We investigate deviations from Lambda Cold Dark Matter ($\mathrm{\Lambda }\mathrm{CDM}$) model by independently parametrizing modifications in the background evolution and the growth of structures. The background is characterized by two parameters, $A$ and $B$, which reduce to $A={\mathrm{\Omega }}_{m0}$ and $B=2/3$ in the $\mathrm{\Lambda }\mathrm{CDM}$ 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 $\mathrm{\Lambda }\mathrm{CDM}$ in the background expansion whereas there is no finite evidence for deviations from $\mathrm{\Lambda }\mathrm{CDM}$ behavior in the growth of structures. This suggests that with the current precision in observational data involving background and the perturbed Universe, a deviation from $\mathrm{\Lambda }\mathrm{CDM}$ behavior 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 the perturbed Universe. We further demonstrate how the future high-precision growth data (from Euclid, for example) can answer such a question using a forecast study.

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• Cosmological parameters
• Cosmology
• Dark energy
• Evolution of the Universe
• Gravitation