Timelike self-similar spherically symmetric models with two scalar fields

Details Timelike self-similar spherically symmetric models with two scalar fields Timelike self-similar spherically symmetric models with two scalar fields

Aug 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cqgra..19.3901c&link_type=abstract

Classical and Quantum Gravity, Volume 19, Issue 15, pp. 3901-3925 (2002).

Mathematics

Logic

2

Scientific paper

We investigate timelike self-similar spherically symmetric cosmological models with two scalar fields with exponential potentials. We determine the governing autonomous system of ordinary differential equations for the model, and by defining bounded variables we are able to apply the theory of dynamical systems. We obtain all of the equilibrium points in the compact dynamical phase space and analyse their local stability. We find a monotonic function, so that we can rule out the existence of periodic orbits or recurrent orbits in the physical phase space and conclude that it is plausible that all orbits asymptote towards equilibrium points, both to the past and to the future. We also identify all equilibrium points on the null surface, through which orbits can be continued into the spacelike self-similar regime. Defining a parameter K, which depends on the two scalar potential parameters, we find that for K < 1, the orbits generically expand away from a massless scalar field model or a static single scalar field model, recollapse and then evolve towards a contracting massless scalar field model or a static single scalar field model. The evolution from a non-static massless scalar field model to a second non-static massless scalar field model is also possible, and in this case the orbits cannot be extended into the spacelike self-similar regime. We note that there are static single scalar field models that are physical attractors, so that there appear to be multiple-scalar field models with exponential potentials for which only a single scalar field dominates at late-times or at early-times. For the parameter range K > 1, all orbits generically expand away from a massless scalar field model, then recollapse and subsequently contract to a massless scalar field model. However, since in this case there always exist equilibrium points on the null boundary, there are orbits that can be continued into the spacelike self-similar regime and subsequently either continue expanding towards an assisted inflationary solution or recollapse to a massless scalar field model which is again on the null boundary.

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