Weak Lensing and Dark Energy

TL;DR

This paper assesses the power of upcoming weak-lensing surveys to constrain dark energy by measuring the convergence power spectrum $P_l^{\kappa}$, which depends on both the distance-redshift relation and the growth of structure. Using a Fisher-matrix forecast with a seven-parameter model including $\Omega_X$ and $w$, and incorporating Planck priors and photometric redshift information, the authors show that a 1000 deg$^2$ survey to $R=27$ could yield constraints on $\Omega_X$ and $w$ comparable to future SNe Ia and galaxy-count probes, provided systematic and theoretical uncertainties are controlled. They highlight the critical roles of the nonlinear matter power spectrum calibration and the source redshift distribution; they further show that weak-lensing tomography can substantially tighten constraints, while the potential to detect dark-energy clustering with lensing alone is limited by cosmic variance. The discussion emphasizes the need for accurate NLPS modeling, realistic treatment of covariances, and complementary probes to fully exploit weak lensing for precision cosmology. Overall, weak lensing emerges as a competitive, multi-probe approach to probing dark energy with significant potential once key systematics are addressed.

Abstract

We study the power of upcoming weak lensing surveys to probe dark energy. Dark energy modifies the distance-redshift relation as well as the matter power spectrum, both of which affect the weak lensing convergence power spectrum. Some dark-energy models predict additional clustering on very large scales, but this probably cannot be detected by weak lensing alone due to cosmic variance. With reasonable prior information on other cosmological parameters, we find that a survey covering 1000 sq. deg. down to a limiting magnitude of R=27 can impose constraints comparable to those expected from upcoming type Ia supernova and number-count surveys. This result, however, is contingent on the control of both observational and theoretical systematics. Concentrating on the latter, we find that the {\it nonlinear} power spectrum of matter perturbations and the redshift distribution of source galaxies both need to be determined accurately in order for weak lensing to achieve its full potential. Finally, we discuss the sensitivity of the three-point statistics to dark energy.

Figures (12)

• Figure 1: The assumed source galaxy distribution $n(z)$.
• Figure 2: Top panel: The convergence power spectrum for three pairs of ($\Omega_X$, $w$). The shaded region represents 1-$\sigma$ uncertainties (corresponding to $\Omega_X=0.7$, $w=-1$ curve) plotted at each $l$. The uncertainties at low $l$ are dominated by cosmic variance, and those at high $l$ by Poisson (shot) noise; see Eq. (\ref{['eq:Delta_P']}). We also show the contribution to $P_l^{\kappa}$ from the linear matter power spectrum only. Bottom Panel:$P_l^{\kappa}/\Delta P_l^{\kappa}$ ("signal-to-noise") for the convergence power spectrum for each individual $l$.
• Figure 3: The weight function $W^2(z)r(z)/H(z)$ for three pairs of ($\Omega_X$, $w$).
• Figure 4: The matter power spectrum at $z=0$ for three pairs of $(\Omega_X, w)$. Linear power spectrum corresponding to the fiducial spectrum is shown by the thin solid curve. Vertical lines delimit the interval which contributes significantly to the WL convergence power spectrum, roughly corresponding to $100\leq l \leq 10000$. It can be seen that the ability to determine cosmological parameters will depend critically upon the knowledge of the nonlinear power spectrum.
• Figure 5: Power spectrum of the convergence assuming matter power spectrum is a delta-function at $k_1$, shown for two different values of $k_1$. This shows the correspondence between physical and angular scales (for $z_s=1$ and our fiducial $\Lambda$CDM cosmology).