Viscous cosmologies

Abstract

We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor R(t) which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with nonzero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann-Lamaître-Robertson-Walker metric. To this end we use a version of the energy-momentum tensor from the Müller-Israel-Stewart theory which leads to causal Navier-Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.

Cosmology from Strong Interactions

“…Second example can be found in Ref. [372] where the relaxation time τ π proportional to the shear viscosity parameter η was used to study evolution of the Universe filled with QGP with non-zero shear viscosity. The authors argue that in General Relativity the following modification of the shear stress tensor…”

“…Using the FLRW metric and taking into account that the compatibility with the isotropy and homogeneity of the Universe demands π µν to be diagonal, the solution of Eq. (193) reads [372] π 00 (t) = π 00 (t 0 ) a(t 0 ) a(t)…”

“…In the Friedmann equations the effect of the traceless viscosity tensor shows up in the modification of the initial energy density (t 0 ) and in the behavior of the energy density at times t t 0 + τ π , which at later times goes over to the standard expression [372] (t) = (t 0 ) + π 00 (t 0 ) a(t 0 ) a(t) − π 00 (t 0 ) a(t 0 ) a(t)…”

Testing a non linear solution of the Israel-Stewart theory with supernovae

“…Some other results can be found in Refs. [22,23], where the role of bulk viscosity is studied in other contexts such as the radial oscillation of relativistic stars and the cosmological implications for universes filled with Quark-Gluon plasma.…”

Unified dissipative dark matter model in a non linear Israel-Stewart theory

“…Some other results can be found in Refs. [13,14], where the role of bulk viscosity is studied in other contexts such as the radial oscillation of relativistic stars and the cosmological implications for universes filled with Quark-Gluon plasma.…”