The effects of non Bunch-Davies initial conditions on gravitationally produced relics

Typical gravitational production of relics from amplification of inflationary perturbations assumes Bunch-Davies initial conditions, i.e. a vacuum with initially no particles. In this paper we investigate the impact of non Bunch-Davies initial conditions to the final abundance of relics, with particular attention to the parameter space where the total dark matter abundance is reproduced. We present a general framework for any initial condition, through which we show their non-trivial effect on both spectrum and late-time abundance. We argue that for particles whose source of conformal symmetry breaking comes only from a mass term (spin-1/2 fermions and conformally coupled scalars), the choice of initial conditions has little impact on the mass range relevant to dark matter. For other particles, e.g. the longitudinal mode of spin-1, we see a large deviation from the standard computation. We exemplify and quantify our results with an initial thermal state and a two-stage inflation scenario, highlighting that the total dark matter can be obtained for a wide range of masses.

💡 Research Summary

**
The paper revisits the mechanism of gravitational particle production (GPP) during inflation, challenging the standard assumption that the fields start in the Bunch‑Davies vacuum (no particles). Instead, the authors allow for generic initial states that may already contain particles, motivated by possible pre‑inflationary dynamics such as a hot pre‑inflationary phase or a preceding stage of inflation. They develop a unified formalism that works for any initial condition, using Weyl‑rescaled fields (scalars, Majorana fermions, and the longitudinal component of massive vectors) and solving the mode equation u″ₖ + ωₖ² uₖ = 0. The initial state |ψ⟩ is characterized by an occupation number ⟨N_in(k)⟩ and a coherence term ⟨C_in(k)⟩. By matching the Hamiltonian expectation value at early and late times, they derive the final particle number density

nₖ = |βₖ|² + (1 ± 2|βₖ|²) ⟨n_in(k)⟩ −