Detectability of weak lensing modifications under Galileon theories

Theories of modified gravity attempt to reconcile physics at the largest and the smallest scales by explaining the accelerated expansion of our Universe without introducing the cosmological constant. One class of such theories, known as Galileon theories, predicts lensing potentials of spherically symmetric bodies, such as dark matter halos, to receive a featurelike modification at the 5% level. With the advent of next-generation photometric surveys, such modifications can serve as novel probes of modified gravity. Assuming an Large Synoptic Survey Telescope-like fiducial data set, we produce halo-shear power spectra for cold dark matter and Galileon scenarios and perform a Fisher analysis including cosmological, nuisance, and Galileon parameters to study the detectability of the aforementioned modifications. With the cold dark matter scenario as our null hypothesis, we conclude, with a number of idealized assumptions and approximations, that the detection of Galileon modifications could in principle reach up to $4\text{−}\sigma$ if present, or strongly excluded in a nondetection, with a tomography of four redshift bins and four mass bins, an Large Synoptic Survey Telescope-like set of survey parameters, and Planck priors on cosmological parameters.

Figure 1

Modification function $\tilde{R}(r)$, representing the fractional change in tangential shear generated by Galileon modification, for NFW halos of different masses and concentrations. Standard Galileon parametrization and scaling parameter $A_{\pi }=1$ are used.

Figure 2

The halo-halo, halo-shear, and shear-shear power spectra, respectively, for redshift bin $0.4<z<0.5$. For the middle panel, the one-halo (dashed) and the two-halo (dotted) contributions to the halo-shear power spectrum are presented.

Figure 3

Galileon modification for the one-halo halo-shear power spectrum $C_{h\kappa }^{1h}$ in redshift bin $0.4<z<0.5$. The top panel shows the LCDM $C_{h\kappa }^{1h}$ (black) and its Galileon modification (red), peaking at values of $l$ corresponding to halo-sized length scales. The bottom panel shows the fractional modification to the power spectrum, with a dashed horizontal line drawn at 1%.

Figure 4

Background (black), signal (red), and magnitude of $1\text{−}\sigma$ errors (blue) for different redshift and mass bins. Errors are calculated assuming 10 multipole bins per decade, i.e., $\mathrm{\Delta }\log l=0.1$. The bottom panel shows the resulting signal-to-noise ratio. We observe improvements in signal-to-noise ratio with higher redshifts and finer mass binnings.

Figure 5

$1\text{−}\sigma$ confidence ellipses for cosmological and nuisance parameters vs scaling parameter $A_{\pi }$, for bin width ($\mathrm{\Delta }\log M$) equal to 1 (green), 0.5 (blue), and 0.25 (red), respectively. With narrower mass bins, we observe tighter constraints on $A_{\pi }$, as well as fewer degeneracies between $A_{\pi }$ and systematics parameters.