Nonlocal gravity and structure in the Universe

The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the Universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and an estimator of gravity $E_G$ that combines spectroscopic information with lensing. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 6.8 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1 sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.

Figure 1

Two functions that quantify deviations from general relativity as defined in Eq. (4). The growth of structure is sensitive to $\mu$ while gravitational lensing, which is determined by photon geodesics, is sensitive to $\mathrm{\Sigma }$.

Figure 2

The growth function $D(z)$ in both nonlocal gravity and general relativity with a cosmological constant.

Figure 3

${\xi }_{+}$ in three different redshift bins as measured in CFHTLenS [25] (black points with error bars). Top and bottom panels show the correlation function in the high and low redshift bins, respectively, while the middle panel shows the cross spectrum. Both model have the redshift-distance relation corresponding to Planck parameters.

Figure 4

The logarithmic derivative of the growth function as a function of redshift; this is directly measured in spectroscopic surveys capable of probing redshift space distortions. Data points come from the WiggleZ survey [27], 2dF [28], BOSS [29] and SDSS LRGs [30].

Figure 5

Estimator of gravity, $E_G$, as a function of redshift in standard and modified gravity models. The data point is from Ref. [33].