Sustaining quasi de-Sitter inflation with bulk viscosity

Abstract

We here investigate bulk-viscosity driven quasi de-Sitter inflation, that is, the period of accelerated expansion in the early universe during which $-\dot{H}\ll H^2$, with $H(t)$ being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics that takes into account non-equilibrium effects associated to bulk viscosity that may be present as the early universe undergoes an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring to introduce additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk-viscosity pressure turns out to be time-dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in presence of bulk-viscosity pressure. In addition, we construct a fluid description of inflation and demonstrated that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely, the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations finding good agreement in most cases.