Inflation from cosmological constant and nonminimally coupled scalar

TL;DR

This paper explores inflation driven by a nonminimally coupled scalar field in a universe with a cosmological constant, showing it can produce observable predictions close to current measurements and can be tested by future data.

Contribution

It introduces a model of inflation with a nonminimally coupled scalar field and a cosmological constant, analyzing its dynamics and observational signatures.

Findings

The model yields a scalar spectral index around 0.955.

It predicts a small tensor-to-scalar ratio, r < 0.01.

The spectral index can be slightly adjusted by nonminimal couplings.

Abstract

We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field, in which the field couples both quadratically and quartically to the Ricci scalar. When considered in the Einstein frame and when the nonminimal couplings are negative, the field starts in slow roll and inflation ends with an asymptotic value of the principal slow roll parameter, $\epsilon_E=4/3$. Graceful exit can be achieved by suitably (tightly) coupling the scalar field to matter, such that at late time the total energy density reaches the scaling of matter, $\epsilon_E=\epsilon_m$. Quite generically the model produces a red spectrum of scalar cosmological perturbations and a small amount of gravitational radiation. With a suitable choice of the nonminimal couplings, the spectral slope can be as large as $n_s\simeq 0.955$, which is about one standard deviation away from the central value measured by the Planck satellite. The model can be ruled out by future measurements if any of the following is observed: (a) the spectral index of scalar perturbations is $n_s>0.960$; (b) the amplitude of tensor perturbations is above about $r\sim 10^{-2}$; (c) the running of the spectral index of scalar perturbations is positive.