Energy conditions in consistent perfect fluid cosmology

Motivated by recent work on consistent fluid couplings in f(R,T) gravity, we study cosmology in the nontrivial model f(R,T)=R+σRT using the Brown variational principle for a barotropic perfect fluid. For a flat FLRW universe, we cast the field equations into Einstein-like form and obtain explicit expressions for the effective energy density, pressure and equation of state (EOS) parameter. This allows us to rewrite the null, weak, strong and dominant energy conditions as simple polynomial inequalities. We show that radiation reproduces standard relativistic cosmology, whereas for dust and σ>0 the effective fluid acquires negative pressure and can drive accelerated expansion. In this dust case, there exists a finite window in the Hubble parameter during which the strong energy condition is violated, but the null, weak, and dominant energy conditions remain satisfied. Conversely, whenever the strong energy condition is imposed, the other conditions are automatically fulfilled. The additional viability requirement 1+σT>0 further restricts the allowed Hubble range and yields an upper bound on σ that still leaves a non-empty accelerating regime. Our analysis provides a transparent energy-condition study of a consistent RT coupling in f(R,T) cosmology, based on qualitative techniques.