The axion coupling accelerates the Universe through PT-symmetric phases

TL;DR

The paper investigates whether a PT-symmetric (non-Hermitian) phase of gravity can regularize infrared singularities in a string-inspired axion Chern–Simons model when gravity is included from the start. Using the Wetterich FRG with a single-metric Einstein–Hilbert truncation, it derives a coupled system for the axion, photon, and graviton anomalous dimensions and shows that gravity shifts but does not remove the Landau-pole-like singularities in the axion coupling. The authors argue that the PT continuation remains a consistent resolution, potentially realizing a repulsive gravity phase at cosmological scales and offering a mechanism for late-time acceleration within a CS-axion framework. They also provide string-theory motivated estimates for coupling magnitudes, illustrating that the axion–photon mixing is typically small relative to gravitational dressings in the considered regimes. Overall, the results bolster the conjecture that PT-symmetric phases of gravity play a role in the cosmological evolution predicted by the String-inspired Running Vacuum Model (StRVM).

Abstract

The conjecture by two of the authors (N.E.M. and S.S.) that a \cPT-symmetric phase plays a role in understanding singular renormalisation group (RG) flows for a Chern-Simons (CS) gauge theory of axions, has been reexamined and significantly improved. We have used the more complete Wetterich equation, which includes gravitational couplings in a systematic way from the start, to understand the emergence of this phase. The singular structure of the RG flows has persisted on including gravitational-couplings, thereby offering further support to the conjecture that \cPT -symmetric phases of (repulsive) gravity characterise string-effective CS gravitational theories, where the axion is the massless string-model independent axion, which can also play a role of a totally-antisymmetric torsion degree of freedom. This has suggested a novel interpretation of the currently observed acceleration of the expansion of the Universe in terms of such a phase at large (cosmological) scales.

Figures (1)

• Figure 1: Left panel: The FRG beta function $\beta_g \equiv \partial_t g^2$ of the Hermitian axion CS electrodynamics theory Eichhorn:2012uv, exhibiting a singular behavior at a finite running coupling $g \equiv (4\pi^2\,f_a)^{-1}$, as well as a fixed point behavior, characterised by the existence of a trivial fixed point at zero coupling, and a non-trivial one at strong coupling, $g_\star^2 \gg 1$. Right Panels: Nonperturbative RG beta function for non-Hermitian case as a function of $\tilde{g}^2$, where $\tilde{g} = i g$. The behaviour is qualitatively different from the Hermitian beta function Eichhorn:2012uv. The area included in the red rectangle includes a nontrivial fixed point (apart from the trivial one at zero coupling), which is indicated explicitly in the lower left panel. Figure synthesized from relevant graphs in Eichhorn:2012uv and Mavromatos:2024ozk.