Finite-time singularities in f(R, T) gravity and the effect of conformal anomaly

We investigate f(R, T) gravity models (where R is the curvature scalar and T is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter to realise the cosmic acceleration and we introduce two parameters, alpha and H-s, which characterise each type of singularity. We address the conformal anomaly and we observe that it cannot remove the sudden singularity or the Big Brake, but, for some values of alpha, the Big Rip and the Big Freeze may be avoided. We also find that, even without taking into account the conformal anomaly, the Big Rip and the Big Freeze may be removed thanks to the presence of the T contribution of the f(R, T) theory.