International Journal of Modern Physics D

The history of science can be recounted in many ways: by addressing the work of one person or school; by starting with the ancients and working chronologically up to the present; by focusing on a particular century; or by tracing a particular important idea as far back and forward as it can be found. The present discussion does none of these. Rather, it adopts the ordering of a standard introductory astronomy textbook, from the solar system via stars and galaxies, to the universe as a whole, and in each regime picks out a few issues that were controversial or wrongly decided for a long time. For each, I attempt to identify a duration of the period of uncertainty or error and some of the causes of the confusion. This is surely not an original idea, though I am not aware of having encountered it elsewhere, and it is not one that is likely to appeal to most 21st century historians of science, for whom the question "Who first got it right?" is not necessarily an important, or even appropriate, one. Some of the stories have been told as historical introductions to conferences and are here summarized and brought up to date. Others I had not previously addressed.

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

We analyze the dynamical behavior of a quasi-isotropic universe in the presence of a cosmological fluid endowed with bulk viscosity. We express the viscosity coefficient as a power law of the fluid energy density: ζ = ζ₀ ∊^s. Then we fix s = 1/2 as the only case in which viscosity plays a significant role in the singularity physics but does not dominate the universe dynamics (as required by its microscopic perturbative origin). The parameter ζ₀ is left free to define the intensity of the viscous effects.

In spirit of the work by Lifshitz and Khalatnikov on the quasi-isotropic solution, we analyze both Einstein and hydrodynamic equations up to first and second order in time. As a result, we get a power law solution existing only in correspondence to a restricted domain of ζ₀.

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior space–time at some constant radius hypersurface. We find an interesting picture; namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.

We propose a new potential in brane inflation theory, which is given by the arctangent of the square of the scalar field. Then we perform an explicit computation for inflationary quantities. This potential has many nice features. In the small field approximation, it reproduces the chaotic and MSSM potentials. It allows one, in the large field approximation, to implement the attractor mechanism for bulk black holes where the geometry on the brane is de Sitter. In particular, we show, up to some assumptions, that the Friedman equation can be reinterpreted as a Schwarzschild black hole attractor equation for its mass parameter.