Abstract
It is conjectured that in cosmological applications the particle current is not modified but finite heat or energy flow. Therefore, comoving Eckart frame is a suitable choice, as it merely ceases the charge and particle diffusion and conserves charges and particles. The cosmic evolution of viscous hadron and parton epochs in casual and non-casual Eckart frame is analyzed. By proposing equations of state deduced from recent lattice QCD simulations including pressure p, energy density ρ, and temperature T, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter H˙, the cosmic energy density ρ˙, and the share η˙ and the bulk viscous coefficient ζ˙. We also suggest how the bulk viscous pressure Π could be related to H. We conclude that the relativistic theory of fluids, the Eckart frame, and the finite viscous coefficients play essential roles in the cosmic evolution, especially in the hadron and parton epochs.
Highlights
Giving a reliable description for matter and/or radiation filling in the cosmological background geometry, the space, is an essential ingredient to determine the temporal evolution of the Universe
The present work aims at solving the field equations in the hadron and the parton epochs and proposing barotropic equation for the bulk viscous pressure Π
While the non-casual Eckart theory violates the second law of thermodynamics so that Π = −3ζ H which is defined as the covariant entropy current stemming from Gibbs equation, the causal Eckart theory-similar the the causal stable Mueller–Israel–Stewart theory-leads to general relativistic causal hydrodynamical equations in the Eckart frame such as bulk viscosity, shear viscosity tensor, and heat flow obtained up to second-order gradients
Summary
Giving a reliable description for matter and/or radiation filling in the cosmological background geometry, the space, is an essential ingredient to determine the temporal evolution of the Universe. The theory of hydrodynamics was first formulated by Euler [6] This was much later extended to nonideal fluids by Navier [7] and Stokes [8] and utilized in determining dissipative quantities like viscosity and heat flow. Under the assumption of conserved charges and finite heat flux, Lahiri started with the second-order gradients expansion in the Eckart frame and developed a causal theory of relativistic non-ideal fluids for various astrophysical applications [14]. General relativistic causal hydrodynamical equations in the Eckart frame like of bulk viscosity, shear viscosity tensor, and heat flow are obtained up to second-order gradients.
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