Cosmological hysteresis in cyclic universe from membrane paradigm
  Cosmological hysteresis is a purely thermodynamical phenomenon caused by the
gradient in pressure, hence the characteristic equation of state during the
expansion and contraction phases of the universe are different, provided that
the universe bounces and recollapses. During hysteresis pressure asymmetry is
created due to the presence of a single scalar field in the dynamical process.
Also such an interesting scenario has vivid implications in cosmology when
applied to variants of modified gravity models described within the framework
of membrane paradigm. Cyclic universe along with scalar field leads to the
increase in the amplitude of the cosmological scale factor at each consecutive
cycles of the universe. Detailed analysis shows that the conditions which
creates a universe with an ever increasing expansion, depend on the signature
of the hysteresis loop integral $\oint pdV$ and on membrane model parameters.
