David Sloan

Loop quantum cosmology and slow roll inflation

In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter vanishes at the bounce and attains a finite universal maximum at the end of super-inflation. These novel features lead to an unforeseen implication: in presence of suitable potentials all LQC dynamical trajectories are funneled to conditions which virtually guarantee slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to certain results in general relativity, where it is argued that the a priori probability of obtaining a slow roll with 68 or more e-foldings is suppressed by a factor e−204.

Asymptotics and Hamiltonians in a first-order formalism

We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the spacetime. We address the subtle but important problems that arise because of logarithmic translations and super translations both in the Lagrangian and Hamiltonian frameworks. As a forthcoming paper will show, the treatment of higher dimensions is considerably simpler. Our first-order framework also suggests a new direction for generalizing the spectral action of non-commutative geometry.

A Hamiltonian Formulation of the BKL Conjecture

The Belinskii, Khalatnikov and Lifshitz conjecture [1] posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by ‘ignoring spatial derivatives in favor of time derivatives.’ In [2] we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity. We now present the details of the analytical part of that investigation. While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.

Inflationary attractors and their measures

Several recent misconceptions about the measure problem in inflation and the nature of inflationary attractors are addressed. We show that within the Hamiltonian system of flat Friedmann-Lema\^itre-Robertson-Walker cosmology coupled to a massive scalar field, the focussing of the Liouville measure on attractor solutions is brought about by a spread in a gauge degree of freedom - the spatial volume. Using this we show how the Liouville measure formulated on a surface of constant Hubble rate induces a probability distribution function on surfaces of other Hubble rates, and the attractor behaviour is seen through the focussing of this function on a narrow range of physical observables. One can conclude then that standard techniques from Hamiltonian dynamics suffice to provide a satisfactory description of attractor solutions and the measure problem. Updated to match published version.

Action and Hamiltonians in higher-dimensional general relativity: first-order framework

We consider d > 4-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle is well defined without the need of infinite counter-terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the isolated system. This work runs parallel to our previous analysis in four dimensions Ashtekar et al (2008 Class. Quantum Grav. 25 095020 (arXiv:0802.2527)). The higher-dimensional analysis is in fact simpler because of the absence of logarithmic and super translation ambiguities.

Bouncing Anisotropic Universes with Varying Constants

We examine the evolution of a closed, homogeneous and anisotropic cosmology subject to a variation of the fine structure “constant” α within the context of the theory introduced by Bekenstein and Sandvik et al. which generalizes Maxwell’s equations and general relativity The variation of α permits an effective ghost scalar field, whose negative energy density becomes dominant at small length scales, leading to a bouncing cosmology. A thermodynamically motivated coupling that describes energy exchange between the effective ghost field and the radiation field leads to an expanding, isotropizing sequence of bounces. In the absence of entropy production, we also find solutions with stable anisotropic oscillations around a static universe.

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

Abstract All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics – it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einsteins equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

A homogeneous model of spinfoam cosmology

We examine spinfoam cosmology by use of a simple graph adapted to homogeneous cosmological models. We calculate dynamics in the isotropic limit, and provide the framework for the anisotropic case. We calculate the transition amplitude between holomorphic coherent states on a single node graph and find that the resultant dynamics is peaked on solutions which have no support on the zero volume state, indicating that big bang type singularities are avoided within such models. Communicated by P Singh

First-order action and Euclidean quantum gravity

We show that the on-shell path integral for asymptotically flat Euclidean spacetimes can be given in the first-order formulation of general relativity, without assuming the boundary to be isometrically embedded in Euclidean space and without adding infinite counter-terms. For illustrative examples of our approach, we evaluate the first-order action for the four-dimensional Euclidean Schwarzschild and NUT-charged spacetimes to derive the corresponding on-shell partition functions, and show that the correct thermodynamic quantities for the solutions are reproduced.

The Resilience of Life to Astrophysical Events

Much attention has been given in the literature to the effects of astrophysical events on human and land-based life. However, little has been discussed on the resilience of life itself. Here we instead explore the statistics of events that completely sterilise an Earth-like planet with planet radii in the range 0.5–1.5R⊕ and temperatures of ∼300 K, eradicating all forms of life. We consider the relative likelihood of complete global sterilisation events from three astrophysical sources – supernovae, gamma-ray bursts, large asteroid impacts, and passing-by stars. To assess such probabilities we consider what cataclysmic event could lead to the annihilation of not just human life, but also extremophiles, through the boiling of all water in Earth’s oceans. Surprisingly we find that although human life is somewhat fragile to nearby events, the resilience of Ecdysozoa such as Milnesium tardigradum renders global sterilisation an unlikely event.