Dynamical de Sitter phase and nontrivial holonomy in strongly coupled
  gauge theories in expanding Universe
  We discuss a new scenario for early cosmology when the inflationary de Sitter
phase emerges dynamically. This genuine quantum effect occurs as a result of
dynamics of the topologically nontrivial sectors in a strongly coupled QCD-
like gauge theory in an expanding universe. We test these ideas by explicit
computations in hyperbolic space $ \mathbb{H}^3_{\kappa}\times
\mathbb{S}^1_{\kappa^{-1}}$. We argue that the key element for this idea to
work is the presence of nontrivial holonomy computed along
$\mathbb{S}^1_{\kappa^{-1}}$. The effect is non-local in nature, non-analytical
in coupling constant and can not be described in terms of any local propagating
degree of freedom such as scalar inflaton field $\Phi(x)$. We discuss some
profound phenomenological consequences of this scenario for inflationary
cosmology. We also suggest to test these ideas in a tabletop experiment by
measuring some specific corrections to the Casimir pressure in the Maxwell
theory formulated on a topologically nontrivial manifold.
