Light deflection in Weyl gravity: constraints on the linear parameter

TL;DR

This paper constrains the linear parameter of Weyl gravity using light deflection experiments, including solar system and gravitational lensing observations, providing tighter bounds than previous galactic rotation curve fits.

Contribution

It provides new upper bounds on the Weyl gravity linear parameter from light deflection data, improving upon previous estimates and analyzing its effects on lensing phenomena.

Findings

CASSINI data constrains Weyl parameter to ~10^{-19} m^{-1}

Gravitational lensing bounds restrict negative Weyl parameter to ~-10^{-31} m^{-1}

Weyl parameter effects are small and not easily mimicked by rescaling mass or radius

Abstract

Light deflection offers an unbiased test of Weyl's gravity since no assumption on the conformal factor needs to be made. In this second paper of our series ``Light deflection in Weyl gravity'', we analyze the constraints imposed by light deflection experiments on the linear parameter of Weyl's theory. Regarding solar system experiments, the recent CASSINI Doppler measurements are used to infer an upper bound, $\sim 10^{-19} $m$^{-1}$, on the absolute value of the above Weyl parameter. In non-solar system experiments, a condition for unbound orbits together with gravitational mirage observations enable us to further constrain the allowed negative range of the Weyl parameter to $\sim -10^{-31} $m$^{-1}$. We show that the characteristics of the light curve in microlensing or gravitational mirages, deduced from the lens equation, cannot be recast into the General Relativistic predictions by a simple rescaling of the deflector mass or of the ring radius. However, the corrective factor, which depends on the Weyl parameter value and on the lensing configuration, is small, even perhaps negligible, owing to the upper bound inferred on the absolute value of a negative Weyl parameter. A statistical study on observed lensing systems is required to settle the question. Our Weyl parameter range is more reliable than the single value derived by Mannheim and Kazanas from fits to galactic rotation curves, $\sim +10^{-26}\ $m$^{-1}$. Indeed, the latter, although consistent with our bounds, is biased by the choice of a specific conformal factor.