Constraining cosmological ultralarge scale structure using numerical relativity
AbstractCosmic inflation, a period of accelerated expansion in the early universe, can give rise to large amplitude ultralarge 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 ultralarge 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 meaningful ensemble 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. To demonstrate the robustness of our conclusions, we also explore a semianalytic model for the ULSS which reproduces our numerical results for the case of planar symmetry, and which can be extended to ULSS with a three-dimensional inhomogeneity structure. Our results illustrate the utility and importance of numerical relativity for constraining early universe cosmology.