A quantum gravitational inflationary scenario in Bianchi-I spacetime
  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.
