A Cyclic Universe With Varying Cosmological Constant in $f(R,T)$ gravity

A new kind of evolution for cyclic models in which the Hubble parameter oscillates and keeps 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 EoS parameter $\omega(t)$ shows a quintom behavior and is restricted to the range $-2.25 \leq \omega(t) \lesssim \frac{1}{3}$. 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.