This paper is available on arxiv under CC 4.0 license.

**Authors:**

(1) Nicolas Bernal, New York University Abu Dhabi;

(2) Partha Konar, Physical Research Laboratory;

(3) Sudipta Show, Physical Research Laboratory.

## Table of Links

- Abstract and Intro
- S-matrix: Unitarity and its Consequences
- Dark Matter Annihilation and Unitarity Bound
- Low-temperature Reheating
- Freeze-out with a Low-temperature Reheating
- Summary and Conclusion
- Acknowledgments and References

## 6. Summary and Conclusion

The requirement of the de Broglie wavelength of dark matter (DM) to hold it inside galaxies and the stability of the stellar galaxy cluster collectively put a broad allowed mass range for DM by providing the lower and upper bound of DM mass, respectively. Specifying some properties of DM can further tighten the mass range. Interestingly, one can put the model-independent upper bound by specifying the thermal production of DM in the early universe. The observed DM abundance and unitarity of partial waves from the scattering matrix jointly place an upper limit on DM mass. Primarily, the upper limits on the inelastic cross section for a general number-changing process 2 → r can be derived with the help of the optical theorem, the matrix elements and the elastic scattering cross section for the process. After that, one can obtain the thermally averaged cross section for the r → 2 process by invoking the principle of detailed balance. Finally, the unitarity bounds on the thermally averaged cross section translate to the upper limits on the DM mass satisfying the relic density constraints. It is known that the maximum allowed DM mass for the 2 → 2 and 3 → 2 DM annihilation processes is around 130 TeV and 1 GeV, respectively. However, these bounds not only depend on the particle physics model, but have a strong dependence on the cosmological evolution of the universe, being valid only if the universe followed the so-called “standard cosmological scenario”.

Instead, this article explores the DM mass bound in nonstandard cosmological setups characterized by low-temperature reheating. In particular, we focus on *i*) kination-like scenarios, where the early universe was dominated by a fluid with an energy density that gets diluted faster than free radiation, and *ii*) early matter-dominated scenarios, where a component with an energy density that scales as nonrelativistic matter dominates the early universe and eventually decays into SM particles.

First, we study the kination-like universe, which demands a larger thermally-averaged annihilation cross section to saturate the observed abundance of DM compared to the standard radiation-dominated picture since, in this case, freeze-out occurs early. As a result, the upper bound on the DM mass becomes more stringent than in the standard case. For example, if the reheating temperature is as low as a few MeVs (corresponding to the start of the Big Bang nucleosynthesis epoch), the usual bound of the DM mass m ≲ 130 TeV can be reduced to a few TeVs for WIMPs.

Before closing, we want to emphasize that the evolution of the early universe is largely unknown. The standard assumption of a universe dominated by standard-model radiation from the end of cosmological inflation until matter-radiation equality, together with a transition from an inflaton-dominated to a radiation-dominated universe occurring at a very early time, cannot be taken for granted. Having that in mind, here we have studied the impact of the unitarity bound on DM in the case of low-temperature reheating scenarios.