March 09, 2006

Surface Paradigm for Dark Energy

There has been indications that the dark energy and dark matter have their origin in general relativity, with some extensions. T.Padmanabhan discusses dark energy as the Mystery of the Millennium (an optimist would hope a decade or two). Dark matter discussion is given in the references of this paper.

The author assumes the dynamics of gravity follows from an approach which uses only the surface term of the Hilbert action for the continuum. Gravity has thermodynamic origin in this approach. The surface term's variation is related to entropy TdS and the matter term's variation gives PdV and dE terms. The entire variation is equivalent to the known equality between these. The main point I quote and condense:

Within the true theory of quantum gravity, measurable quantities should be the fluctuations in the vacuum energy and not the absolute value of the vacuum energy. The cosmological constant is most likely a low energy relic of quantum gravitational effects, arising from the surface term alone. This procedure is applicable to a large class of theories, including Gauss-Bonnet type actions in higher dimensions (superstrings). This suggests that the mechanism for ignoring the bulk cosmological constant is likely to survive quantum gravitational corrections which are likely to bring in additional, higher derivative, terms to the action. In a universe with two length scales L_Lambda (proportional to the Hubble radius) and L_p, the vacuum fluctuations will contribute an energy density of the correct order of magnitude r_DE =√rho_IR rho_UV, according to the author.
Addendum (more refs.)

March 02, 2006

General Relativity and Galactic Distances

My colleague T. Perko informed me of a paper by H. Balasin and D. Grumiller titled Significant reduction of galactic dark matter by general relativity.  The authors model the matter content of a galaxy by a pressureless perfect fluid. Stationarity and axial symmetry are also imposed on the solutions of Einstein equations. Using some simplifications they solve the linear partial differential equations and conclude that the Newtonian approximation over-estimates the amount of matter in a galaxy by about a third. GR reduces the amount of dark matter needed to explain the flat rotation curves.

An earlier paper by F. I. Cooperstock and S. Tieu, titled General Relativity Resolves Galactic Rotation Without Exotic Dark Matter, makes a stronger claim of the dark matter needed in galaxies. Using a similar perfect fluid model they end up to one linear and one non-linear equation relating the angular velocity to the fluid density. From their calculation the authors conclude that the need for a massive halo of exotic dark matter is removed.

We most likely will see other studies of general relativistic galactic systems, and new estimates of the amount of dark matter in the universe. For the present, we tend consider the latter paper's conclusion somewhat striking.