Cosmic inflation, a period of accelerated expansion in the early universe,
can give rise to large amplitude ultra-large scale inhomogeneities on distance
scales comparable to or larger than the observable universe. The cosmic
microwave background (CMB) anisotropy on the largest angular scales is
sensitive to such inhomogeneities and can be used to constrain the presence of
ultra-large scale structure (ULSS). We numerically evolve nonlinear
inhomogeneities present at the beginning of inflation in full General
Relativity to assess the CMB quadrupole constraint on the amplitude of the
initial fluctuations and the size of the observable universe relative to a
length scale characterizing the ULSS. To obtain a statistically significant
number of simulations, we adopt a toy model in which inhomogeneities are
injected along a preferred direction. We compute the likelihood function for
the CMB quadrupole including both ULSS and the standard quantum fluctuations
produced during inflation. We compute the posterior given the observed CMB
quadrupole, finding that when including gravitational nonlinearities, ULSS
curvature perturbations of order unity are allowed by the data, even on length
scales not too much larger than the size of the observable universe. Our
results illustrate the utility and importance of numerical relativity for
constraining early universe cosmology.Comment: 14 pages, 6 figures v3: Clarifications added regarding the generality
of results - conclusions unchanged, version accepted for publication in PRD,
v2: updated with minor clarifications, submitte
