Inflation and primordial gravitational waves in scale-invariant quadratic gravity

Abstract

In scale-invariant models of fundamental physics all mass scales are generated via spontaneous symmetry breaking. In this work, we study inflation in scale-invariant quadratic gravity, in which the Planck mass is generated classically by a scalar field, which evolves from an unstable fixed point to a stable one thus breaking scale-invariance. We investigate the dynamics by means of dynamical system standard techniques. By computing the spectral indices and comparing them with data, we put some constraints on the three dimensionless parameters of the theory. We show that certain regions of the parameter space will be within the range of future CMB missions like CMB-S4, LITBird and STPol. The second half of the paper is dedicated to the analysis of inflationary first-order tensor perturbations and the calculation of the power spectrum of the gravitational waves. We comment on our results and compare them with the ones of mixed Starobinsky-Higgs inflation.

On the stability of scale-invariant black holes

“…Taking into account the most recent results obtained in the cosmological setting [30], we expect α to be much smaller than ξ 2 λ , and then the presence of black holes will always decrease the tunnelling probability of an unstable de Sitter spacetime.…”

“…In particular, at the stable fixed point the scalar field stabilizes and the coefficient of the linear term in R of the action can be identified as the Planck mass squared, while the others become negligible. During the transition between the two fixed points the Universe expands exponentially, giving rise to a competitive model of inflation [25,30], which is also robust against quantum corrections [31].…”

“…we obtain the expression for the Lagrangian that we will use in the following (for full details see [30]), namely…”

“…Before considering black holes, we briefly summarize the results of [29,30]. By imposing the flat Robertson-Walker metric ds 2 = −dt 2 + a(t) 2 δ ij dx i dx j in the equations of motion, one finds two second-order equations in the scalar field φ and the Hubble parameter H = ȧ/a, namely…”

“…where Λ s is still arbitrary, is an attractor. It turns out that the evolution from the unstable to the stable point yields an inflationary phase, thoroughly studied in [30]. The interesting feature is that, at the stable fixed point, the scalar field has a non-trivial value and the coefficient of R in the action (2.1) classically stabilizes around at a certain value that can be identified with the Planck mass squared, while the other terms become negligible.…”