# $\Delta N_{\text{eff}}$ and entropy production from early-decaying gravitinos

## TL;DR

This paper uses observational bounds on the effective number of relativistic degrees of freedom ($N_{eff}$) to constrain the properties and decay of gravitinos, providing tighter limits on reheating temperature and gravitino mass than previous methods.

## Contribution

It introduces a novel approach to constrain gravitino decay parameters using $N_{eff}$ bounds, improving upon previous BBN constraints for certain mass ranges.

## Key findings

- Current $N_{eff}$ bounds limit reheating temperature to $5 imes 10^{10}$ to $5 imes 10^{11}$ GeV for gravitino masses below $10^5$ GeV.
- Constraints on gravitino masses above $4 imes 10^3$ GeV are nearly 100 times more stringent than previous BBN bounds.
- The method provides new insights into the interplay between gravitino decay, entropy production, and early universe cosmology.

## Abstract

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.