Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models

TL;DR

The paper develops a cosmological consistency test that jointly uses expansion-history probes (Type Ia supernovae and CMB) and growth probes (weak lensing and CMB) to check the GR link between $H(z)$ and the growth factor $D(a)$. By simulating a fiducial modified gravity model (DGP) and fitting DE parameters separately to expansion and growth data, the authors show that the resulting DE-parameter spaces become significantly inconsistent if gravity is modified. This mismatch serves as a practical, model-agnostic signature of modified gravity that future surveys could detect without invoking new physics beyond the two data streams. The approach provides a pathway to decisively discriminate between dark energy and modified gravity as the source of cosmic acceleration, with implications for fundamental physics and cosmology.

Abstract

If general relativity is the correct theory of physics on large scales, then there is a differential equation that relates the Hubble expansion function, inferred from measurements of angular diameter distance and luminosity distance, to the growth rate of large scale structure. For a dark energy fluid without couplings or an unusual sound speed, deviations from this consistency relationship could be the signature of modified gravity on cosmological scales. We propose a procedure based on this consistency relation in order to distinguish between some dark energy models and modified gravity models. The procedure uses different combinations of cosmological observations and is able to find inconsistencies when present. As an example, we apply the procedure to a universe described by a recently proposed 5-dimensional modified gravity model. We show that this leads to an inconsistency within the dark energy parameter space detectable by future experiments.

Figures (7)

• Figure 1: Supernova Hubble diagrams for several dark energy and DGP models. Note that the $\Lambda$CDM model (red solid line) and the $\Omega_m=0.20$ DGP model (blue dotted) have nearly identical Hubble diagrams, but different growth factors as shown in Fig.\ref{['fig:growth1']}. The same is true of the SUGRA (green dashed) and $\Omega_m=0.27$ DGP (black double dotted) models.
• Figure 2: Growth factors of linear density perturbations for several dark energy and DGP models. Comparisons among several dark energy and DGP models growth factors of linear density perturbations. Note that the growth factor in the $\Omega_m=0.27$ DGP model is suppressed with respect to that in the $\Lambda$CDM model, which has the same $\Omega_m$.
• Figure 3: CMB power spectra for several dark energy and DGP models: $\Lambda$CDM model is in red solid line; SUGRA model is in green dashed line; $\Omega_m=0.27$ DGP model is in black double dotted line; $\Omega_m=0.20$ DGP model is in blue dotted line; Following Deffayet3, a modified version of CMBFASTZaldarriaga was used to generate the DGP plots.
• Figure 4: Lensing convergence power spectra for several dark energy and DGP models: $\Lambda$CDM model is in red solid line; SUGRA model is in green dashed line; $\Omega_m=0.27$ DGP model is in black double dotted line; $\Omega_m=0.20$ DGP model is in blue dotted line;
• Figure 5: Equations of state found using two different combinations of data sets. Solid contours are for fits to SN Ia and CMB data, while dashed contours are for fits to weak lensing and CMB data. The significant difference (inconsistency) between the equations of state found using these two combinations is a signature of the DGP model and should be detectable by future experiments described in sections IV and V. The inconsistency is an observational detection of the underlying modified gravity DGP model (assumed here to generate the data).