F (T) gravity: effects on astronomical observations and Solar system experiments and upper bounds

Abstract

The effects of the f (T) gravity have previously been investigated and constrained by using perihelion advances. As an extension of previous work and as an attempt to find more stringent constraints on its parameters, we investigate here its effects on astronomical observations and on experiments conducted in the Solar system. The expression for f (T) contains a quadratic correction of α*T2 (where α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, in addition to the light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. From these results, we find qualitatively that the light deflection provides a unique bound on α, without dependence on Λ, and that the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observations and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper bounds quantitatively: |α| ≤ 1.2 × 102 m2 and |Λ| ≤ 1.8 × 10−43 m−2, which are at least 10 times tighter than the previous results.