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Measuring cosmological parameters with galaxy surveys

Max Tegmark

TL;DR

The paper addresses how future galaxy surveys can measure cosmological parameters and how their information content complements CMB data. It develops a practical Fisher-information framework, deriving a simple approximation based on the galaxy power spectrum $P(k)$ that links parameter information to derivatives $\partial \ln P/\partial \theta_i$ and survey geometry through a weight function $w(k)$. The authors show that, in principle, surveys like SDSS can substantially tighten Planck's constraints on the power normalization $Q$ and the reionization optical depth $\tau$, provided information from mildly non-linear scales can be robustly extracted; non-linearities and bias introduce caveats and degeneracies that must be carefully modeled. They argue that joint analyses of galaxy surveys and CMB data can break key parameter degeneracies, yielding percent-level constraints on important cosmological quantities, while also highlighting the significant modeling challenges posed by non-linear clustering and bias. Overall, the work demonstrates a promising synergy between galaxy surveys and CMB measurements for precision cosmology, contingent on accurate treatment of non-linear clustering and bias in the mildly non-linear regime.

Abstract

We assess the accuracy with which future galaxy surveys can measure cosmological parameters by deriving a handy approximation that we validate numerically. We find that galaxy surveys are quite complementary to future Cosmic Microwave Background (CMB) experiments. By breaking parameter degeneracies of the Planck CMB satellite in a cold dark matter cosmology, the Sloan Digital Sky Survey might be able to reduce the Planck error bars by about an order of magnitude on the large-scale power normalization and the reionization optical depth, down to percent levels. However, pinpointing attainable accuracies to within better than a factor of a few depends crucially on whether it will be possible to extract useful information from the mildly nonlinear regime.

Measuring cosmological parameters with galaxy surveys

TL;DR

The paper addresses how future galaxy surveys can measure cosmological parameters and how their information content complements CMB data. It develops a practical Fisher-information framework, deriving a simple approximation based on the galaxy power spectrum that links parameter information to derivatives and survey geometry through a weight function . The authors show that, in principle, surveys like SDSS can substantially tighten Planck's constraints on the power normalization and the reionization optical depth , provided information from mildly non-linear scales can be robustly extracted; non-linearities and bias introduce caveats and degeneracies that must be carefully modeled. They argue that joint analyses of galaxy surveys and CMB data can break key parameter degeneracies, yielding percent-level constraints on important cosmological quantities, while also highlighting the significant modeling challenges posed by non-linear clustering and bias. Overall, the work demonstrates a promising synergy between galaxy surveys and CMB measurements for precision cosmology, contingent on accurate treatment of non-linear clustering and bias in the mildly non-linear regime.

Abstract

We assess the accuracy with which future galaxy surveys can measure cosmological parameters by deriving a handy approximation that we validate numerically. We find that galaxy surveys are quite complementary to future Cosmic Microwave Background (CMB) experiments. By breaking parameter degeneracies of the Planck CMB satellite in a cold dark matter cosmology, the Sloan Digital Sky Survey might be able to reduce the Planck error bars by about an order of magnitude on the large-scale power normalization and the reionization optical depth, down to percent levels. However, pinpointing attainable accuracies to within better than a factor of a few depends crucially on whether it will be possible to extract useful information from the mildly nonlinear regime.

Paper Structure

This paper contains 10 sections, 8 equations, 2 figures.

Table of Contents

  1. INTRODUCTION
  2. METHOD
  3. The brute force approach
  4. A useful approximation
  5. RESULTS AND CONCLUSIONS
  6. A linear clustering example
  7. Single-parameter accuracy
  8. Degeneracies
  9. Non-linear clustering
  10. Combining galaxy surveys and CMB experiments

Figures (2)

  • Figure 1: The top panel shows the weight functions $w(k)$ for main and BRG samples of the SDSS, together with our fiducial linear and nonlinear CDM power spectra in $(h^{-1}{\rm Mpc})^3$ units. The second panel shows the logarithmic derivatives of the linear power spectrum with respect to its amplitude, horizontal location, slope and baryon content. The third panel shows the accuracy with which these parameters can be measured using information on wavenumbers up to $k={k_{max}}$ when the other parameters are already known, and the bottom panel shows the corresponding accuracies when all four parameters must be determined simultaneously. The vertical line indicates $k_*$, the location where $P(k)$ peaks.
  • Figure 2: Similar to Figure 1, but using nonlinear power spectra. In the bottom plot, all parameters except $Q$ and $b$ are assumed to be independently known.