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Cosmological hysteresis is a purely thermodynamical phenomenon caused by thegradient in pressure, hence the characteristic equation of state during theexpansion and contraction phases of the universe are different, provided thatthe universe bounces and recollapses. During hysteresis pressure asymmetry iscreated due to the presence of a single scalar field in the dynamical process.Also such an interesting scenario has vivid implications in cosmology whenapplied to variants of modified gravity models described within the frameworkof membrane paradigm. Cyclic universe along with scalar field leads to theincrease in the amplitude of the cosmological scale factor at each consecutivecycles of the universe. Detailed analysis shows that the conditions whichcreates a universe with an ever increasing expansion, depend on the signatureof the hysteresis loop integral $\oint pdV$ and on membrane model parameters.

Cosmological hysteresis in cyclic universe from membrane paradigm