Towards nonlinear axion-dilaton electrodynamics: How can axionic dark matter mimic dilaton-photon interactions?

Abstract

In the framework of the Einstein-Maxwell-axion-aether theory we establish the model, the Lagrangian of which contains the sin-type generalization of the term describing the axion-photon coupling, and the axionically induced cosine-type modification of the term attributed to the dilatonphoton interactions. The extension of the axion-dilaton-aether electrodynamics is inspired by the Jackson's idea concerning the internal symmetry of the equations of electromagnetism. The application of the extended theory to the anisotropic homogeneous cosmological model of the Bianchi-I type is considered. The exact solutions to the model evolutionary equations are obtained for the case, when the axionic dark matter is in the state of equilibrium, which is characterized by vanishing potential of the pseudoscalar field and its first derivative. The state of the axion-photon system, which is of a new type and is indicated as a dynamic equilibrium, is studied in the framework of electrodynamics with axionic non-linearity. We show that the nonlinear axion-photon interactions can mimic the dilaton-photon coupling. We discuss the stability of the model with respect to homogeneous fluctuations of the axion field.

Introductory Notes on Non‐linear Electrodynamics and its Applications

“…In addition to Born-Infeld and Heisenberg-Euler theories, there exists a variety of models of non-linear electrodynamics containing such instances as logarithmic, double-logarithmic, exponential, rational, arcsin, power-law, inverse, quasitopological and other NEDs (see e.g. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]). They have been created for applications in gravity and cosmology, as well as for a DOI: 10.1002/prop.202200092 gravity/CMT holographic description of certain strongly-coupled condensed matter systems.…”

“…In addition to Born-Infeld-like, Heisenberg-Euler-like and the generic NED, in the last more than two decades there has been a rather extensive activity in constructing a variety of other (heuristic) models of non-linear electrodynamics (see e.g. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]) and using them for applications in gravity, cosmology and CMT. For instance, NEDs coupled to gravity have been used to construct new black hole solutions and study their properties and stability (see e.g.…”