J. -P. Bruneton, J. Larena
We explore observables in a lattice Universe described by a recently found solution to Einstein field equations. This solution models a regular lattice of evenly distributed objects of equal masses. This inhomogeneous solution is perturbative, exact at second order in a small parameter, and expands at a rate exactly equal to the one expected in a dust dominated Friedmann-Lema\^itre-Robertson-Walker (FLRW) model with the equivalent, smoothed, energy density. Therefore, the kinematics of both cosmologies are identical. Looking at the behaviour of the redshift and angular distance, we find a condition on the compactness of the objects at the centre of each cell under which corrections to the FLRW observables remain small. Nevertheless, we show that, if this condition is violated, namely, if the objects are too compact, our perturbative scheme breaks down as far as the calculations of observables are concerned, even though the kinematics of the lattice remains exactly identical to its FLRW counter-part. This may be an indication of an actual fitting problem, i.e. a situation in which the FLRW model obtained from lightcone observables does not correspond to the FLRW model obtained by smoothing the spatial distribution of matter.
View original:
http://arxiv.org/abs/1208.1411
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