Emergent Cosmos in Einstein-Cartan Theory

Abstract

Based on the Padmanabhan's proposal, the accelerated expansion of the universe can be driven by the difference between the surface and bulk degrees of freedom in a region of space, described by the relation $dV/dt=N_{sur}-N_{bulk}$ where $N_{sur}$ and $N_{bulk}=-N_{em}+N_{de}$ are the degrees of freedom assigned to the surface area and the matter-energy content inside the bulk such that the indexes $"em"$ and $"de"$ represent energy-momentum and dark energy, respectively. In the present work, the dynamical effect of the Weyssenhoff perfect fluid with intrinsic spin and its corresponding spin degrees of freedom in the framework of Einstein-Cartan (EC) theory are investigated. Based on the modification of Friedmann equations due to the spin-spin interactions, a correction term for the Padmanabhan's original relation $dV/dt=N_{sur}+N_{em}-N_{de}$ including the number of degrees of freedom related to this spin interactions is obtained through the modification in $N_{bulk}$ term as $N_{bulk}=-N_{em}+N_{spin}+N_{de}$ leading to $dV /d t=N_{sur}+N_{em}-N_{spin} -N_{de}$ in which $N_{spin}$ is the corresponding degrees of freedom related to the intrinsic spin of the matter content of the universe. Moreover, the validity of the unified first law and the generalized second law of thermodynamics for the Einstein-Cartan cosmos are investigated. Finally, by considering the covariant entropy conjecture and the bound resulting from the emergent scenario, a total entropy bound is obtained. Using this bound, it is shown that the for the universe as an expanding thermodynamical system, the total effective Komar energy never exceeds the square of the expansion rate with a factor of $\frac{3}{4\pi}$.Comment: 12 Pages, Accepted for Publication in Eur. Phys. J.