Cosmic Variation of Proton to Electron Mass Ratio with an interacting
  Higgs Scalar Field
  We discuss that it is quite possible to realize the smooth transition of the
universe between a matter/radiation dominated deceleration and a dark energy
dominated acceleration, even with a variation of proton-to-electron mass ratio.
The variation is incorporated into the theory of gravity using a cosmological
Higgs scalar field with a non-trivial self-interaction potential, leading to a
varying Higgs vacuum expectation value (VEV). This matches well with the data
from molecular absorption spectra of a series of Quasars. In comparison with
late-time cosmology, an observational consistency is reached using a Markov
chain Monte Carlo simulation and JLA+OHD+BAO data sets. We find that the
pattern of variation is embedded within the evolving Equation of State (EOS) of
the scalar Dark Energy/Matter components, but leaves negligible trace on the
effective EOS of the system. We discuss three cases of scalar extended theory
of gravity, (a) a minimally coupled scalar, (b) a non-minimally coupled scalar
and (c) a generalized Brans-Dicke setup. We also give a toy model of a unified
cosmic history from inflation to the present era and discuss how the Higg VEV
might have changed as a function of look back time.
