Cosmological Magnetic Field and Dark Energy as two sides of the same coin

Abstract: It has been recently argued \cite{Barvinsky:2017lfl} that the de Sitter phase in cosmology might be naturally generated as a result of dynamics of the topologically nontrivial sectors in a strongly coupled QCD-like gauge theory in expanding universe. It is known that the de Sitter phase is realized in the history of our Universe twice: the first occurrence is coined as the inflation, while the second time (which is occurring now) is dubbed as the dark energy (DE). The crucial element of the proposal \cite{Barvinsky:2017lfl} is the presence of a nontrivial gauge holonomy which is the source of the vacuum energy leading to the de Sitter behaviour. It has been also argued that the anomalous coupling of the system with the Standard Model (SM) particles leads to the reheating epoch in case of the {\it inflationary} phase. A similar anomalous coupling of the system with the Maxwell $E&M$ field during the {\it DE epoch} generates the cosmological magnetic field. The intensity of the field is estimated on the level of $10^{-10}$G while the corresponding correlation length reaches the scale of the visible Universe.