The area of a rough black hole.

We investigate the consequences for the black hole area of introducing fractal structure for the horizon geometry. We create a three-dimensional spherical analogue of a 'Koch Snowflake' using a infinite diminishing hierarchy of touching spheres around the Schwarzschild event horizon. We can create a fractal structure for the horizon with finite volume and infinite (or finite) area. This is a toy model for the possible effects of quantum gravitational spacetime foam, with significant implications for assessments of the entropy of black holes and the universe, which is generally larger than in standard picture of black hole structure and thermodynamics, potentially by very considerable factors. The entropy of the observable universe today becomes S ≈ 10 120 ( 1 + Δ / 2 ) , where 0 ≤ Δ ≤ 1 , with Δ = 0 for a smooth spacetime structure and Δ = 1 for the most intricate. The Hawking lifetime of black holes is also reduced.

Limits on the dependence of the fine-structure constant on gravitational potential from white-dwarf spectra.

We propose a new probe of the dependence of the fine-structure constant α on a strong gravitational field using metal lines in the spectra of white-dwarf stars. Comparison of laboratory spectra with far-UV astronomical spectra from the white-dwarf star G191-B2B recorded by the Hubble Space Telescope Imaging Spectrograph gives limits of Δα/α=(4.2±1.6)×10(-5) and (-6.1±5.8)×10(-5) from FeV and NiV spectra, respectively, at a dimensionless gravitational potential relative to Earth of Δφ≈5×10(-5). With better determinations of the laboratory wavelengths of the lines employed these results could be improved by up to 2 orders of magnitude.

New solution of the cosmological constant problems.

We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) to a field which can take many possible values. Variation gives a new integral constraint equation for the classical value of the effective CC that dominates the wave function of the Universe. The expected value of the effective CC, is calculated from measurable quantities to be O(t(U)(-2)) as observed, where t(U) is the present age of the Universe in Planck units. This also leads to a falsifiable prediction for the observed spatial curvature parameter of Ω(k0) = -0.0055. Our proposal requires no fine-tunings or extra dark-energy fields but suggests a new view of time evolution.

Four direct measurements of the fine-structure constant 13 billion years ago.

Observations of the redshift z = 7.085 quasar J1120+0641 are used to search for variations of the fine structure constant, α, over the redshift range 5.5 to 7.1. Observations at z = 7.1 probe the physics of the universe at only 0.8 billion years old. These are the most distant direct measurements of α to date and the first measurements using a near-IR spectrograph. A new AI analysis method is employed. Four measurements from the x-shooter spectrograph on the Very Large Telescope (VLT) constrain changes in a relative to the terrestrial value (α0). The weighted mean electromagnetic force in this location in the universe deviates from the terrestrial value by Δα/α = (α z - α0)/α0 = (-2.18 ± 7.27) × 10-5, consistent with no temporal change. Combining these measurements with existing data, we find a spatial variation is preferred over a no-variation model at the 3.9σ level.

Szekeres universes with homogeneous scalar fields.

We consider the existence of an "inflaton" described by an homogeneous scalar field in the Szekeres cosmological metric. The gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski-Sachs spacetime and an inhomogeneous FLRW(-like) spacetime with spatial curvature a constant. The main differences with the original Szekeres spacetimes containing only pressure-free matter are discussed. We investigate the stability of the two families of solution by studying the critical points of the field equations. We find that there exist stable solutions which describe accelerating spatially-flat FLRW geometries.

Reconstructions of the dark-energy equation of state and the inflationary potential.

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations n s and the tensor to scalar ratio r. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that n s - 1 = h r . For the function h r , we consider three cases, where h r is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

Varying constants.

We review properties of theories for the variation of gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that are consistent with time variation in the fine structure constant since a redshift of 3.5. The behaviour of a simple class of varying-alpha cosmologies is outlined in the light of all the observational constraints.

A simple cosmology with a varying fine structure constant.

We investigate the cosmological consequences of a theory in which the electric charge e can vary. In this theory the fine structure "constant," alpha, remains almost constant in the radiation era, undergoes a small increase in the matter era, but approaches a constant value when the universe starts accelerating because of a positive cosmological constant. This model satisfies geonuclear, nucleosynthesis, and cosmic microwave background constraints on time variation in alpha, while fitting the observed accelerating Universe and evidence for small alpha variations in quasar spectra. It also places specific restrictions on the nature of the dark matter. Further tests, involving stellar spectra and Eötvös experiments, are proposed.