Inflaton as an auxiliary topological field in a QCD-like system

Abstract

We propose a new scenario for early cosmology, where inflationary de Sitter phase dynamically occurs. The effect emerges as a result of dynamics of the topologically nontrivial sectors in expanding universe. Technically the effect can be described in terms of the auxiliary fields which effectively describe the dynamics of the topological sectors in a gauge theory. Inflaton in this framework is an auxiliary topological non-propagating field with no canonical kinetic term, similar to known topologically ordered phases in condensed matter systems. We explain many deep questions in this framework using the so-called weakly coupled "deformed QCD" toy model.While this theory is weakly coupled gauge theory, it preserves all the crucial elements of strongly interacting gauge theory, including confinement, nontrivial $\theta$ dependence, degeneracy of the topological sectors, etc. We discuss a specific realization of these ideas using a scaled up version of QCD, coined as \qcd, with the scale M_{PL}\gg \Lbar\gg \sqrt[3]{M_{EW}^2M_{PL}}\sim 10^8 {\mathrm{GeV}}. If no other fields are present in the system de Sitter phase will be the final destination of evolution of the universe. If other interactions are present in the system, the inflationary de Sitter phase lasts for a finite period of time. The inflation starts from the thermal equilibrium state long after the \qcd -confinement phase transition at temperature T_{i}\sim \Lbar\sqrt{\frac{\Lbar}{M_{PL}}}. The end of inflation is triggered by the coupling with gauge bosons from the Standard Model. The corresponding interaction is unambiguously fixed by the triangle anomaly. Number of e-folds in the \qcd-inflation framework is determined by the gauge coupling constant at the moment of inflation, and estimated as N_{\rm inf}\sim \alpha_s^{-2}\sim 10^2.Comment: new references and comment

Topological Casimir effect in a quantum LC circuit: Real-time dynamics

“…The second instance where the vacuum energy plays a dominant role corresponds to the present epoch when the vacuum energy is identified with the so-called dark energy ρ DE which constitutes almost 70% of the critical density. In the proposal [34][35][36] the vacuum energy density can be estimated as ρ DE ∼ HΛ 3 QCD ∼ (10 −4 eV) 4 , which is amazingly close to the observed value.…”

“…The unique feature of the system where an extra energy is not related to any physical propagating degrees of freedom was the main motivation for the proposal [34][35][36] that the vacuum energy of the Universe may have, in fact, precisely such non-dispersive nature.…”

“…The main argument behind this interpretation is the observation that the integer parameter k which enters (34) originally appeared in the Euclidean path integrals as the instanton action describing the interpolation between two topologically distinct states according to Eq. (4).…”

“…Furthermore, the radiation from the vacuum in a time-dependent background (which is the main subject of this work) is very similar in all respects to the radiation which might be responsible for the end of inflation in that proposal. The cosmological ideas of the proposal [34][35][36] can hopefully be tested in a tabletop experiment (which is the subject of the present paper) where the vacuum energy in a time-dependent background can be transferred to real propagating degrees of freedom as described in Section V. In cosmology, the corresponding period plays a crucial role and calls the reheating epoch which follows inflation with the vacuum energy being the dominant component of the Universe.…”

“…Essentially, the proposal [34][35][36] identifies the observed vacuum energy with the topological Casimir type energy, which however is originated not from the dynamics of the physical propagating degrees of freedom, but rather from the dynamics of the topological sectors that are always present in gauge systems, and which are highly sensitive to arbitrary large distances. An explicit manifestation of this "non-dispersive" nature of the vacuum energy in the model considered in the present work is the "wrong sign" of the kinetic term in the effective Lagrangians describing the dynamics of the auxiliary no-propagating fields (23,31).…”