Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology**Supported in part by the National Natural Science Foundation of China (NNSCF) under Grant Nos. 11375153 and 11675145. T.Z. is supported in part by NFSC under Grant No. 11675143 and the Fundamental Research Funds for the Provincial Universities of Zhejiang in China under Grant No. RF-A2019015

Abstract

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein’s and Jordan’s frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.