Vacuum Brans-Dicke theory in the Jordan and Einstein frames: can they be distinguished by lensing?

TL;DR

This paper investigates whether weak field lensing observations can distinguish between the Jordan and Einstein frames in vacuum Brans-Dicke theory, highlighting differences in predictions and the experimental precision required.

Contribution

It demonstrates that the weak field lensing predictions differ between the two conformal frames, providing a potential method to experimentally distinguish them.

Findings

WFL observables differ between frames for the Brans-Dicke class 1 solution.

Cassini data constrains the precision needed to differentiate the frames.

Differences in total magnification factors are significant for certain parameter ranges.

Abstract

Vacuum Brans-Dicke theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. Despite this, the conformal frames are inequivalent describing different geometries. It is shown that the predictions of the weak field lensing (WFL) observables in the EF are different from those recently obtained in the JF for the vacuum Brans-Dicke class 1 solution. The value of the Brans-Dicke coupling parameter $\omega$ from the Cassini spacecraft experiment reveals the degree of accuracy needed to experimentally distinguish the WFL measurements including the total magnification factor in the two frames.