Cosmological perturbations in \bar{QCD}- inflation. Estimates confronting the observations, including BICEP2

We discuss a new scenario for early cosmology, when inflationary de Sitter phase dynamically emergent. This genuine quantum effect occurs as a result of dynamics of the topologically nontrivial sectors in a (conjectured) strongly coupled QCD- like gauge theory with scale ${\Lambda_{\overline{\mathrm{QCD}}}} \sim 10^{17}$ GeV in expanding universe. Inflaton in this ${\overline{\mathrm{QCD}}}$- inflation framework is an auxiliary non-propagating field, similar to an effective field known to emerge in topologically ordered condensed matter systems. Number of e-folds in the ${\overline{\mathrm{QCD}}}$-inflation framework is determined by the gauge coupling constant at the moment of inflation, and estimated as $N_{\rm inf}\sim \alpha^{-2}(H_0)\sim 10^2$. We analyze the equation of state in this framework at the end of inflation in terms of the gauge dynamics and confront our estimates with observations. We make predictions for the tensor tilt, $n_t \simeq -0.02$, the running of the tensor tilt $\alpha_t= {\partial n_t}/{\partial \ln k}\sim \alpha^4(H_0)\sim 10^{-4}$ and the running for the spectral index $\alpha_s= {\partial n_s}/{\partial \ln k}\sim \alpha^4(H_0)\sim 10^{-4}$ in terms of the same gauge coupling constant $\alpha(H_0)$, which is fixed in our framework by recent BICEP2 measurements of the tensor fraction $r\simeq 0.2$.