Δneff and entropy production from early-decaying gravitinos

Gravitinos are a fundamental prediction of supergravity, their mass (mG) is informative of the value of the SUSY breaking scale, and, if produced during reheating, their number density is a function of the reheating temperature (Trh). As a result, constraining their parameter space provides, in turn, significant constraints on particle physics and cosmology. We have previously shown that for gravitinos decaying into photons or charged particles during the (μ and y) distortion eras, upcoming CMB spectral distortions bounds are highly effective in constraining the Trh-mG space. For heavier gravitinos (with lifetimes shorter than a few ×106 sec), distortions are quickly thermalized and energy injections cause a temperature rise for the CMB bath. If the decay occurs after neutrino decoupling, its overall effect is a suppression of the effective number of relativistic degrees of freedom (Neff). In this paper, we utilize the observational bounds on Neff to constrain gravitino decays and, hence, provide new constraints on gravitinos and reheating. For gravitino masses less than ≈105 GeV, current observations give an upper limit on the reheating scale in the range of ≈5×1010-5×1011 GeV. For masses greater than ≈4×103 GeV, this can be more stringent than previous bounds from BBN constraints, coming from photodissociation of deuterium, by almost 2 orders of magnitude.