Mass-Temperature relation in $\Lambda$CDM 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,
$M \propto T^{3/2}$, 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.
