Higgs-Dilaton inflation in Einstein-Cartan gravity

Abstract

We study the phenomenology of the Higgs-Dilaton model in the context of Einstein-Cartan gravity, focusing on the separate impact of the Holst and Nieh-Yan terms on the inflationary observables. Using analytical and numerical techniques, we show the predictions of these scenarios to display an attractor-like behaviour intrinsically related to the curvature of the field-space manifold in the metric formulation of the theory. Beyond that, the analysis of the Nieh-Yan case reveals the existence of an additional attractor solution induced by a cubic pole in the inflaton kinetic term that becomes relevant at large dilaton couplings. This constitutes a unique feature of the Einstein-Cartan formulation as compared to the metric and Palatini counterparts.

Preheating in Einstein-Cartan Higgs Inflation: oscillon formation

“…While the results of this paper have been explicitly derived assuming a simple Nieh-Yan interaction (2.14), they can be easily extended to the more general constant c scenarios within the EC multiverse 11 [35], including also scale-invariant extensions [55] or even TDiff generalizations [47,115]. Indeed, the main condition for oscillon formation is effectively encoded in the field redefinition d χ/d h entering eq.…”

“…As shown in refs. [32,33,55], this specific choice provides a smooth parametric interpolation between the metric (ξ η = ξ) and Palatini formulations of HI (ξ η = 0), a property that, as we will show in section 3, will turn out to be critical for oscillon formation. Note, however, that most of our results can be easily extended to more general settings within the EC multiverse (2.5), provided that they effectively lead to a constant value of c in the field range of interest.…”

“…Therefore, as far as inflation is concerned, a change in the Higgs self-coupling λ can be always compensated by a change of the parameter c, meaning that a strict relation between cosmological observables and SM parameters can only be established once the running of λ is JCAP12(2023)002 ) with different values of the non-minimal coupling ξ (following the procedure in [33,55]), together with the recently updated constraints (green shaded regions) from the BICEP/Keck collaboration [77], at 68% and 95% C.L.…”

“…In fact, assuming no Beyond SM physics between the electroweak and the Planck scale, it is a priori possible to compute the running of the experimentally known SM couplings, allowing, in principle, for a comprehensive study of the preheating stage. This scenario has been studied in different formulations of gravity, ranging from the standard metric case [10,[12][13][14][15][16][17][18][19][20][21][22] to the Palatini [23][24][25][26][27][28][29][30], teleparallel [31], Einstein-Cartan [32][33][34][35] and metric-affine formulations [36][37][38], including also several scale-invariant extensions [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Conversely, the post-inflationary evolution ha...…”

“…Figure 1. Numerical results (blue curve) in the n s − r plane for the action (2.9) with different values of the non-minimal coupling ξ (following the procedure in[33,55]), together with the recently updated constraints (green shaded regions) from the BICEP/Keck collaboration[77], at 68% and 95% C.L.…”