  In our paper we constrain Friedman Robertson Walker (FRW) model with
``radiation-like'' contribution to the Friedmann equation against the
astronomical data. We analyze the observational limitations on a $(1+z)^4$ term
from SNIa data, FRIIb radio galaxy (RG) data, baryon oscillation peak and CMBR
observations. We argue that it is not possible to determine the energy
densities of individual components scaling like radiation from a kinematic
astronomical test. The bounds for density parameter for total radiation-like
term can be obtained. We find different interpretations of the presence of
scaling like radiation term: FRW universe filled with a massless scalar field
in a quantum regime (Casimir effect), Friedmann-Robertson-Walker (FRW) model in
a semi-classical approximation of loop quantum gravity, FRW model in the
Randall Sundrum scenario with dark radiation or cosmological model with global
rotation. In this paper we mainly concentrate on Casimir effect arising from
quantum effects of the scalar field. This contribution can describe decaying
part of cosmological constant. We discuss the back reaction of gravity on
Casimir-type force which is a manifestation of the vacuum fluctuations of the
quantum scalar field at low temperature. It is shown that while the Casimir
energy gives rise to accelerating Universe, the cosmological constant term is
still required. We argue that a small negative contribution of a radiation-like
term can reconcile the tension between the observed primordial ${}^4He$ and $D$
abundance. Moreover the presence of such contribution can also remove the
disagreement between Hubble parameter $H_0$ values obtained from both SNIa and
Wilkinson Microwave Anisotropy Probe (WMAP) satellite data.
