  We describe analytically the cosmological evolution of primordial gravity
waves (tensor perturbations) taking into account their coupling to relic
neutrinos. We prove that as a consequence of causality the neutrino-induced
phase shift of subhorizon tensor oscillations tends on small scales to zero.
For the tensor modes that reenter the horizon in the radiation era after
neutrino decoupling we calculate the neutrino suppression factor as
1-5rho_nu/9rho+O[(rho_nu/rho)^2]. This result is consistent with the value
obtained for three neutrino flavors by Weinberg and is in agreement with
numerical Boltzmann evolution. A minimal formula with the correct asymptotic
form on small and large scales reproduces to about ten percent the evolution on
all scales probed by the CMB. A more accurate solution (in terms of elementary
functions) shows that the modes reentering the horizon in the radiation era are
slightly enhanced and the phase of their temporal oscillations is shifted by
subdominant nonrelativistic matter. The phase shift grows logarithmically on
subhorizon scales until radiation-matter equality; the accumulated shift scales
for k>>k_eq as (ln k)/k. The modes reentering the horizon after equality are,
in turn, affected by the residual radiation density. These modes follow the
naive matter-era evolution which is advanced by a redshift and scale
independent increment of conformal time. In an appendix, we introduce a general
relativistic measure of radiation intensity that in any gauge obeys a simple
transport equation and for decoupled particles is conserved on superhorizon
scales for arbitrary initial conditions in the full nonlinear theory.
