CνB damping of primordial gravitational waves and the fine-tuning of the CγB temperature anisotropy

Damping of primordial gravitational waves due to the anisotropic stress contribution owing to the cosmological neutrino background (C$\nu$B) is investigated in the context of a radiation-to-matter dominated Universe. Besides its inherent effects on the gravitational wave propagation, the inclusion of the C$\nu$B anisotropic stress into the dynamical equations also affects the tensor mode contribution to the anisotropy of the cosmological microwave background (C$\gamma$B) temperature. Given that the fluctuations of the C$\nu$B temperature in the (ultra)relativistic regime are driven by a multipole expansion, the mutual effects on the gravitational waves and on the C$\gamma$B are obtained through a unified prescription for a radiation-to-matter dominated scenario. The results are confronted with some preliminary results for the radiation dominated scenario. Both scenarios are supported by a simplified analytical framework, in terms of a scale independent dynamical variable, $k \eta$, that relates cosmological scales, $k$, and the conformal time, $\eta$. The background relativistic (hot dark) matter essentially works as an effective dispersive medium for the gravitational waves such that the damping effect is intensified for the Universe evolving to the matter dominated era. Changes on the temperature variance owing to the inclusion of neutrino collision terms into the dynamical equations result into spectral features that ratify that the multipole expansion coefficients $C_{l}^{T}$'s die out for $l \sim 100$.