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 ($T_{\mathrm{rh}}$). 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 ($\mu$ and $y$) distortion eras, upcoming CMB spectral distortions bounds are highly effective in constraining the $T_{\mathrm{rh}}-m_G$ space. For heavier gravitinos (with lifetimes shorter than a few $\times {10}^6\sec$), 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 ($N_{\mathrm{eff}}$). In this paper, we utilize the observational bounds on $N_{\mathrm{eff}}$ to constrain gravitino decays and, hence, provide new constraints on gravitinos and reheating. For gravitino masses less than $\approx {10}^5\mathrm{GeV}$, current observations give an upper limit on the reheating scale in the range of $\approx 5\times {10}^{10}–5\times {10}^{11}\mathrm{GeV}$. For masses greater than $\approx 4\times {10}^3\mathrm{GeV}$, this can be more stringent than previous bounds from BBN constraints, coming from photodissociation of deuterium, by almost 2 orders of magnitude.

• Received 5 June 2017

DOI:https://doi.org/10.1103/PhysRevD.98.023006

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Published by the American Physical Society