Andrew P. Billyard

Interactions in scalar field cosmology

We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the scalar field is transferred to the matter fields, consistent with a term that arises from scalar-tensor theory under a conformal transformation and field redefinition. The governing ordinary differential equations reduce to a dynamical system when appropriate normalized variables are defined. We analyze the dynamical system and find that the interaction term can significantly affect the qualitative behavior of the models. The late-time behavior of these models may be of cosmological interest. In particular, for a specific range of values for the model parameters there are late-time attracting solutions, corresponding to a novel attracting equilibrium point, which are inflationary and in which the scalar field’s energy-density remains a fixed fraction of the matter field’s energy density. These scalar field models may be of interest as late-time cosmologies, particularly in view of the recent observations of the current accelerated cosmic expansion. For appropriate values of the interaction coupling parameter, this equilibrium point is an attracting focus, and hence as inflating solutions approach this late-time attractor the scalar field oscillates. Hence these models may also be of importance in the study of inflation in the early universe.

Stability of cosmological scaling solutions

We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant satisfying 0 2/3, and particularly for realistic matter with gamma >= 1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequences of these results.

Asymptotic behavior of cosmological models in scalar-tensor theories of gravity

We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behaviour of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focussed on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important role in describing the asymptotic behaviour of more general models (e.g., those cosmological models that act as early-time and late-time attractors).

Dynamics of M-theory cosmology

A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non-trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behavior of the solutions ~i.e., the nature of the equilibrium points!. The only past-attracting solution ~source in the system! may be interpreted in the elevendimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.

Scalar field cosmologies with barotropic matter: models of Bianchi class B

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field with an exponential potential V() = ek. In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention to whether the models isotropize (and inflate) to the future, and we discuss the genericity of the cosmological scaling solutions.

Qualitative analysis of string cosmologies

A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies derived from the string effective action when the combined effects of a dilaton, modulus, two-form potential and central charge deficit are included. The latter has significant effects on the qualitative dynamics. The analysis is also directly applicable to the anisotropic Bianchi type I cosmology. @S0556-2821~99!01112-1#

Qualitative analysis of early universe cosmologies

A qualitative analysis is presented for a class of homogeneous cosmologies derived from the string effective action when a cosmological constant is present in the matter sector of the theory. Such a term has significant effects on the qualitative dynamics. For example, models exist which undergo a series of oscillations between expanding and contracting phases due to the existence of a heteroclinic cycle in the phase space. Particular analytical solutions corresponding to the equilibrium points are also found.

Qualitative analysis of anisotropic and curved string cosmologies

A complete qualitative study of the dynamics of string cosmologies is presented for the class of isotopic curvature universes. These models are of Bianchi types I, V and IX and reduce to the general class of Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy. A non-trivial 2-form potential and cosmological constant terms are included in the system. In general, the 2-form potential and spatial curvature terms are only dynamically important at intermediate stages of the evolution. In many of the models, the cosmological constant is important asymptotically and anisotropy becomes dynamically negligible. There also exist bouncing cosmologies.