Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology

Abstract

Recently the background independent nonperturbative quantization technique has been extended to 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 loop quantum cosmology (BDLQC) is one such theory 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 BDLQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in Brans-Dick theory, it is not 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 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 observational data, we also find out the allowed data space of initial conditions that would produce 60 e-folds of expansion during the slow roll inflation.