Galilean-Invariant Scalar Fields Can Strengthen Gravitational Lensing

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 can enhance gravitational lensing. Because the enhancement appears at a fixed scaled location for dark matter halos of a wide range of masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.

Figure 1

Radial dependence of the fractional change in the lensing potential, Eq. (8), for a pointlike 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 $r_{*}\sim \mathrm{kpc}$, for a typical galaxy $r_{*}\sim \mathrm{Mpc}$, and for a galaxy cluster $r_{*}\sim 10\mathrm{Mpc}$. The peak change of $\sim 4\%$ is achieved for $r\simeq 0.37r_{*}$.

Figure 2

The fractional change in the tangential shear for three NFW halo profiles as a function of radius scaled by the halo’s virial radius ($r/r_{200}$), assuming $a_1=-1/2$, $a_2=1/2$, and $r_c=3000\mathrm{Mpc}$ in the scalar field equations. These plots describe halos with any virial mass $M_{200}\propto r_{200}^3$. The three concentrations plotted are $c=8$ (solid red line), $c=6$ (dashed blue line), and $c=4$ (dash-dotted black line).