Topological Inflation
  We discuss a novel scenario for early cosmology, when the inflationary
quasi-de Sitter phase dynamically originates from the initial quantum state
represented by the microcanonical density matrix. This genuine quantum effect
occurs as a result of the dynamics of the topologically nontrivial sectors in a
(conjectured) strongly coupled QCD-like gauge theory in expanding universe. The
crucial element of our proposal is the presence in our framework of a
nontrivial $\mathbb{S}^1$ which plays the dual role in construction: it defines
the periodic gravitational instanton (on the gravity side) and it also defines
a nontrivial gauge holonomy (on the gauge side) generating the vacuum energy.
The effect is global in nature and cannot be formulated in terms of a gradient
expansion in an effective local field theory. We also discuss a graceful exit
from holonomy inflation due to the helical instability. The number of e-folds
in the holonomy inflation framework is determined by the gauge coupling
constant at the moment of inflation, and estimated as $N_{\rm infl}\sim
\alpha^{-2}(H_0)\sim 10^2$. We also comment on the relation of our framework
with the no-boundary and tunneling cosmological proposals and their recent
criticism.
