Constraints on the normal branch of DGP gravity from SPT galaxy clusters with DES and HST weak-lensing mass calibration and from P l a n c k PR4 CMB anisotropies

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We present constraints on the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld gravity model from the abundance of massive galaxy clusters. On scales below the nDGP crossover scale r c , the nDGP model features an effective gravitylike fifth force that alters the growth of structure, leading to an enhancement of the halo mass function (HMF) on cluster scales. The enhanced cluster abundance allows for constraints on the nDGP model using cluster samples. We employ the South Pole Telescope (SPT) cluster sample, selected through the thermal Sunyaev-Zel’dovich effect with the SPT and with mass calibration using weak-lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample contains 1,005 clusters with redshifts 0.25 < z < 1.78 , which are confirmed with the multicomponent matched filter algorithm using optical and near-infrared data. Weak-lensing data from DES and HST enable a robust mass measurement of the cluster sample. We use DES Year 3 data for 688 clusters with redshifts z < 0.95 , and HST data for 39 clusters with redshifts 0.6 < z < 1.7 . We account for the enhancement in the HMF through a semi-analytic correction factor to the standard cosmology HMF derived from the spherical collapse model in the nDGP model. We then further calibrate this model using N -body simulations. In addition, for the first time, we analyze the primary CMB temperature and polarization anisotropy measurements from Planck PR4 within the nDGP model. We obtain a competitive constraint from the joint analysis of the SPT cluster abundance with the Planck PR4 data, and report an upper bound of 1 / H 0 r c < 1.41 at 95% when assuming a cosmology with massive neutrinos.

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