Inflation by Variation of the Strong Coupling Constant: update for Planck 2018

Abstract

We apply the standard cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is non-minimally coupled to gravity. Accommodating Planck 2018 data requires a length scale shorter than Planck Length L pl . However, a variant of the model, represented by a two-exponentials potential, fits the data with > L pl .

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

“…We continued in this letter the work of [1] on the inflationary model generated by varying strong coupling constant, and studied here the effect of the quadratic kinetic energy term which appears upon introducing an f (R) gravity, represented by an αR 2 -term in the pure gravity Lagrangian. We investigated in Palatini formalism two extreme cases corresponding first to (α >> 1), which represents thus a highly non-canonical k-inflation, and second to (α << 1) where we kept terms to first order in α and examined a specific type of the k-inflation, namely the constant roll inflation.…”

“…In [1], α was taken to be small in a way to neglect the quadratic kinetic energy term. In fact, upon perturbing the metric then the (αδg)-term would give higher order terms, whereas the α(∂ β χ∂ β χ) 2 would give, in the slow-roll inflationary era, contributions of order α χ4 which is subdominant compared to the α-correction in U .…”

“…In fact, upon perturbing the metric then the (αδg)-term would give higher order terms, whereas the α(∂ β χ∂ β χ) 2 would give, in the slow-roll inflationary era, contributions of order α χ4 which is subdominant compared to the α-correction in U . Thus, in [1], one could apply the shortcut "potential method", using U as an effective potential. We intend now to refine this analysis, and consider the effect of the quadratic kinetic energy, keeping first order in α when α is small, and studying, in addition, the case where α is large.…”

“…In [1], we adopted a model of variations of constants in order to generate an inflationary scenario, where the strong coupling was assumed to vary in time encoded in a scalar field representing this variation. Although current geophysical and astronomical data preclude any variation of constants, be it strong coupling [2], or Higgs vev [3], or electric charge [4], however no data precludes variation in very early times.…”

“…In [5], a connection between variation of constants and inflation was suggested, whereas in [6] this idea was pursued further into a concrete model shown to be able to accommodate data in some variants involving multiple inflaton fields. Alternatively, the single inflaton model was shown in [1] to be viable provided one changes the gravitational sector and assumes f (R) gravity. The addition of an αR 2 term in the pure gravity Lagrangian changed the potential into an effective one, but also led to a quadratic kinetic energy term which was dropped in [1] on the ground that it involved an α-coupling which could be argued to be small perturbatively, and this allowed to derive formulae for the spectral index n s and the scalar-to-tensor ratio r contrasted with planck data 2018 [7] separately or combined with other experiments [8].…”