Palatini $f(R)$ gravity and variants of k-/constant roll/warm inflation within variation of strong coupling scenario

Abstract

We show that upon applying Palatini f (R), characterized by an αR 2 -term, within a scenario motivated by a temporal variation of strong coupling constant, then one gets a quadratic kinetic energy. We do not drop this term, but rather study two extreme cases: α << 1 and α >> 1. In both cases one can generate an inflationary paradigm, legitimately called thus a k-inflation, which fits the Planck 2018 data.

Natural Inflation with non minimal coupling to gravity in $R^2$ gravity under the Palatini formalism

“…Secondly, we examine the limit α 1 in which the model is reduced to a kinflation model with a non-canonical scalar field. Numerous studies were carried out to refine the k-inflationary scenario within the framework of the Non-canonical scalar fields [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].Inflationary models within string theory exhibit unusual scalar field dynamics involving non-minimal kinetic terms [43,44].In [45] a loop-quantum gravity inspired modification of general relativity is considered. the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined.…”