Modified gravity constraints with Planck ISW-lensing bispectrum

We present updated constraints on modified gravity by including the Integrated Sachs-Wolfe (ISW) effect from CMB lensing-CMB temperature cross-correlations, based on the latest Planck PR4 maps. Utilizing the Effective Field Theory of dark energy approach and adopting the $w_0w_a$CDM background cosmological model, we find that including the CMB ISW lensing cross-correlations tighten constraints on the modified gravity parameters by approximately $20\%$, reducing the viable parameter space by $40-80\%$. We derive constraints from Planck CMB, Planck and ACT CMB lensing, DESI DR1 BAO, CMB ISW-lensing, and type Ia supernovae (SN Ia) data. The constraints on the EFT parameters controlling the kinetic braiding and non-minimal coupling are consistent with General Relativity (GR) at the $95\%$ CL. In particular, we obtain a bound on the kinetic braiding parameter, $c_B < 1.2$ at $95\%$ CL. In the $w_0$-$w_a$ parameter space, our results imply a crossing of the phantom divide, $w=-1$. The modified gravity model shows a mild preference over $\Lambda$CDM at the $1.8\sigma$, $2.6\sigma$ and $3.2\sigma$ levels for the combinations with Pantheon+, Union3 and DESY5 supernova datasets. We find that using the latest $\texttt{HiLLiPoP}+\texttt{LoLLiPoP}$ likelihoods alleviates the departure of modified gravity parameters from the GR-values compared to results using {\it Planck} 2018 data. This paper underlines the importance of the ISW lensing probe in constraining late-time modifications of gravity.