[Paper Review] How Tomographic Cosmic Shear Maps Lead to Constraints on Dark Energy Properties

Hu Zhan, Lloyd Knox|arXiv (Cornell University)|Nov 6, 2006

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates how cosmic shear tomography constrains dark energy by analyzing the sensitivity of shear power spectra to distance and growth factors. It shows that lensing kernel ratios enable distance ratio measurements without standard rulers, and that growth information is critical for breaking degeneracies, enabling absolute distance reconstruction when combined with parametric models of growth and distance evolution.

ABSTRACT

Using a number of numerical tests and analytic arguments we investigate how measurements of cosmic shear lead to constraints on dark energy. We find that, in contrast to the case with galaxy number density correlation functions, standard rulers in the matter power spectrum play no significant role. Sensitivity to distance ratios is provided by the ratios in the lensing kernel. An absolute distance scale can only be established by breaking a potential degeneracy between growth and distance which can be done if the growth-redshift relation and distance-redshift relations are parameterized with sufficiently few parameters. For the quality of dark energy determination, growth determination is primarily important because it improves the distance reconstructions. The information about dark energy in the growth-redshift relation is always of secondary importance though the amount it contributes is highly dependent on what priors are taken in the cosmological parameter space. We also explain the dependence of dark energy constraints from cosmic shear, relative distance measures (supernovae) and absolute distance measures (baryon acoustic oscillations) on assumptions about the mean curvature.

Motivation & Objective

• To clarify how cosmic shear two-point correlation functions constrain dark energy, contrasting with galaxy clustering and standard candles.
• To investigate the role of matter power spectrum features—especially standard rulers like baryon acoustic oscillations—in cosmic shear constraints.
• To determine how growth and distance information from shear data can be disentangled to reconstruct cosmological parameters.
• To assess the impact of model assumptions, particularly on curvature and parametric forms of growth and distance evolution.
• To compare the effectiveness of cosmic shear with supernovae and baryon acoustic oscillations in constraining dark energy under varying priors and assumptions.

Proposed method

• Uses numerical tests and analytic approximations with scale-free and CDM power spectra to isolate the effects of distance and growth on shear power spectra.
• Applies lensing kernel formalism to show that distance ratios are encoded in the kernel's redshift dependence, enabling relative distance constraints without standard rulers.
• Employs parametric models for growth and distance-redshift relations to break the degeneracy between amplitude normalization and distance scale in shear power spectra.
• Compares constraints from cosmic shear with those from BAO and supernovae, analyzing sensitivity to curvature and prior assumptions.
• Uses signal-to-noise analysis to evaluate the impact of nonlinear evolution and shot noise on shear-based distance reconstruction.
• Analyzes the role of non-linear evolution in boosting signal-to-noise on small scales, particularly in noisy regimes.

Experimental results

Research questions

• RQ1 How do cosmic shear maps constrain dark energy parameters, and what mechanisms underlie this sensitivity?
• RQ2 To what extent do standard rulers in the matter power spectrum (e.g., baryon acoustic oscillations) contribute to dark energy constraints from cosmic shear?
• RQ3 How does the lensing kernel's dependence on distance ratios enable reconstruction of relative distance measures without relying on standard rulers?
• RQ4 What role does the growth factor play in improving distance reconstruction, and how does it break degeneracies in shear power spectra?
• RQ5 How do assumptions about spatial curvature and parametric forms of $D(z)$ and $G(z)$ affect the precision of dark energy constraints from cosmic shear?

Key findings

• Standard rulers in the matter power spectrum, such as baryon acoustic oscillations, play no significant role in cosmic shear-based dark energy constraints, even in the nonlinear regime.
• The lensing kernel's dependence on distance ratios enables direct measurement of relative distance ratios $D_A(z_1)/D_A(z_2)$, forming the primary route to distance constraints.
• Absolute distance scale reconstruction is only possible by breaking the degeneracy between distance and growth amplitude, which requires parametric modeling of $G(z)$ or $D_A(z)$.
• Growth information is more critical than distance information for constraining dark energy, as it improves distance reconstruction precision, even though the direct dark energy signal in $G(z)$ is secondary.
• In the absence of noise, nonlinear evolution features do not enhance constraints from cosmic shear, but in realistic, noisy conditions, they boost signal-to-noise and tighten constraints.
• Cosmic shear constraints are more sensitive to shot noise than BAO or supernova constraints, and nonlinear evolution can improve shear-based distance reconstruction in noisy regimes, contrary to noise-free expectations.