Mass-temperature relation in ΛCDM and modified gravity

We derive the mass-temperature relation using an improved top-hat model and a continuous formation model which takes into account the effects of the ordered angular momentum acquired through tidal-torque interaction between clusters, random angular momentum, dynamical friction, and modifications of the virial theorem to include an external pressure term usually neglected. We show that the mass-temperature relation differs from the classical self-similar behavior, M proportional to T-3/2, and shows a break at 3-4 keV and a steepening with a decreasing cluster temperature. We then compare our mass-temperature relation with those obtained in the literature with N-body simulations for f(R) and symmetron models. We find that the mass-temperature relation is not a good probe to test gravity theories beyond Einstein's general relativity, because the mass-temperature relation of the Lambda CDM model is similar to that of the modified gravity theories.