In this paper, we analyze the quantum vacuum in a radiation-dominated and $CPT$-invariant universe by further imposing the quantum states to be ultraviolet regular i.e., satisfying the Hadamard/adiabatic condition. For scalar fields, this is enforced by constructing the vacuum via the states of low-energy proposal. For spin-$\frac{1}{2}$ fields, we extend this proposal for a FLRW spacetime and apply it for the radiation-dominated and $CPT$-invariant universe. We focus on minimizing the smeared energy density around the big bang and give strong evidence that the resulting states satisfy the Hadamard/adiabatic condition. These states are then self-consistent candidates as effective big bang quantum vacuum from the field theory perspective.

• Received 19 April 2022
• Revised 22 February 2023
• Accepted 29 March 2023

DOI:https://doi.org/10.1103/PhysRevD.107.085018