Rigidity and stability of cold dark solid universe model

Abstract

Observational evidence suggests that the large scale dynamics of the universe is presently dominated by dark energy, meaning a non-luminous cosmological constituent with a negative value of the pressure to density ratio $w=P/ρ$, which would be unstable if purely fluid, but could be stable if effectively solid with sufficient rigidity. It was suggested by Bucher and Spergel that such a solid constituent might be constituted by an effectively cold (meaning approximately static) distribution of cosmic strings with $w=-1/3$, or membranes with the observationally more favoured value $w=-2/3$, but it was not established whether the rigidity in such models actually would be sufficient for stabilisation. The present article provides an explicit evaluation of the rigidity to density ratio, which is shown to be given in both string and membrane cases by $μ/ρ=4/15$, and it is confirmed that this is indeed sufficient for stabilisation.