Spherical collapse in modified gravity with the Birkhoff-theorem

We study structure formation in a phenomenological model of modified gravity which interpolates between ΛCDM and phenomenological DGP-gravity. Generalisation of spherical collapse by using the Birkhoff-theorem along with the modified growth equation shows that the overdensity for spherical collapse δc in these models is significantly lowered compared to ΛCDM, leading to enhanced number densities of massive clusters and enhanced cluster merging rates. We find that δc(z) is well fitted by a function of the form δc(z) = a−b exp(−cz). We examine the sensitivity of PLANCK’s and SPT’s Sunyaev-Zel’dovich survey to constrain the modified gravity parameterisation and find that these experiments can easily distinguish between models with a cosmological constant and modified gravity, if prior constraints from CMB temperature and polarisation anisotropies are included.