Constraining the runaway dilaton and quintessential dark energy
  Dark Energy is some of the weirdest and most mysterious stuff in the universe
that tends to increase the rate of expansion of the universe. Two commonly
known forms of dark energy are the cosmological constant, a constant energy
density filling space homogeneously, and scalar fields such as quintessence or
moduli whose energy density can vary with time. We explore one particular model
for dynamic dark energy; quintessence driven by a scalar dilaton field. We
propose an ansatz for the form of the dilaton field, $|\phi(a)|/m_P \equiv
\alpha_1 \ln t+ \alpha_2 t^n=\alpha\ln a+ \beta\, a^{2\zeta}$, where $a$ is the
scale factor and $\alpha$ and $\zeta$ are parameters of the model. This
phenomenological ansatz for $\phi$ can be motivated by generic solutions of a
scalar dilaton field in many effective string theory and string-inspired
gravity models in four dimensions. Using a compilation of current data
including type Ia supernovae, we impose observational constraints on the slope
parameters like $\alpha$ and $\zeta$ and then discuss the relation of our
results to analytical constrains on various cosmological parameters, including
the dark energy equation of state. Sensible constraints are imposed on model
parameters like $\alpha$ and $\zeta$ as well as on the dark energy/dark matter
couplings using results from structure formation. The constraints of this model
are shown to encompass the cosmological constant limit within $1\sigma$ error
bars.
