  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.
