Final answer:
Relic neutrino-antineutrino pairs have energies too low to significantly produce photons through annihilation. Any such process in the present universe would be highly suppressed and exceptionally rare, with no established estimation for such a rare event's rate or timescale.
Step-by-step explanation:
Relic neutrinos, which are low-energy neutrinos from the early universe, have energies that are indeed too low to directly produce electron-positron pairs through annihilation. They are also very unlikely to interact to form photon pairs directly due to the weak interaction governing neutrino processes. Such annihilation to photons, if it occurs at all, would proceed through highly suppressed and indirect pathways making the rate exceptionally low. Also, given that there are as yet no conclusive experimental confirmations of such processes for relic neutrinos, the rate or time scale for such annihilations is not well-defined in the literature and would be expected to be extremely long, far exceeding the current age of the universe.
In the high-energy environment of the early universe, particle-antiparticle annihilation to photons was more common. For instance, electron-positron annihilation typically produced photons through the reaction e+ + e- → 2γ. However, current relic neutrinos, with their extremely low energies, do not have a significant interaction rate with matter or antimatter partners to produce observable radiation, much less to impact the cosmic microwave background.