MG12 - Talk detail
 

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Abstract

Stability of the Einstein static universe in modified thoeries of gravity

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) and f(G) modified theories of gravity. By considering generic forms of f(R) and f(G), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) and f(G) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications of general relativity can stabilize solutions which are unstable in general relativity.

Bounds on 2m/r for static objects with a positive cosmological constant

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant $\Lambda,$ and we investigate the influence of $\Lambda$ on the bound of M/R, where M is the ADM mass and R is the area radius of the boundary of the static object. We find that for any solution which satisfies the energy condition $p+2p_{\perp}\leq\rho,$ where $p\geq 0$ and $p_{\perp}$ are the radial and tangential pressures respectively, and $\rho\geq 0$ is the energy density, and for which $0\leq \Lambda R^2\leq 1,$ the inequality M/R \leq 2/9 - \Lambda R^2 /3 + 2/9 \sqrt{1+3\Lambda R^2}, holds. If $\Lambda=0$ it is known that infinitely thin shell solutions uniquely saturate the inequality, i.e. the inequality is sharp in that case. The situation is quite different if $\Lambda>0.$ Indeed, we show that infinitely thin shell solutions do not generally saturate the inequality except in the two degenerate situations $\Lambda R^2=0$ and $\Lambda R^2=1$. In the latter situation there is also a constant density solution, where the exterior spacetime is the Nariai solution, which saturates the inequality, hence, the saturating solution is non-unique. In this case the cosmological horizon and the black hole horizon coincide. This is analogous to the charged situation where there is numerical evidence that uniqueness of the saturating solution is lost when the inner and outer horizons of the Reissner-Nordstr\"{o}m solution coincide. We also apply the inequality to the Virgo cluster and obtain an upper bound for $\Lambda$ from real observational data.

Dark spinors with torsion in cosmology

We solve one of the open problems in Einstein-Cartan theory, namely we find a natural matter source whose spin angular momentum tensor is compatible with the cosmological principle. We analyze the resulting evolution equations and find that an epoch of accelerated expansion is an attractor. The torsion field quickly decays in that period. Our results are interpreted in the context of the standard model of cosmology.

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