A quantum gravitational inflationary scenario in Bianchi-I spacetime

TL;DR

This paper explores how loop quantum cosmology modifies the early universe's dynamics in Bianchi-I spacetime, resolving singularities, promoting isotropization, and affecting inflation, with results showing bounded energy densities and non-monotonic inflation dependence on initial anisotropy.

Contribution

It demonstrates that quantum gravitational effects in loop quantum cosmology replace singularities with bounces and allow for isotropization and viable inflation from highly anisotropic initial conditions.

Findings

Classical singularity replaced by a quantum bounce.

Energy density and shear remain bounded during evolution.

Inflation amount does not monotonically depend on initial anisotropy.

Abstract

We investigate the $\phi^2$ inflationary model in the Bianchi-I spacetime using effective spacetime description of loop quantum cosmology to understand the issues of the resolution of initial singularity, isotropization, effect of anisotropies on amount of inflation, and the phase space attractors in the presence of non-perturbative quantum gravitational modifications. A comparative analysis with the classical theory by including more general initial conditions than the ones previously considered in the latter is also performed. We show that, in general, the classical singularity is replaced by a bounce of the mean scale factor in loop quantum cosmology. Due to the underlying quantum geometric effects, the energy density of the inflaton and the anisotropic shear remain bounded throughout the non-singular evolution. Starting from arbitrary anisotropic initial conditions, a loop quantum universe isotropizes either before or soon after the onset of slow-roll inflation. We find a double attractor behavior in the phase space dynamics of loop quantum cosmology, similar to the one in classical theory, but with some additional subtle features. Quantum modifications to the dynamical equations are such that, unlike the classical theory, the amount of inflation does not monotonically depend on the initial anisotropy in loop quantum cosmology. Our results suggest that a viable non-singular inflationary model can be constructed from highly anisotropic initial conditions in the Planck regime.