TO APPEAR IN THE PHYSICAL REVIEW D We examine , from both a qualitative and a numerical point of view , the evolution of Kantowski–Sachs cosmological models whose source is a mixture of a gas of weakly interacting massive particles ( WIMP ’ s ) and a radiative gas made up of a “ tightly coupled ” mixture of electrons , baryons and photons .
Our analysis is valid from the end of nucleosynthesis up to the duration of radiative interactions ( 10 ^ { 6 } K > T > 4 \times 10 ^ { 3 } K ) .
In this cosmic era annihilation processes are negligible , while the WIMP ’ s only interact gravitationally with the radiative gas and the latter behaves as a single dissipative fluid that can be studied within a hydrodynamical framework .
Applying the full transport equations of Extended Irreversible Thermodynamics , coupled with the field and balance equations , we obtain a set of governing equations that becomes an autonomous system of ordinary differential equations once the shear viscosity relaxation time , \tau _ { \hbox { \tiny { rel } } } , is specified .
Assuming that \tau _ { \hbox { \tiny { rel } } } is proportional to the Hubble time , the qualitative analysis indicates that models begin in the radiation dominated epoch close to an isotropic equilibrium point ( saddle ) .
We show how the form of \tau _ { \hbox { \tiny { rel } } } governs the relaxation timescale of the models towards an equilibrium photon entropy , leading to “ near-Eckart ” and transient regimes associated with “ abrupt ” and “ smooth ” relaxation processes , respectively .
Assuming the WIMP particle to be a super-symmetric neutralino with mass m _ { \hbox { \tiny w } } \sim 100 GeV , the numerical analysis reveals that a physically plausible evolution , compatible with a stable equilibrium state and with observed bounds on CMB anisotropies and neutralino abundance , is only possible for models characterized by initial conditions associated with nearly zero spatial curvature and total initial energy density very close to unity .
An expression for the relaxation time , complying with physical requirements , is obtained in terms of the dynamical equations .
It is also shown that the “ truncated ” transport equation does not give rise to acceptable physics .