# On large lepton number asymmetries of the Universe

## TL;DR

This paper explores how a large lepton asymmetry in the universe can be consistent with cosmological data, requiring entropy production from saxion decay to dilute the asymmetry, and constrains related Peccei-Quinn parameters.

## Contribution

It demonstrates that a significant lepton asymmetry can be maintained through late-time saxion decay, linking cosmological observations with particle physics parameters.

## Key findings

- A large lepton asymmetry of order 0.1-1 is compatible with cosmological data.
- Entropy release from saxion decay can dilute pre-existing asymmetries to observed levels.
- Constraints on saxion mass and VEV are derived to ensure consistent entropy production.

## Abstract

A large lepton number asymmetry of $\mathcal{O}(0.1-1)$ at present universe might not only be allowed but also necessary for consistency among cosmological data. We show that, if a sizeable lepton number asymmetry were produced before the electroweak phase transition, the requirement for not producing too much baryon number asymmetry through sphalerons processes, forces the high scale lepton number asymmetry to be larger than about $30$. Therefore a mild entropy release causing $\mathcal{O}(10-100)$ suppression of pre-existing particle density should take place, when the background temperature of the universe is around $T = \mathcal{O}(10^{-2} - 10^2) {\rm GeV}$ for a large but experimentally consistent asymmetry to be present today. We also show that such a mild entropy production can be obtained by the late-time decays of the saxion, constraining the parameters of the Peccei-Quinn sector such as the mass and the vacuum expectation value of the saxion field to be $m_\phi \gtrsim \mathcal{O}(10) {\rm TeV}$ and $\phi_0 \gtrsim \mathcal{O}(10^{14}) {\rm GeV}$, respectively.