Cosmic Evolution of Viscous QCD Epoch in Causal Eckart Frame

• Main Authors: Eman Abdel Hakk, Abdel Nasser Tawfik, Afaf Nada, Hayam Yassin
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Universe
• Subjects: observational cosmology; mathematical and relativistic aspects of cosmology; quark-gluon plasma
• Online Access: https://www.mdpi.com/2218-1997/7/5/112

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 <i>p</i>, energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>, and temperature <i>T</i>, the Friedmann equations are solved. We introduce expressions for the temporal evolution of the Hubble parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>H</mi><mo>˙</mo></mover></semantics></math></inline-formula>, the cosmic energy density <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>ρ</mi><mo>˙</mo></mover></semantics></math></inline-formula>, and the share <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>η</mi><mo>˙</mo></mover></semantics></math></inline-formula> and the bulk viscous coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>ζ</mi><mo>˙</mo></mover></semantics></math></inline-formula>. We also suggest how the bulk viscous pressure <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Π</mi></semantics></math></inline-formula> could be related to <i>H</i>. 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.