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

TL;DR

This paper investigates how inhomogeneous LTB cosmological models affect solar system dynamics and uses observational data to constrain their parameters, providing limits much tighter than cosmological estimates.

Contribution

It analytically derives the long-term orbital perturbations caused by LTB inhomogeneities and constrains their parameters using solar system data, a novel approach linking cosmology and local dynamics.

Findings

Constraints on LTB parameters are tighter than cosmological estimates.

Orbital precession data limit K_1 and K_2 to 10^-27 s^-2.

Oort cloud orbit distortions suggest even smaller K_1/2 values.

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 Lemaitre-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 K_1 = -\ddot R/R and K_2 = -\ddot R^'/R^' of the LTB metric in the Fermi frame by using different kinds of solar system data. The corrections $\Delta\dot\varpi$ 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 K_1 = (4+8) 10^-26 s^-2, K_2 = (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 obtain K_1/2 = 10^-27 s^-2. 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 K_1/2 <= 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 \approx K2 = -4 10^-36 s^-2.