Towards a Composite Framework for Simultaneous Exploration of New Physics in Background and Perturbed Universe

TL;DR

The paper develops a model-agnostic, composite cosmology framework that decouples background evolution from perturbation growth via parameters $A$ and $B$ for the background and a growth index $γ$ for structure formation, with ΛCDM recovered when $A=Ω_{m0}$, $B=2/3$, and $γ=6/11$. It derives a generalized expansion history $E(z)=\sqrt{A(1+z)^{2/B}+(1-A)}$ and a robust $fσ_8$ fitting form that uses $Ω_m^{γ}$ and a hypergeometric function to capture deviations, enabling tests of evolving dark energy versus modified gravity without committing to a specific model. Using DESI-DR2 BAO, SN Ia data (Pantheon+ and DES-5YR), and RSD measurements, the authors find significant evidence for deviations in the background evolution from ΛCDM, while the growth data remain consistent with GR predictions ($γ\approx 6/11$). They also show how representative DDE and MG scenarios fit within the framework and provide forecasted gains from future high-precision RSD surveys (e.g., Euclid), which could reveal correlations between background and perturbation parameters and decisively distinguish between competing explanations for cosmic acceleration.

Abstract

We investigate deviations from $Λ$CDM by independently parameterizing modifications in the background evolution and the growth of structures. The background is characterized by two parameters, $A$ and $B$, which reduce to $A=Ω_{m0}$ and $B=2/3$ in the $Λ$CDM limit, while deviations in the growth of structures are captured through a fitting function for $fσ_8$ involving the growth index $γ$. Using recent observational datasets involving background expansion and growth of structures (related to observations involving redshift space distortions), we find significant evidence for departures from $Λ$CDM in the background expansion whereas there is no finite evidence for deviations from $Λ$CDM behaviour in the growth of structures. This suggests that with the current precision in observational data involving background and perturbed Universe, a deviation from $Λ$CDM behaviour is confirmed (as shown in the recent DESI-DR2 results). But whether this deviation is due to an evolving Dark Energy or due to the modification of gravity at cosmological scales is still an open question, largely due to less precise data from perturbed Universe. We further demonstrate how the future high-precision growth data (from Euclid, for example) can answer such question using a forecast study.

Figures (7)

• Figure 1: Plots for $f\sigma_8$ values as a function of $\Omega_m$ obtained using the fitting form in Eq. \ref{['fs8fit']} (red line) and from solving Eq. \ref{['greqlcdm']} (dashed blue line). Here we have used $\Omega_{m0}=0.315,~ \sigma_{8,0}=0.811, \gamma=\frac{6}{11}$ and assumed $\delta(a)\approx a$ and $\delta'(a)\approx 1$ in the matter dominated era.
• Figure 2: One-dimensional marginalized posterior distributions, 2-dimensional contour plots at 68% and 95% C.L. limits for relevant parameters of the composite model using BAO and SNIa datasets.
• Figure 3: One-dimensional marginalized posterior distributions, 2-dimensional contour plots at 68% and 95% C.L. limits for parameters of the composite model using RSD data.
• Figure 4: One-dimensional marginalized posterior distributions, 2-dimensional contour plots at 68% and 95% C.L. limits for parameters of the composite model using RSD in combination with BAO/SNIa data.
• Figure 5: One-dimensional marginalized posterior distributions, 2-dimensional contour plots at 68% and 95% C.L. limits for parameters of the composite model using combined BAO, SNIa and RSD datasets.