Abstract
The Null Energy Condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or non-minimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but non-perturbative) QFT and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the Averaged Null Energy Condition should not be violated by this mechanism. Nevertheless, the transient behaviour could have profound impacts in Early Universe Cosmology.
Highlights
In general relativity, an energy condition consists in assuming that matter satisfies “physical” properties, common to all forms of known matter
The null energy condition (NEC), defined more formally below, plays an important role in cosmology, and for a perfect fluid in a homogeneous and isotropic universe, it translates to the requirement that ρ þ p ≥ 0, where ρ and p are respectively the density and pressure of the fluid in its comoving frame
NEC violation ρ þ p < 0 provides a loophole in the singularity theorems that state that a collapsing universe ends at a singularity [1], and allows the possibility for a cosmological bounce [2]
Summary
An energy condition consists in assuming that matter satisfies “physical” properties, common to all forms of known matter. If one allows quantum fluctuations to overlap between different vacua, which can happen in a finite volume, one should consider instead the full partition function, involving all the vacua and allowing tunnelling between these In this case the competition between different saddle points leads to a convex effective potential [9], which restores symmetry instead of allowing SSB. Seff 1⁄2φ0 1⁄4 VUeff ðφ0; VÞ; ð1Þ where Ueff is the convex effective potential evaluated at the constant classical field φ0, and depends on V This nonextensive property was already mentioned in [13], and is at the origin of a nonstandard pressure, leading to the NEC violation. We start by defining the regime where tunnelling is expected to occur, and explain in Sec. III which saddle points dominate the partition function Z, in order to define the semiclassical approximation to calculate Z, and derive the effective action. Much work remains to fully elucidate this interesting effect, and we conclude by discussing future directions
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