Low-energy states and CPT invariance at the big bang

Abstract

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-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 selfconsistent candidates as effective big bang quantum vacuum from the field theory perspective.

States of low energy in the Schwinger effect

“…Since then, they have been applied in the context of LQC [40,41], where it was found that they heavily depend on the choice of smearing function only in regards to whether its support includes or excludes the bounce of LQC. Recently, they have also been applied to fermionic fields in a radiation-dominated CPT-invariant universe [42].…”

“…These two works have shown an interesting dependence of SLEs on the smearing function: they are independent of it as long as it is wide enough around the bounce of LQC [40], but very sensitive to whether the moment of the bounce is included in the support of the smearing function [41]. The notion of SLEs has been recently extended to fermionic fields in [42], where they are applied in a radiation-dominated CPT-invariant Universe.…”

Black holes, conformal symmetry, and fundamental fields

“…Remarkably, the FLRW geometry (4.2) provides a natural arena for the construction of Hadamard states around the Big Bang. The so-called 'smeared' states of low energy [23,25] solve the problem. They minimize the averaged energy density…”

“…However, from a phenomenological point of view, the approach to the Big Bang can be parameterized by a temporal window function. It is a mathematical tool of quantum field theory in curved spacetime to construct a low-energy vacuum state that satisfies the Hadamard condition [23][24][25]. This point is also discussed in section 4.…”