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

We investigate deviations from $\Lambda$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 $A=\Omega_{m0}$ and $B=2/3$ in the $\Lambda$CDM limit, while deviations in the growth of structures are captured through a fitting function for $f\sigma_8$ involving the growth index $\gamma$. 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 $\Lambda$CDM in the background expansion whereas there is no finite evidence for deviations from $\Lambda$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 $\Lambda$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.