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

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

Cosmological Constraints on a Dynamical Electron Mass

Motivated by recent astrophysical observations of quasar absorption systems, we formulate a simple theory where the electron to proton mass ratio $\mu =m_{e}/m_{p}$ is allowed to vary in space-time. In such a minimal theory only the electron mass varies, with $\alpha$ and $m_{p}$ kept constant. We find that changes in $\mu$ will be driven by the electronic energy density after the electron mass threshold is crossed. Particle production in this scenario is negligible. The cosmological constraints imposed by recent astronomical observations are very weak, due to the low mass density in electrons. Unlike in similar theories for spacetime variation of the fine structure constant, the observational constraints on variations in $\mu$ imposed by the weak equivalence principle are much more stringent constraints than those from quasar spectra. Any time-variation in the electron-proton mass ratio must be less than one part in $10^{9}$since redshifts $z\approx 1.$This is more than one thousand times smaller than current spectroscopic sensitivities can achieve. Astronomically observable variations in the electron-proton must therefore arise directly from effects induced by varying fine structure 'constant' or by processes associated with internal proton structure. We also place a new upper bound of $2\times 10^{-8}$ on any large-scale spatial variation of $\mu$ that is compatible with the isotropy of the microwave background radiation.Comment: New bounds from weak equivalence principle experiments added, conclusions modifie

Cosmologies with Energy Exchange

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.Comment: 12 pages, 1 figur

Vector Perturbations in a Contracting Universe

In this note we show that vector perturbations exhibit growing mode solutions in a contracting Universe, such as the contracting phase of the Pre Big Bang or the Cyclic/Ekpyrotic models of the Universe. This is not a gauge artifact and will in general lead to the breakdown of perturbation theory -- a severe problem that has to be addressed in any bouncing model. We also comment on the possibility of explaining, by means of primordial vector perturbations, the existence of the observed large scale magnetic fields. This is possible since they can be seeded by vorticity.Comment: v3. Two reference added; Identical with version accepted for publication at PR

Almost-homogeneity of the universe in higher-order gravity

In the $R+\alpha R^2$ gravity theory, we show that if freely propagating massless particles have an almost isotropic distribution, then the spacetime is almost Friedmann-Robertson-Walker (FRW). This extends the result proved recently in general relativity ($\alpha=0$), which is applicable to the microwave background after photon decoupling. The higher-order result is in principle applicable to a massless species that decouples in the early universe, such as a relic graviton background. Any future observations that show small anisotropies in such a background would imply that the geometry of the early universe were almost FRW.Comment: 14 pages LaTeX, no figures; to appear in General Relativity and Gravitatio

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

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

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

Cosmological milestones and energy conditions

Until recently, the physically relevant singularities occurring in FRW cosmologies had traditionally been thought to be limited to the "big bang", and possibly a "big crunch". However, over the last few years, the zoo of cosmological singularities considered in the literature has become considerably more extensive, with "big rips" and "sudden singularities" added to the mix, as well as renewed interest in non-singular cosmological events such as "bounces" and "turnarounds". In this talk, we present an extensive catalogue of such cosmological milestones, both at the kinematical and dynamical level. First, using generalized power series, purely kinematical definitions of these cosmological events are provided in terms of the behaviour of the scale factor a(t). The notion of a "scale-factor singularity" is defined, and its relation to curvature singularities (polynomial and differential) is explored. Second, dynamical information is extracted by using the Friedmann equations (without assuming even the existence of any equation of state) to place constraints on whether or not the classical energy conditions are satisfied at the cosmological milestones. Since the classification is extremely general, and modulo certain technical assumptions complete, the corresponding results are to a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in Nafplio, Greec