Modified Gravity Constraints from the Full Shape Modeling of Clustering Measurements from DESI 2024

We present cosmological constraints on deviations from general relativity (GR) from the first-year of clustering observations from Dark Energy Spectroscopic Instrument (DESI) in combination with other datasets. We first consider $\mu(a,k)$-$\Sigma(a,k)$ modified gravity (MG) parametrization (as well as $\eta(a,k)$) in flat $\Lambda$CDM and $w_0 w_a$CDM backgrounds. Using a functional form for time-only evolution gives $\mu_0=0.11^{+0.44}_{-0.54}$ from DESI(FS+BAO)+BBN and a wide prior on $n_{s}$. Using DESI(FS+BAO)+CMB+DESY3+DESY5-SN, we obtain $\mu_0=0.05\pm 0.22$ and $\Sigma_0=0.008\pm 0.045$ in the $\Lambda$CDM background. In $w_0 w_a$CDM, we obtain $\mu_0=-0.24^{+0.32}_{-0.28}$ and $\Sigma_0=0.006\pm 0.043$, consistent with GR, and still find a preference for dynamical dark energy with $w_0>-1$ and $w_a<0$. We then use binned forms in the 2 backgrounds starting with 2 bins in redshift and then adding 2 bins in scale for a total of 4 and 8 MG parameters, respectively. All MG parameters are found consistent with GR. We also find that the tension reported for $\Sigma_0$ with GR from Planck PR3 goes away when using LoLLiPoP+HiLLiPoP likelihoods. As noted previously, this seems to indicate the tension is related to CMB lensing anomaly in PR3 which is also resolved when using these likelihoods. We then constrain the class of Horndeski theory in both EFT-basis and $\alpha$-basis. Assuming a power law for the non-minimal coupling function $\Omega$, we obtain $\Omega_0=0.012^{+0.001}_{-0.012}$ and $s_0=0.996^{+0.54}_{-0.20}$ from DESI(FS+BAO)+DESY5SN+CMB in a $\Lambda$CDM background, consistent with GR. Using the $\alpha$-basis with no-braiding ($\alpha_B=0$) gives $c_M<1.14$, in agreement with GR. However, we see a mild yet consistent indication for $c_B>0$ when $\alpha_B$ is varied which will require further study to determine whether this is due to systematics or new physics. [Abridged]