Bulk Viscosity and Varying Constants

When investigating various issues in cosmology and other areas of general relativity, a perfect fluid is usually considered. A perfect fluid is one with negligible viscosity and heat conduction. However, this is only an idealisation, and in more realistic situations, dissipative effects need to be considered. Secondly, there are several "constants of nature" such as Newton's gravitational constant $G$, the cosmological constant $\Lambda$, the speed of light $c$, the fine-structure constant $\alpha$, Boltzmann’s constant $\Bar{h}$, Planck’s constant and Fermi’s constant $G_F$, which may not necessarily be constant, but could be varying. There have been several studies carried out with bulk viscosity together with variable $G$ and $\Lambda$. In these studies, the modified energy conservation equation can be split up into the traditional equation, plus an equation involving the parameters $G$ and $\Lambda$. However, many authors have split the full equation in such a way that the viscosity appears in the wrong equation. In such a situation, it is not possible to obtain the correct general relativistic limiting case. In this work, the relevant equations are re-analysed, showing that the bulk viscosity needs to be incorporated into the other equation and highlighting how the general relativistic limit is obtained.