Mark S. Madsen

Scalar fields in curved spacetimes

The author examines the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions. The author shows that the stress tensor of the scalar field always has the structure of a fluid stress tensor. In the case that the scalar field is minimally coupled to gravity, this reduces to a perfect-fluid structure. In addition, the author obtains a generally non-trivial form of the Bianchi identities for this theory, investigates the kinematics of the scalar field and shows how to extend the analysis to include complex scalars and scalar multiplets. Finally, the author discusses the ground-state solutions of the theory, with special attention given to the case when the scalar field potential is polynomial in the fields. The author shows that the gravity-scalar coupling has interesting consequences for the spontaneous breakdown of gauge symmetries and for the observable value of the cosmological constant.

THE STRUCTURE AND FORMATION OF BOSON STARS

Boson stars are gravitationally bound conglomerates of scalar particles. We review their structure and stability, and discuss possible means by which they might form in the early universe.

De Sitter ground states and boundary terms in generalised gravity

Abstract The conditions are derived for existence of maximally symmetric N-dimensional De Sitter space-times in gravity theories derived from the variation of an action containg a lagrangian which is an arbitrary analytic function of the quadratic curvature invariants formed from the scalar, Ricci, and Riemann curvatures. Corresponding existence conditions are also derived for the Lovelock lagrangians. The form of the boundary term required to cancel the surface terms arising in the gravitational action is calculated for gravity theories derived from lagrangians which are arbitrary analytic functions of the scalar curvature when the space-time is maximally symmetric.

The plane gravitational wave in quadratic gravity

The Peres plane gravitational wave solutions (1960) are derived in the general four-dimensional quadratic curvature gravitational theory. It is found that if the quadratic extension from general relativity includes only the scalar Ricci curvature in the action, then these solutions are the same as those found in general relativity. When the tensor part of the Ricci curvature contributes to the quadratic part of the action, however, the plane-wave solutions are more complicated, involving modes not present in the general relativistic solution. The solutions presented here are all of the Kerr-Schild form (1965), and can all be extended to admit a null dust, corresponding to a plane electromagnetic wave tracking the gravitational wave. The solution found in such a case possesses a resonance between the gravitational and electromagnetic waves which is not present in the general relativistic analogue.

The cosmological formation of boson stars

Abstract The formation of boson stars by gravitational collapse in the early universe is considered. It is demonstrated that while the simplest models are unfavourable for boson star formation, the inclusion of a boson self-interaction and consideration of a boson-antiboson asymmetry allow substantial possibilities for the cosmological formation of boson stars.

The stability of vacuum solutions in generalised gravity

Abstract The stability of the Ricci-flat solutions of a large class of generalised gravity theories is examined. It is shown by use of complementary methods that all such solutions are stable in a given theory if that theory admits a truncation to a quadratic theory in which the solution is stable. In particular, this means that the exterior Schwarzschild solution is stable in any gravity theory constructed purely from the Ricci scalar, provided that it exists in that theory.

The success of inflation with quadratic gravity

Abstract We consider the inflationary behaviour of the R2 model with a FRW background. For initial scalar curvatures Ri>0 the universe collapses more readily than for the massive scalar field case when spatial curvatures are present. Only a small fraction of initial conditions lead to inflation when −MPl2⩽Ri⩽MPl2. We also comment on a recent instability suggested by Suen.

The role of Hawking radiation in the inflationary universe

The effects of Hawking radiation on the evolution of the universe are examined in the context of the chaotic inflationary models. Since inflation will not end if Hawking radiation dominates the energy density, a constraint can be derived which relates the density of massless states to the Hubble parameter during the inflationary period. The form of this constraint shows that particle theories having larger values of the density of states near the Planck mass are more vulnerable to the inflationary flatness problem. A model of Hawking radiation in an expanding universe is constructed which shows that despite the domination of the passive gravitational mass by the Hawking radiation, the gauge-invariant amplitude of the metric perturbations is not significantly decreased by its presence. Some of the issues arising from the necessity of a pre-inflationary radiation-dominated phase are discussed.