Pre-inflationary dynamics of Starobinsky inflation and its generization in Loop Quantum Brans-Dicke Cosmology

TL;DR

This paper investigates the pre-inflationary dynamics of Starobinsky and alpha-attractor inflation models within loop quantum Brans-Dicke cosmology, revealing quantum effects influence initial conditions and transition to slow-roll inflation.

Contribution

It systematically analyzes how quantum geometry effects in loop quantum Brans-Dicke cosmology affect the pre-inflationary phase and initial conditions for these inflation models.

Findings

Pre-inflationary quantum phase can be expanding or contracting.

Quantum effects influence initial conditions for inflation.

Restricted initial conditions yield at least 60 e-folds of inflation.

Abstract

Recently, the nonperturbative quantization scheme of loop quantum gravity has been extended to the Brans-Dicke theory and the corresponding loop quantum Brans-Dicke cosmology has been derived, which provides an essential platform to explore inflationary models in this framework. In this paper, we consider two inflation models, the Starobinsky and $\alpha$-attractor inflation whose cosmological predictions are in excellent agreement with Planck data, and study systematically their pre-inflationary dynamics as well as the slow-roll inflation. We show that for both models, the background evolution of a flat Friedmann-Lema\^{i}tre-Robertson-Walker universe in general can be divided into three different phases: the pre-inflationary quantum phase, quantum-to-classical transition, and the slow-roll inflation. The pre-inflationary dynamics are dominated by the quantum geometry effects of loop quantum Brans-Dicke cosmology and the corresponding Universe could be either initially expanding or contracting, depending on the initial velocity of inflaton field. It is shown that the detailed evolution of pre-inflationary quantum phase also depend on specific inflation models. After the pre-inflationary quantum phase, the universe gradually evolves into the slow-roll inflation with some of initial conditions for Starobinsky and $\alpha$-attractor potentials. In addition, to be consistent with observational data, we also find the restricted parameter space of initial conditions that could produce at least $60$ $e$-folds during the slow-roll inflation.