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Recently the Chiral Cosmological Model (CCM) coupled to cold dark matter(CDM) has been investigated as $\sigma$CDM model to study the observedaccelerated expansion of the Universe. Dark sector fields (as Dark Energycontent) coupled to cosmic dust were considered as the source of Einsteingravity in Friedmann-Robertson-Walker (FRW) cosmology. Such model had abeginning at the matter-dominated era. The purposes of our presentinvestigation are two folds: to extend <<life>> of the $\sigma$CDM for earliertimes to radiation-dominated era and to take into account variation of theexponential potential via variation of the interaction parameter $\lambda $.  We use Markov Chain Monte Carlo (MCMC) procedure to investigate possiblevalues of initial conditions constrained by the measured amount of the darkmatter, dark energy and radiation component today.  Our analysis includes dark energy contribution to critical density, the ratioof the kinetic and potential energies, deceleration parameter, effectiveequation of state and evolution of DE equation of state with variation ofcoupling constant $\lambda $. A comparison with the $\Lambda$CDM model wasperformed. A new feature of the model is the existence of some values ofpotential coupling constant, leading to a $\sigma$CDM solution without transitinto accelerated expansion epoch.

$\sigma$CDM coupled to radiation. Dark energy and Universe acceleration