Phenomenological constraints on Lemaître-Tolman-Bondi cosmological inhomogeneities from solar system dynamics

Abstract

We, first, analytically work out the long-term, i.e. averaged over one orbital revolution, perturbations on the orbit of a test particle moving in a local Fermi frame induced therein by the cosmological tidal effects of the inhomogeneous Lemaître-Tolman-Bondi (LTB) model. The LTB solution has recently attracted attention, among other things, as a possible explanation of the observed cosmic acceleration without resorting to dark energy.Then, we phenomenologically constrain both the parameters and of the LTB metric in the Fermi frame by using different kinds of solar system data. The corrections Δϖ̇ to the standard Newtonian/Einsteinian precessions of the perihelia of the inner planets recently estimated with the EPM ephemerides, compared to our predictions for them, yield preliminarily K1 = (4±8) × 10−26 s−2, K2 = (3±7) × 10−23 s−2. The residuals of the Cassini-based Earth-Saturn range, compared with the numerically integrated LTB range signature, allow to preliminarily obtain K1 ≈ K2 ≈ 10−27 s−2. Actually, the LTB effects should be explicitly modeled in the ephemerides softwares, so that the entire planetary and spacecraft data sets should be accordingly re-processed. The LTB-induced distortions of the orbit of a typical object of the Oort cloud with respect to the commonly accepted Newtonian picture, based on the observations of the comet showers from that remote region of the solar system, point towards K1 ≈ K2≲10−30−10−32 s−2. Such figures have to be compared with those inferred from cosmological data which are of the order of K1 ≈ K2 = −4 × 10−36 s−2.