Stable Isotropic Cosmological Singularities in Quadratic Gravity

We show that, in quadratic lagrangian theories of gravity, isotropic cosmological singularities are stable to the presence of small scalar, vector and tensor inhomogeneities. Unlike in general relativity, a particular exact isotropic solution is shown to be the stable attractor on approach to the initial cosmological singularity. This solution is also known to act as an attractor in Bianchi universes of types I, II and IX, and the results of this paper reinforce the hypothesis that small inhomogeneous and anisotropic perturbations of this attractor form part of the general cosmological solution to the field equations of quadratic gravity. Implications for the existence of a 'gravitational entropy' are also discussed.Comment: 18 pages, no figure

Anisotropically Inflating Universes

We show that in theories of gravity that add quadratic curvature invariants to the Einstein-Hilbert action there exist expanding vacuum cosmologies with positive cosmological constant which do not approach the de Sitter universe. Exact solutions are found which inflate anisotropically. This behaviour is driven by the Ricci curvature invariant and has no counterpart in the general relativistic limit. These examples show that the cosmic no-hair theorem does not hold in these higher-order extensions of general relativity and raises new questions about the ubiquity of inflation in the very early universe and the thermodynamics of gravitational fields.Comment: 5 pages, further discussion and references adde

Cosmological Co-evolution of Yang-Mills Fields and Perfect Fluids

We study the co-evolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis and the bound is comparatively weak, and Omega_YM < 0.105 Omega_rad.Comment: 13 pages, 5 figures, submitted to PR

Cosmological Bounds on Spatial Variations of Physical Constants

We derive strong observational limits on any possible large-scale spatial variation in the values of physical 'constants' whose space-time evolution is driven by a scalar field. The limits are imposed by the isotropy of the microwave background on large angular scales in theories which describe space and time variations in the fine structure constant, the electron-proton mass ratio, and the Newtonian gravitational constant, G. Large-scale spatial fluctuations in the fine structure constant are bounded by 2x10^-9 and 1.2x10^-8 in the BSBM and VSL theories respectively, fluctuations in the electron-proton mass ratio by 9x10^-5 in the BM theory and fluctuations in G by 3.6x10^-10 in Brans-Dicke theory. These derived bounds are significantly stronger than any obtainable by direct observations of astrophysical objects at the present time.Comment: 13 pages, 1 table, typos corrected, refs added. Published versio

Bouncing Universes with Varying Constants

We investigate the behaviour of exact closed bouncing Friedmann universes in theories with varying constants. We show that the simplest BSBM varying-alpha theory leads to a bouncing universe. The value of alpha increases monotonically, remaining approximately constant during most of each cycle, but increasing significantly around each bounce. When dissipation is introduced we show that in each new cycle the universe expands for longer and to a larger size. We find a similar effect for closed bouncing universes in Brans-Dicke theory, where $G$ also varies monotonically in time from cycle to cycle. Similar behaviour occurs also in varying speed of light theories

Solving the Flatness and Quasi-flatness Problems in Brans-Dicke Cosmologies with a Varying Light Speed

We define the flatness and quasi-flatness problems in cosmological models. We seek solutions to both problems in homogeneous and isotropic Brans-Dicke cosmologies with varying speed of light. We formulate this theory and find perturbative, non-perturbative, and asymptotic solutions using both numerical and analytical methods. For a particular range of variations of the speed of light the flatness problem can be solved. Under other conditions there exists a late-time attractor with a constant value of \Omega that is smaller than, but of order, unity. Thus these theories may solve the quasi-flatness problem, a considerably more challenging problem than the flatness problem. We also discuss the related \Lambda and quasi-\Lambda problem in these theories. We conclude with an appraisal of the difficulties these theories may face.Comment: 21 pages, 6 figure

Time variation of the fine structure constant in decrumpling or TVSD model

Within the framework of a model universe with time variable space dimension (TVSD), known as decrumpling or TVSD model, we study the time variation of the fine structure constant. Using observational bounds on the present time variation of the fine structure constant, we are able to obtain the present time variation of spatial dimensions.Comment: 10 pages, accepted for publication in Int.J.Mod.Phys.

Cosmological dynamics of exponential gravity

We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite and asymptotic regimes. The results show that cosmic histories exist which admit a double de-Sitter phase which could be useful for describing the early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure

The Andante Regime of Scalar Field Dynamics

The andante regime of scalar field dynamics in the chaotic inflationary Universe is defined as the epoch when the field is rolling moderately slowly down its interaction potential, but at such a rate that first-order corrections to the slow-roll approximation become important. These conditions should apply towards the end of inflation as the field approaches the global minimum of the potential. Solutions to the Einstein-scalar field equations for the class of power law potentials $V(\phi) \propto \phi^{2n}$ are found in this regime in terms of the inverse error function.Comment: 11 pages of plain Latex, FNAL-Pub-94/226-

Structure and stability of the Lukash plane-wave spacetime

We study the vacuum, plane-wave Bianchi $VII{}_{h}$ spacetimes described by the Lukash metric. Combining covariant with orthonormal frame techniques, we describe these models in terms of their irreducible kinematical and geometrical quantities. This covariant description is used to study analytically the response of the Lukash spacetime to linear perturbations. We find that the stability of the vacuum solution depends crucially on the background shear anisotropy. The stronger the deviation from the Hubble expansion, the more likely the overall linear instability of the model. Our analysis addresses rotational, shear and Weyl curvature perturbations and identifies conditions sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra