that can give rise to a successful inflationary phase, with signatures consistent with Planck 2015 results. Additionally, using nonminimal coupling of the scalar field with massive neutrino matter, we obtain the standard thermal history of the Universe, with late-time cosmic acceleration as the last stage of evolution. In both cases, inflation and late-time acceleration are connected by a tracker solution.

In this paper, we focus on general features of quintessential inflation, which is an effort to unify inflation and dark energy using a single scalar field. We describe a class of models of quintessential inflation which can give rise to the tensor to scalar ratio of perturbations consistent with recent BICEP2 measurements. The scale of inflation in the model is around the grand unified theory scale and there is large parameter space consistent with the recent findings.

One class of single-field inflationary models compatible with the recently-conjectured Swampland criteria would be those in which a Hubble slow-roll arameter ϵ _H is not the same as ϵ _V ∼ (V ^′ /V)². However, a roadblock for these models (with a convex potential) lie in the unacceptably high tensor-to-scalar ratio, r, generically predicted by them. In this work, illustrating through an explicit example, we point out that having a non-Bunch-Davies component to the initial state of cosmological perturbations makes the value of r compatible with observations. In this way, we lay down a new path even for standard models of slow-roll inflation to be consistent with the Swampland criteria by invoking deviations from the Bunch-Davies initial state.