[Paper Review] The Non-Linear Fisher Information content of cosmic shear surveys

Olivier Doré, Tingting Lu+1 more|ArXiv.org|May 4, 2009

Statistical and numerical algorithms1 references3 citations

TL;DR

This paper quantifies the non-linear Fisher information content in cosmic shear surveys using N-body simulations, demonstrating that non-linear growth induces non-Gaussianity that reduces the Dark Energy figure of merit by a factor of 4 in ideal conditions—though realistic noise reduces this to ~1.5×. It introduces a new covariance matrix estimation scheme that improves accuracy by an order of magnitude with only twice as many simulations as prior methods.

ABSTRACT

We quantify the Fisher information content of the cosmic shear survey two-point function as a function of noise and resolution. The two point information of dark matter saturates at the trans-linear scale. We investigate the impact of non-linear non-Gaussianity on the information content for lensing, which probes the same dark matter. To do so we heavily utilize N-body simulations in order to probe accurately the non-linear regime. While we find that even in a perfect survey, there is no clear saturation scale, we observe that non-linear growth induced non-Gaussianity could lead to a factor of ~4 reduction for the common Dark Energy figure of merit. This effect is however mitigated by realistic levels of shot noise and we find that for future surveys, the effect is closer to a factor of 1.5. To do so, we develop a new scheme to compute the relevant covariant matrix. It leads us to claim an unbiased estimator with an order of magnitude improvement in accuracy with only twice more simulations than previously used. Finally, we evaluate the error on the errors using bootstrap methods.

Motivation & Objective

• To quantify the Fisher information content of cosmic shear surveys in the non-linear regime, particularly focusing on the impact of non-Gaussianity induced by structure growth.
• To assess whether there exists a saturation scale in the Fisher information for the two-point shear function, which would imply diminishing returns from higher resolution surveys.
• To develop a more accurate method for estimating the covariance matrix of cosmic shear power spectra using N-body simulations.
• To evaluate the error on the error using bootstrap techniques, improving confidence in forecast uncertainties.
• To extend findings to CMB lensing, assessing the relevance of non-linear effects in that context.

Proposed method

• Uses large-scale N-body simulations to model the non-linear evolution of dark matter and cosmic shear in the fully non-linear regime.
• Develops a novel scheme for computing the covariance matrix of the shear two-point function, enabling an order-of-magnitude improvement in accuracy over previous methods.
• Applies a bootstrap resampling technique to estimate the error on the figure of merit (FoM), quantifying uncertainty in forecast precision.
• Projects Fisher information onto the amplitude and Dark Energy figure of merit, analyzing its evolution with angular scale (ℓ_max).
• Compares results across different survey configurations, including optical surveys and CMB lensing, to assess the robustness of non-linear effects.
• Neglects baryonic physics but accounts for survey volume effects and shot noise, focusing on intrinsic non-Gaussianity from non-linear structure formation.

Experimental results

Research questions

• RQ1 Does the Fisher information content of cosmic shear surveys saturate at a specific scale due to non-linear structure growth?
• RQ2 To what extent does non-linear, non-Gaussian structure formation reduce the constraining power for Dark Energy parameters compared to Gaussian forecasts?
• RQ3 How does realistic shot noise affect the impact of non-Gaussianity on the figure of merit in future surveys?
• RQ4 Can a new covariance matrix estimation technique significantly improve the accuracy of error forecasts with only a modest increase in simulation count?
• RQ5 How do non-linear effects manifest in CMB lensing, and is the information saturation effect observable in that context?

Key findings

• Non-linear growth of structures induces non-Gaussianity that reduces the Dark Energy figure of merit by a factor of 4 in a noiseless, ideal survey.
• With realistic levels of shot noise, the reduction in the figure of merit is mitigated to approximately a factor of 1.5, indicating a more modest impact in practice.
• The proposed covariance matrix estimation method achieves an order-of-magnitude improvement in accuracy over previous methods, using only twice as many simulations.
• The error on the error, estimated via bootstrap resampling, is found to be around 25% at large scales and sub-percent at small scales, indicating high reliability of the uncertainty estimates.
• The information content in the fully non-linear regime exhibits sub-Gaussian scaling, suggesting that this regime holds significant untapped information for cosmological constraints.
• A saturation effect in Fisher information is not clearly observed in the cosmic shear two-point function, even in the absence of noise, indicating no sharp scale beyond which additional resolution yields diminishing returns.