Signatures of Modified Gravity on Linear Scales in a Dynamical Dark Energy Background

Abstract

Cosmological data from the cosmic microwave background (CMB), baryon acoustic oscillations, and Type Ia supernovae suggest that the component driving the accelerated expansion of the Universe may be dynamical at the $\sim 2.5$-$3\sigma$ CL. The best-fit CPL model produces a level of cosmic structure similar to that of $\Lambda$CDM, with both models exhibiting mild tension with redshift-space distortion data. In this {\it Letter}, we parametrize possible departures of the effective gravitational coupling from Newton's constant in the late Universe, below a comoving scale $\lambda_c$, using two redshift bins, $0 \leq z < 1$ and $1 \leq z \leq 3$. We then determine the optimal values of $\lambda_c$ and the amplitude of these deviations from General Relativity, assuming a background with dynamical dark energy in CPL form. We find that, in order to achieve the required suppression of structure growth at low redshifts while remaining consistent with CMB constraints -- primarily from the late-time ISW effect at low $\ell$ and lensing at high $\ell$ -- we must require modified gravity effects to have a characteristic scale of $\lambda_c \lesssim 150\,\mathrm{Mpc}$ (95\% CL). This places the relevant scales squarely within the range probed by galaxy surveys. The best-fit value is $\lambda_c \simeq 40\,\mathrm{Mpc}$, well below the 95\% CL upper limit. Using Planck PR4, DESI DR2, Pantheon+ (or DES-Dovekie) and redshift-space distortions data we confirm that a CPL background with standard gravity is moderately preferred over $\Lambda$CDM; this preference strengthens to a mildly strong level when modified gravity effects are included. This enhancement leaves the CPL parameters largely unchanged, but shifts them slightly further into the quintom region.