Gravitinos are a fundamental prediction of supergravity, their mass ($m_{ G}$) 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 ($T_{ \text{ rh}}$). As a result, constraining their parameter space provides in turn significant constraints on particles physics and cosmology. We have previously shown that for gravitinos decaying into photons or charged particles during the ($\mu$ and $y$) distortion eras, upcoming CMB spectral distortions bounds are highly effective in constraining the $T_{ \text{ rh}}-m_{ G}$ space. For heavier gravitinos (with lifetimes shorter than a few $\times10^6$ 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 ($N_{ \text{ eff}}$). In this paper, we utilize the observational bounds on $N_{ \text{ eff}}$ to constrain gravitino decays, and hence provide new constaints on gravitinos and reheating. For gravitino masses less than $\approx 10^5$ GeV, current observations give an upper limit on the reheating scale in the range of $\approx 5 \times 10^{ 10}- 5 \times 10^{ 11}$GeV. For masses greater than $\approx 4 \times 10^3$ GeV they are more stringent than previous bounds from BBN constraints, coming from photodissociation of deuterium, by almost 2 orders of magnitude.
Categories: hep-ph astro-ph.CO hep-th