Measuring the dark side (with weak lensing)

TL;DR

Measuring the dark side (with weak lensing) develops a practical framework to test dark energy and modified gravity by parameterizing the expansion history with $H(z)$ and first-order perturbations via $Q$, $\eta$, and $\Sigma$, and by introducing the growth index $\gamma$. The authors argue that weak lensing, especially tomographic surveys like DUNE, can constrain $\gamma$ and $\Sigma$ with high precision, enabling discrimination between LCDM, DGP, and scalar-tensor theories. They provide explicit formulas for several models (LCDM, Quintessence, DGP, $\Lambda$DGP, scalar-tensor) and forecast that a DUNE-like survey could determine $\gamma$ to ~0.015–0.036 and place strong bounds on $\Sigma$ across redshift, with capabilities to rule out DGP at high significance. They also discuss the interpretive power of detecting or constraining anisotropic stress and modified Poisson terms as diagnostic handles on the underlying physics.

Abstract

We introduce a convenient parametrization of dark energy models that is general enough to include several modified gravity models and generalized forms of dark energy. In particular we take into account the linear perturbation growth factor, the anisotropic stress and the modified Poisson equation. We discuss the sensitivity of large scale weak lensing surveys like the proposed DUNE satellite to these parameters. We find that a large-scale weak-lensing tomographic survey is able to easily distinguish the Dvali-Gabadadze-Porrati model from LCDM and to determine the perturbation growth index to an absolute error of 0.02-0.03.

Figures (11)

• Figure 1: The $\eta$ parameter of the anisotropic stress as a function of $a$ for $\Omega_{m}=0.3$. The black solid line shows the actual value while the red dashed curve shows the recovered $\eta$ using the fitting formula for $\gamma$.
• Figure 2: The growth parameter $\gamma$ of DGP, comparison between the fitting formula (red dashed curve) and the numerical result (black solid line) for $\Omega_{m}=0.3$.
• Figure 3: The $Q$ parameter of DGP, $\Omega_{m}=0.3$. The black solid curve shows the exact value while the red dashed line is the result recovered with the fitting formula for $\gamma$.
• Figure 4: FOM for $w_{0},w_{p}$vs. marginalized parameters of the model GDE1.
• Figure 5: Confidence regions at 68% for the benchmark survey $z_{mean}=0.9,d=35$ (outer contour) and for $d=50,75$ (inner contours).