  The effective theory of the Anton-Schmidt cosmic fluid within the Debye
approximation is investigated. In this picture, the universe is modeled out by
means of a medium without cosmological constant. In particular, the
Anton-Schmidt representation of matter describes the pressure of crystalline
solids under deformations imposed by isotropic stresses. The approach scheme is
related to the fact that the universe deforms under the action of the cosmic
expansion itself. Thus, we frame the dark energy term as a function of scalar
fields and obtain the corresponding dark energy potential $V(\varphi)$.
Different epochs of the universe evolution are investigated in terms of the
evolution of $\varphi$. We show how the Anton-Schmidt equation of state is
capable of describing both late and early epochs of cosmic evolution. Finally,
numerical bounds on the Anton-Schmidt model with $n=-1$ are derived through a
Markov Chain Monte Carlo analysis on the combination of data coming from type
Ia Supernovae, observations of Hubble parameter and baryon acoustic
oscillations. Statistical comparison with the $\Lambda$CDM model is performed
by the AIC and BIC selection criteria. Results are in excellent agreement with
the low-redshift data. A further generalization of the model is presented to
satisfy the theoretical predictions at early-stage cosmology.
