Cluster formation and the Sunyaev-Zel'dovich power spectrum in modified gravity: the case of a phenomenologically extended DGP model

We investigate the effect of modified gravity on cluster abundance and the Sunyaev-Zel'dovich angular power spectrum. Our modified gravity is based on a phenomenological extension of the Dvali-Gabadadze-Porrati model which includes two free parameters characterizing deviation from Lambda-CDM cosmology. Assuming that Birkhoff's theorem gives a reasonable approximation, we study the spherical collapse model of structure formation and show that while the growth function changes to some extent, modified gravity gives rise to no significant change in the linear density contrast at collapse time. The growth function is enhanced in the so called normal branch, while in the "self-accelerating" branch it is suppressed. The Sunyaev-Zel'dovich angular power spectrum is computed in the normal branch, which turns out to be amplified compared to the Lambda-CDM case. This allows us to put observational constraints on the parameters of the modified gravity model using small scale CMB observation data.