Scalaron from R²-gravity as a heavy field

Abstract

We study a model of inflation in which a scalar field χ is non-minimally coupled to Starobinsky's R 2 gravity. After transforming it to the Einstein frame, a new scalar field, the scalaron φ, will appear and couple to χ with a nontrivial field metric, while χ acquires a positive mass via the non-minimal coupling. Initially inflation occurs along the φ direction with χ trapped near its origin by this induced mass. After φ crosses a critical value, it starts rolling down rapidly and proceeds to damped oscillations around an effective local minimum determined by the value of χ, while inflation still continues, driven by the χ field at this second stage where the effect of the non-minimal coupling becomes negligible. The presence of the damped oscillations during the transition from the first to second stage of inflation causes enhancement and oscillation features in the power spectrum of the curvature perturbation. Assuming that the oscillations may be treated perturbatively, we calculate these features by using the δN formalism, and discuss its observational implications to large scale CMB anomalies or primordial black hole formation, depending on the scale of the features.

Primordial black holes from inflation with nonminimal derivative coupling

“…Thus, after getting the inflaton value φ * = 4.99M pl corresponding to N * = 60, the scalar spectral index and the tensor-to-scalar ratio at the pivot scale k * can be calculated by using Eqs. (27) and (28) to be n s = 0.9666 and r = 0.0431, which are compatible with the current observational constraints in Eq.…”

Dynamical emergence of scalaron in Higgs inflation

“…For more comprehensive analysis on the inflationary perturbation, see Refs. [22,[73][74][75][76][77].…”

Scalar induced gravitational waves in inflation with gravitationally enhanced friction

“…The mechanisms of amplifying the small-scale curvature perturbations within the infla- 1 It is worthing pointing out that the scalar induced GWs are gauge independent [26][27][28]. tionary scenario have been extensively studied in recent years [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The most common mechanism is the single-field inflection-point inflation [38][39][40][41][42][43][44][45], which requires that the potential of the inflaton field has an approximate inflection point.…”