Résumé
Class. Quantum Grav. 30 (2013) 025002 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, and, up to second order in a small parameter, it expands at a
rate exactly equal to the one expected in a dust dominated
Friedmann-Lemaître-Robertson-Walker (FLRW) model with the equivalent,
smoothed, energy density. Therefore, the kinematics of both cosmologies are
identical up to the order of perturbation studied. 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, i.e. of order of a few percents at most.
Nevertheless, we show that, if this condition is violated, i.e. 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
identical to its FLRW counter-part (at the perturbative order considered). 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. Fully
non-perturbative treatments of the observables will be necessary to answer that
question.