R. J. van den Hoogen

Dynamics of multi-scalar-field cosmological models and assisted inflation

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where m

Qualitative viscous cosmology

The Full (non--truncated) Israel--Stewart theory of bulk viscosity is applied to dissipative FRW spacetimes. Dimensionless variables and dimensionless equations of state are used to write the Einstein--thermodynamic equations as a plane autonomous system and the qualitative behaviour of this system is determined. Entropy production in these models is also discussed.

Homogeneous scalar field cosmologies with an exponential potential

We shall study spatially homogeneous cosmological models containing a self-interacting scalar field with an exponential potential of the form V(φ)=Λekφ. The asymptotic properties of these models are discussed. In particular, their possible isotropization and inflation are investigated for all values of the parameter k. A particular class of models is analyzed qualitatively using the theory of dynamical systems, illustrating the general asymptotic behavior.

Scaling solutions in Robertson-Walker spacetimes

We investigate the stability of cosmological scaling solutions describing a barotropic fluid with p = (-1) and a non-interacting scalar field with an exponential potential V() = V0e-. We study homogeneous and isotropic spacetimes with non-zero spatial curvature and find three possible asymptotic future attractors in an ever-expanding universe. One is the zero-curvature power-law inflation solution where 1 ( (2/3),2 3). We find that this matter scaling solution is unstable to curvature perturbations for > (2/3). The third possible future asymptotic attractor is a solution with negative spatial curvature where the scalar field energy density remains proportional to the curvature with 2/2 ( > (2/3),2 > 2). We find that solutions with 0 are never late-time attractors.

Qualitative analysis of viscous fluid cosmological models satisfying the Israel-Stewart theory of irreversible thermodynamics

Isotropic and spatially homogeneous viscous fluid cosmological models are investigated using the truncated Israel-Stewart theory of irreversible thermodynamics to model the bulk viscous pressure. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is then utilized to complete the system. The resulting dynamical system is analysed using geometric techniques from dynamical systems theory to find the qualitative behaviour of the Friedmann-Robertson-Walker models with bulk viscosity. In these models there exists a free parameter such that the qualitative behaviour of the models can be quite different (for certain ranges of values of this parameter) from that found in models satisfying the Eckart theory studied previously. In addition, the conditions under which the models inflate are investigated.

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.

Qualitative analysis of diagonal Bianchi type V imperfect fluid cosmological models

The Einstein field equations for diagonal Bianchi type V imperfect fluid cosmological models with both viscosity and heat conduction are set up as an autonomous system of differential equations using dimensionless variables and a set of dimensionless equations of state. Models with and without a cosmological constant, λ, are investigated using the techniques from dynamical systems theory. It is shown that all models that satisfy the weak energy conditions isotropize. The introduction of viscosity (in particular) allows for a variety of different qualitative behaviors (including, for example, models with a negative deceleration parameter). Exact solutions that correspond to the singular points of the dynamical system are found. It is shown that the past asymptotic states are represented by self‐similar cosmological models and, if λ=0, the future asymptotic states are also, in general, represented by self‐similar cosmological models; in the exceptional cases the late time asymptotic state is represented by ...

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 causal anisotropic viscous-fluid cosmological models

The truncated Israel--Stewart theory of irreversible thermodynamics is used to describe the bulk viscous pressure and the anisotropic stress in a class of spatially homogeneous viscous-fluid cosmological models. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is utilized to complete the system. The resulting dynamical system is then analysed using standard geometric techniques. It is found that the presence of anisotropic stress plays a dominant role in the evolution of the anisotropic models. In particular, in the case of the Bianchi type-I models it is found that anisotropic stress leads to models that violate the weak energy condition and to the creation of a periodic orbit in some instances. The stability of the isotropic singular points is analysed in the case with zero heat conduction; it is found that there are ranges of parameter values such that there exists an attracting isotropic Friedmann--Robertson--Walker model. In the case of zero anisotropic stress but, with non-zero heat conduction, the stability of the singular points is found to be the same as in the corresponding case with zero heat conduction; hence the presence of heat conduction does not apparently affect the global dynamics of the model.

Bianchi type II brane-world cosmologies(U>~0)

The asymptotic properties of the Bianchi type II cosmological model in the Brane-world scenario are investigated. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. The isotropic braneworld solution is determined to represent the initial singularity in all brane-world cosmologies. Additionally, it is shown that it is the kinetic energy of the scalar field which dominates the initial dynamics in these brane-world cosmologies. It is important to note that, the dynamics of these brane-world cosmologies is not necessarily asymptotic to general relativistic cosmologies to the future in the case of a zero four-dimensional cosmological constant.