Setting up stasis with gravitational interactions

An epoch known as cosmological stasis may have taken place in the early Universe. During matter-radiation stasis, a population of non-relativistic particles with different masses gradually decay into relativistic particles, and the effective equation of state $w$ remains approximately constant at a value between that of matter ($w=0$) and that of radiation ($w=1/3$). In this work, we investigate how to set up the appropriate initial conditions for stasis using gravitational interactions. We consider two scenarios: that the tower of non-relativistic particles is populated by the evaporation of primordial black holes (PBHs) and that the tower is populated by cosmological gravitational particle production (CGPP) during inflation. We calculate the abundance of particles on different levels of the tower to assess whether stasis is viable. We find that both scenarios can provide the needed initial conditions for stasis, and that they predict distinctive scaling exponents $\Omega_l \propto m_l^\alpha$ with mass $m_l$.