Backreaction and FRW consistency conditions

Abstract

If the FRW metric is a good approximation on large scales, then the distance and the expansion rate, as well different notions of distance, satisfy certain consistency conditions. We fit the JLA SNIa distance data to determine the expected amplitude of the violation of these conditions if accelerated expansion is due to backreaction. Adding cosmic clock and BAO expansion rate data, we also model-independently determine the current observational limits on such violation. We find that the predicted maximum backreaction amplitude |kH| ≲ 1 (95% C.I.) is of the same order as the current observational constraints |kH| ≲ 1, the precise numbers depending on the adopted fitting method (polynomials or splines) and stellar population evolution model. We also find that constraints on the value of H0 determined from expansion rate data are sensitive to the stellar evolution model. We forecast constraints from projected LSST+Euclid-like SNIa plus Euclid galaxy differential age data. We find improvement by factor of 6 for the backreaction case and 3 for the model-independent case, probing an interesting region of possible signatures.