  Initial conditions in cosmology in the form of the microcanonical density
matrix of the Universe predict a thermal nature of the primordial CMB power
spectrum with a nonzero temperature of the resulting relict temperature
distribution. This effect generates a thermal contribution to the red tilt of
this spectrum, additional to its vacuum component. In the cosmological model
with a large number of free fields conformally coupled to gravity the magnitude
of this effect is determined by the Gauss-Bonnet coefficient
$\mbox{\boldmath$a$}$ of the trace anomaly. For low spins it is too small to be
presently observable, but it can be amplified by the mechanism of the
$\mbox{\boldmath$a$}$-theorem applied to the renormalization group flow which
interpolates between the ultraviolet and infrared domains associated
respectively with early and late stages of cosmological evolution.
