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