Cosmological sudden singularities in f(R, T) gravity

In this work, we study the possibility of finite-time future cosmological singularities appearing in $f(R,T)$ gravity, where $R$ is Ricci scalar and $T$ trace stress-energy tensor. We present theory both geometrical dynamically equivalent scalar-tensor representation obtain respective equations motion. a background Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe with an arbitrary curvature for generic $C^\infty$ function $f(R,T)$, prove that conservation tensor prevents appearance sudden context at any order time-derivatives scale factor. However, if assumption dropped, allows to appear level third time-derivative factor $a(t)$, which are compensated by divergences either first energy density $\rho(t)$ or isotropic pressure $p(t)$. For these cases, introduce model featuring singularity consistent current measurements parameters, namely, Hubble constant, deceleration parameter, age universe, provide predictions still unmeasured jerk snap parameters. Finally, analyse constraints on particular guarantees system evolves direction favorable conditions divergence time.