Galilean-invariant scalar fields can strengthen gravitational lensing

TL;DR

This Letter points out that a massive-gravity-inspired coupling of Galileons to stress energy can enhance gravitational lensing and says that stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.

Abstract

The mystery of dark energy suggests that there is new gravitational physics on long length scales. Yet light degrees of freedom in gravity are strictly limited by Solar System observations. We can resolve this apparent contradiction by adding a Galilean-invariant scalar field to gravity. Called Galileons, these scalars have strong self-interactions near overdensities, like the Solar System, that suppress their dynamical effect. These nonlinearities are weak on cosmological scales, permitting new physics to operate. In this Letter, we point out that a massive gravity inspired coupling of Galileons to stress energy gravity can have a surprising consequence: enhanced gravitational lensing. Because the enhancement appears at a fixed scaled location for a wide range of dark matter halo masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.

Figures (1)

• Figure 1: Radial dependence of the fractional change in the lensing potential, Eqn. \ref{['rat']}, for a point-like central mass, assuming $a_1=-1/2$ and $a_2=1/2$ (which gives $\alpha=1$, $\beta=1$, $\eta=1$, $\mu=3/2$, and $\nu=1/2$) in the scalar field equations. The radius is scaled by $r_* = (r_s r_c^2)^{1/3}$, where $r_s$ is the Schwarzschild radius of the source and $r_c$ is the Compton wavelength (or inverse mass) of the graviton, typically $\sim c/H_0$. For the sun, $r_* \sim$ kpc; for a typical galaxy $r_* \sim$ Mpc; and for a galaxy cluster, $r_* \sim$ 10 Mpc. The peak change of $\sim$4% is achieved for $r\simeq0.33\, r_*$