Modified gravity constraints with the Planck ISW-lensing bispectrum

We present updated constraints on modified gravity by including the integrated Sachs-Wolfe (ISW) effect from cosmic microwave background (CMB) lensing-CMB temperature cross-correlations, based on the latest Planck PR4 maps. Utilizing the effective field theory (EFT) of dark energy approach and adopting the ${w}_{0}{w}_{a}\mathrm{C}\mathrm{D}\mathrm{M}$ background cosmological model, we find that including the CMB ISW-lensing cross-correlations tightens 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 Atacama Cosmology Telescope CMB lensing, Dark Energy Spectroscopic Instrument Data Release 1 (DR1) BAO, CMB ISW-lensing, and type Ia supernovae data. The constraints on the EFT parameters controlling the kinetic braiding and nonminimal coupling are consistent with general relativity (GR) at the 95% C.L. In particular, we obtain a bound on the kinetic braiding parameter, ${c}_{B}<1.2$, at the 95% C.L. In the ${w}_{0}--{w}_{a}$ parameter space, our results imply a crossing of the phantom divide, $w=\ensuremath{-}1$. The modified gravity model shows a mild preference over $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at the $1.8\ensuremath{\sigma}$, $2.6\ensuremath{\sigma}$, and $3.2\ensuremath{\sigma}$ levels for the combinations with Pantheon+, Union3, and DESY5 supernova datasets. We find that using the latest hillipop+lollipop likelihoods alleviates the departure of modified gravity parameters from the GR values compared to results using Planck 2018 data. This paper underlines the importance of the ISW-lensing probe in constraining late-time modifications of gravity.