[Paper Review] Constraining the growth factor with baryon oscillations

D. Sapone, Luca Amendola|ArXiv.org|Sep 18, 2007

Astronomy and Astrophysical Research14 citations

TL;DR

This paper proposes using baryon acoustic oscillations (BAOs) in future galaxy surveys to constrain the growth factor of cosmic structure, parameterized by the growth index γ. Using Fisher matrix forecasts, it shows that spectroscopic surveys of 5,000 deg² up to z ≈ 3 can measure γ with a precision of Δγ ≈ 0.06, while photometric surveys achieve Δγ ≈ 0.15, offering a powerful consistency test for ΛCDM and constraints on modified gravity models.

ABSTRACT

The growth factor of linear fluctuations is probably one of the least known quantity in observational cosmology. Here we discuss the constraints that baryon oscillations in galaxy power spectra from future surveys can put on a conveniently parametrized growth factor. We find that spectroscopic surveys of $5000 deg^2$ extending to $z \approx 3$ could estimate the growth index $γ$ within 0.06; a similar photometric survey would give $Δγ\approx 0.15$. This test provides an important consistency check for standard cosmological model and could constrain modified gravity models. We discuss the errors and the figure of merit for various combinations of redshift errors and survey size.

Motivation & Objective

• To improve constraints on the growth factor of linear fluctuations, a poorly measured quantity in cosmology.
• To test the consistency of the standard cosmological model using the growth index γ as a probe.
• To evaluate the sensitivity of future large-scale surveys to deviations from general relativity via modified gravity models.
• To quantify the impact of survey geometry, redshift error, and area on the precision of γ estimation using BAOs.
• To compare the constraining power of BAO-based growth factor measurements with other dark energy probes like weak lensing and SNIa.

Proposed method

• Adapts the baryon acoustic oscillation (BAO) method as a standard ruler in galaxy power spectra to probe the growth factor G(z).
• Uses the Fisher matrix formalism to forecast constraints on cosmological parameters, including the growth index γ.
• Models the observed galaxy power spectrum as a function of redshift, bias, and redshift-space distortion parameter β.
• Considers both spectroscopic (δz = 0) and photometric (δz/z = 0.04) redshift measurements across multiple survey areas (1000–10,000 deg²).
• Analyzes two cases: (I) γ fixed and w(z) varied, and (II) γ treated as a free parameter alongside w₀ and w₁.
• Computes the figure of merit (FOM) for w₀–γ and wₚ–w₁ parameter pairs to assess constraining power across survey configurations.

Experimental results

Research questions

• RQ1 Can baryon acoustic oscillations in future galaxy surveys provide competitive constraints on the growth index γ?
• RQ2 How does the precision of γ estimation depend on survey area, redshift range, and redshift error (spectroscopic vs. photometric)?
• RQ3 To what extent can BAO-based growth factor measurements distinguish between ΛCDM and modified gravity models like DGP?
• RQ4 How does the FOM for γ compare with other dark energy probes such as weak lensing and SNIa in future experiments?
• RQ5 What level of statistical uncertainty can be expected on γ from a 5,000 deg² spectroscopic survey extending to z ≈ 3?

Key findings

• A spectroscopic survey of 5,000 deg² extending to z ≈ 3 can constrain the growth index γ with a marginalized error of Δγ ≈ 0.06.
• A similar photometric survey yields a larger error of Δγ ≈ 0.15, due to redshift uncertainty.
• The error on γ decreases from 0.099 to 0.05 for spectroscopic surveys as the survey area increases from 1,000 to 10,000 deg².
• For photometric surveys, the error on γ reduces from 0.301 to 0.114 over the same area range.
• The BAO method achieves a figure of merit (FOM) for w₀–γ that is roughly 4–6 times higher for spectroscopic than for photometric surveys with 4% redshift error.
• With a 20,000 deg² survey from z = 0 to z = 1.5, the error on γ reduces to Δγ ≈ 0.06, approaching the precision of other leading methods like weak lensing.