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 ${\mathbb{S}}_{{\kappa }^{-1}}^1$. 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 $\mathrm{\Phi }(x)$. 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.