Confronting Cosmology and New Physics with Fundamental Constants
  The values of the fundamental constants such as $\mu = m_P/m_e$, the proton
to electron mass ratio and $\alpha$, the fine structure constant, are sensitive
to the product $\sqrt{\zeta_x^2(w+1)}$ where $\zeta_x$ is a coupling constant
between a rolling scalar field responsible for the acceleration of the
expansion of the universe and the electromagnetic field with x standing for
either $\mu$ or $\alpha$. The dark energy equation of state $w$ can assume
values different than $-1$ in cosmologies where the acceleration of the
expansion is due to a scalar field. In this case the value of both $\mu$ and
$\alpha$ changes with time. The values of the fundamental constants, therefore,
monitor the equation of state and are a valuable tool for determining $w$ as a
function of redshift. In fact the rolling of the fundamental constants is one
of the few definitive discriminators between acceleration due to a cosmological
constant and acceleration due to a quintessence rolling scalar field. $w$ is
often given in parameterized form for comparison with observations. In this
manuscript the predicted evolution of $\mu$, is calculated for a range of
parameterized equation of state models and compared to the observational
constraints on $\Delta \mu / \mu$. We find that the current limits on $\Delta
\mu / \mu$ place significant constraints on linear equation of state models and
on thawing models where $w$ deviates from $-1$ at late times. They also
constrain non-dynamical models that have a constant $w$ not equal to $-1$.
These constraints are an important compliment to geometric tests of $w$ in that
geometric tests are sensitive to the evolution of the universe before the epoch
of observation while fundamental constants are sensitive to the evolution of
the universe after the observational epoch. Abstract truncated.
