Void lensing as a test of gravity

We propose a consistency test of gravity based on the weak lensing signal of cosmic voids. For a given void profile, as traced by galaxies, the lensing signal can vary in different gravity theories. Thus the comparison of the lensing shear profile of such voids with the general relativistic prediction can test for deviations from general relativity (GR). For concreteness, we calculate the expected lensing signal in two gravity theories involving scalar fields with derivative couplings. We find that the scalar field has the potential to boost the tangential shear both within and outside the void radius. Reversing the method, one can infer the void central density parameter from the lensing signal, and compare to the value estimated independently using the galaxy tracer profiles of voids. Hence, one can check for consistency between the behavior of light and matter under the assumption of GR. We use voids traced by luminous red galaxies in SDSS to demonstrate our methodology, finding that the void central density parameter can shift from its GR value by up to 20% in some Galileon gravity models. Although Galileon gravity is now disfavored as a source of cosmic acceleration by other data sets, the methods we demonstrate here can be used to test for more general fifth force effects with upcoming void lensing data.

Figure 1

Upper panel: The void density profile of Eq. (17), shown here with a central depth ${\delta }_v=-0.5$ and the fiducial parameters of Eq. (18). Lower panel: Corresponding tangential shear profiles in GR, the cubic Galileon and the quartic Galileon gravity theories. Recall (from Sec. 2c) that after applying the tracker ansatz the cubic Galileon has no free parameters, whilst the quartic Galileon has one; we take this here to be $\xi =1.9$. This figure is shown at $z=0$.

Figure 2

The effect of varying $\xi$ in the quartic Galileon model; in the cubic Galileon model this parameter is fixed to $\xi \sim 2.1$. The void density profile and parameters are the same as in Fig. 1.

Figure 3

Upper panel: The cubic density profile of Eq. (15). Lower panel: The corresponding shear profiles in GR and the cubic Galileon model. Overplotted are SDSS void lensing measurements.

Figure 4

The best-fit values of the void central density parameter ${\delta }_v$, as inferred from the lensing profiles of the SDSS DR7-Full LRG catalog. The black curve is for GR, while the dashed, blue curve assumes the cubic Galileon model. We assume that the relation of galaxies to mass is not altered in modified gravity, based on simulation studies (Barreira et al., 2015).

Figure 5

Upper panel: Realizations of the density profile in Eq. (17), with varying values of $s_2$. This parameter mainly controls the height of the compensating ridge. Lower panel: Corresponding shear profiles in GR. The lensing amplitude and the location of the minimum of the signal are affected substantially by the ridge height.

Figure 6

Variation of lensing tangential shear with void depth and gravity model, for the density profile of Eq. (17), shown for $z=0$, $R_V=23\mathrm{Mpc}$. One can see the onset of pathological behavior for the cubic Galileon case with ${\delta }_v=-0.7$ (top panel, red curve). All void profile parameters except ${\delta }_v$ are held at the default values of Eq. (18).

Figure 7

Parameter space showing the onset of pathologies in the cubic Galileon, for the density profile of Eq. (17). The color map indicates the radius of the pathological region, in units of $R_V$. For example, for the dark blue regions no pathologies are present anywhere throughout the void; for the reddest region in the lower right corner, pathologies are present for all radii $0<R_{\mathrm{sing}}\lesssim 0.8$, where $R_{\mathrm{sing}}=r_{\mathrm{sing}}/R_V$.