[Paper Review] Testing consistency of general relativity with kinematic and dynamical probes

Xiao-Wei Duan, Min Zhou+1 more|arXiv (Cornell University)|May 12, 2016

Cosmology and Gravitation Theories10 references3 citations

TL;DR

This paper tests the consistency between kinematic probes (Hubble parameter H(z)) and dynamical probes (growth rate fσ₈) to assess general relativity on cosmological scales. Using parametric and non-parametric H(z) methods, it proposes trigonometric parameterizations for consistency relations and finds no significant deviation from general relativity at 1σ confidence level, with modified gravity models like DGP showing clear inconsistencies.

ABSTRACT

In this work, we test consistency relations between a kinematic probe, the observational Hubble data, and a dynamical probe, the growth rates for cosmic large scale structure, which should hold if general relativity is the correct theory of gravity on cosmological scales. Moreover, we summarize the development history of parametrization in testings and make an improvement of it. Taking advantage of the Hubble parameter given from both parametric and non-parametric methods, we propose three equations and test two of them performed by means of two-dimensional parameterizations, including one using trigonometric functions we propose. As a result, it is found that the consistency relations satisfies well at $1σ$ CL and trigonometric functions turn out to be efficient tools in parameterizations. Furthermore, in order to confirm the validity of our test, we introduce a model of modified gravity, DGP model and compare the testing results in the cases of $Λ$CDM, "DGP in GR" and DGP model with mock data. It can be seen that it is the establishing of consistency relations which dominates the results of the testing. Overall, the present observational Hubble data and growth rate data favor convincingly that the general relativity is the correct theory of gravity on cosmological scales.

Motivation & Objective

• To test the consistency between kinematic (H(z)) and dynamical (fσ₈) probes as a signature of general relativity on cosmological scales.
• To develop improved two-dimensional parameterizations for redshift-dependent consistency relations, avoiding reliance on uncertain parameters like Ωₘ₀σ₈(0)/δ(0).
• To validate the testing framework using a modified gravity model (DGP) and mock data to confirm that consistency relations, not H(z) fitting, drive the results.
• To assess whether current observational data favor general relativity over alternative gravity theories.

Proposed method

• Proposes three consistency relations between H(z) and fσ₈, testing two using parametric (Method A) and non-parametric (Method B) H(z) estimation.
• Employs two-dimensional parameterizations to model redshift dependence of consistency, including a novel trigonometric function parameterization.
• Uses observational Hubble data (OHD) and growth rate data (fσ₈) to compute χ²/d.o.f. and assess confidence levels.
• Compares results across ΛCDM, "DGP in GR", and full DGP models using mock data to isolate the role of consistency relations.
• Applies fourth-order Runge-Kutta method to solve DGP model equations for theoretical H(z) traces.
• Performs statistical testing via marginalized posterior distributions and contour plots to evaluate consistency at 1σ confidence level.

Experimental results

Research questions

• RQ1 Do the observed Hubble parameter and growth rate data satisfy the consistency relation predicted by general relativity on cosmological scales?
• RQ2 Can trigonometric functions serve as efficient parameterizations for redshift-dependent deviations from general relativity?
• RQ3 How do modified gravity models like DGP affect the consistency between kinematic and dynamical probes?
• RQ4 Is the observed consistency driven by the H(z) fitting or by the underlying consistency relation?

Key findings

• The consistency relations between H(z) and fσ₈ show no significant deviation from general relativity at the 1σ confidence level across all tested parameterizations.
• Trigonometric functions prove to be highly effective in parameterizing redshift-dependent deviations, outperforming standard polynomial forms.
• The DGP model fails the consistency test, while ΛCDM and "DGP in GR" pass, indicating that the failure is due to the breakdown of consistency, not poor H(z) fitting.
• Theoretical H(z) traces for DGP and ΛCDM are nearly indistinguishable, yet only DGP fails the consistency test, proving that consistency relations are the dominant factor in the outcome.
• The marginalized posterior for Ωₘ₀σ₈(0)/δ(0) is constrained to 0.3369 ± 0.0496 in ΛCDM, supporting the consistency of the data with GR.
• The CRO (consistency relation of growth) test shows tighter constraints than CRI, and both support general relativity at 1σ.