Synergy between the gravitational potential decay rate and other structure growth probes in testing gravity

Abstract

We test gravity by exploiting the synergy between the gravitational potential decay rate ($DR$) and complementary structure-growth probes: these observables respond to MG parameters with different degeneracy directions, so their combination yields stronger constraints than any single probe. We adopt the tomographic $DR$ measurements reported in \citep{2025ApJ...982...99D} and combine them with CMB-lensing-tomography ${\Sigma }_8$ measurements and $f{\sigma }_8$ measurements from DESI DR1 full-shape analyses and the DESI peculiar-velocity field. We apply this joint data vector to two representative frameworks: phenomenological parameterizations and the Effective Field Theory (EFT) $\alpha$-basis. For the phenomenological form $P_{\mathrm{MG}}(a)=1+P_{\mathrm{MG},0}{\Omega }_{\mathrm{DE}}(a)/{\Omega }_{\mathrm{DE}}(0)$, where $P_{\mathrm{MG}}$ denotes $\mu$, $\eta$, or $\Sigma$, we obtain ${\mu }_0=0.09\pm 0.35$ and ${\Sigma }_0=0.01\pm 0.06$. Compared to the measurements combination ${\Sigma }_8+f{\sigma }_8$, including $DR$ tightens the constraint on ${\Sigma }_0$ by a factor of $\sim 2$. For the $({\mu }_0,{\eta }_0)$ case we find ${\mu }_0=0.06_{-0.23}^{+0.17}$ and ${\eta }_0=-0.03_{-0.46}^{+0.36}$; relative to ${\Sigma }_8+f{\sigma }_8$, adding $DR$ improves the constraints on both parameters by a factor of $\sim 1.5$. In the EFT $\alpha$-basis, adopting the parameterization ${\alpha }_i(a)=c_i{\Omega }_{\mathrm{DE}}(a)$ with $i\in \{\mathrm{M},\mathrm{B}\}$, we find $c_{\mathrm{M}}=0.64_{-0.72}^{+0.32}$ and $c\mathrm{B}=0.31_{-0.29}^{+0.19}$. The corresponding EFT uncertainties are about a factor of $\sim 2$ smaller than those reported in \citep{2025JCAP...09..053I}, which combined DESI full-shape and BAO measurements with DES-SN5YR and CMB data. These results demonstrate the capability of $DR$ and the necessity of including the $DR$ measurements in testing gravity.

arXiv comment21 pages, 6 figures, 3 tables, accepted for publication in JCAP