Abstract
A new kind of evolution for cyclic models in which the Hubble parameter oscillates and remains positive has been explored in a specific f(R, T) gravity reconstruction. A singularity-free cyclic universe with negative varying cosmological constant has been obtained, which supports the role suggested for negative Lambda in stopping the eternal acceleration. The cosmological solutions have been obtained for the case of a flat universe, supported by observations. The cosmic pressure grows without singular values; it is positive during the early-time decelerated expansion and negative during the late-time accelerating epoch. The time-varying equation of state parameter omega(t) shows quintom behavior and is restricted to the range -2.25 <= omega(t) <= 1/3. The validity of the classical linear energy conditions and the sound speed causality condition has been studied. The non-conventional mechanism of negative cosmological constant that are expected to address the late-time acceleration has been discussed.