  Cosmological analysis of extended Jordan-Brans-Dicke (eJBD) gravity is
presented in the Einstein metric frame in which gravitational interaction is
readily understandable. Our formulation is the first systematic investigation
of how to introduce lagrangian of standard particle physics in eJBD framework
consistently with the general principle of spontaneously broken gauge symmetry,
which makes it possible to confront eJBD-based cosmology with observational and
laboratory bounds on time variation of parameters, masses, and coupling
constants, caused by time evolution of eJBD fields. Decomposition of standard
particle physics lagrangian into independent gauge invariant pieces is proposed
to avoid serious conflict that may arise from standard lagrangian transformed
from the Jordan frame. Independent conformal factors are assigned to each of
five gauge invariant pieces. The formulation is most unambiguously made
possible by defining fields having canonical kinetic terms that allow us to use
the canonical quantization rule of field theory. This construction gives as one
of its consequences the canonical eJBD field $\chi$ that couples to the
universal fermion current, a linear combination of baryon and lepton number
currents, $\partial_{\mu} \chi (\frac{1}{3} j_B^{\mu} + j_L^{\mu})$, in
addition to the conventional trace of the energy-momentum tensor. Field
equation of eJBD field along with gravitational equation is analyzed by using a
simplified polynomial class of potential and conformal functions, giving time
evolution of radiation, matter and dark energy densities consistent with
observations when an appropriate set of model parameters are used. Finite
temperature corrections are further calculated to give temperature dependent
terms in eJBD field potential.
