Session S4: Gravitation Physics

Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.   

Einstein's Gravity as an Emergent Local Gauge Tetrad/Spin Connection Field

Einstein's 1915 General Relativity with curvature but no torsion is a local gauge theory of the abelian 4-parameter translation subgroup of the non-compact Poincare group. The gauge potentials are the four ``Dirac square root'' tetrads not the Levi-Civita field that is bilinear in the 16 tetrad components and their first partial derivatives. Since the tetrads are Lorentz 4-vectors, the basic gravity field is spin 1 and is, therefore, renormalizable. The spin 2 metric field is composite. The analogy with electroweak-strong nonabelian compact Lie group gauge theories becomes apparent when the full Poincare group is locally gauged adding a dynamically independent torsion field to the curvature field. A unification of post-inflation emergent Einstein gravity with the strong force of quantum chromodynamics is also apparent in the tetrad formulation. The tetrad fields are analogous to the superfluid flow field that is the gradient of a ground state coherent multi-valued Goldstone phase.   

An Educational Look at an alternative to the Expanding Universe Model

The author often toys with an alternative view to the expanding universe model and believes it would be a good way to teach the Scientific method. In the author's (R.M. Kriske) model the red shift is a result of magnifying the horizon of a 4 dimensional surface. On a two dimensional surface such as the earth the horizon is not maginifiable since things on the surface naturally tilt away from the observer in every direction and everything is transformed into a curved line (the Horizon) (the students can verify this as a globe can be used with some pins in it-for example). Likewise one would expect this signature of curvature to show up on three curved space dimensions, and instead of pins, a perpendicular time dimension. As the observer looks toward the pins they tilt away from him/her and in four dimensions this means they are accelerating away from him/her even though the globe is standing still. At each point a pair is being produced with its attendant gamma ray emission, but the points are of course seen as accelerating away, simply due to the curvature of the globe and nothing else, resulting in a red shift. This author produced model has never been suggested before and never presented to the Scientific community. The students would then need to compare this to the current simpler model that point sources accelerating away from the observer undergo a redshift due to the Doppler Effect. The Students would then have to review these models and determine the size of the globe for the amount of red shift seen from the two competing models. One model has a cut- off mode, since the pins not only tip backward in the curved space model but are also cut off. How does this cut-off show up, is it simply dimming, and can an experiment be done for it? The last step of this exercise is to see if one could tell the difference between these models, and if a mixed model is better, since the Globe could also be expanding (Of course the instructor could also ask what the result would be if the globe where contracting).   

Standing gravitational waves from domain walls

We construct a plane symmetric, standing gravitational wave for a domain wall plus a massless scalar field. The scalar field can be associated with a fluid which has the properties of ``stiff'' matter, i.e., matter in which the speed of sound equals the speed of light. Although domain walls are observationally ruled out in the present era, the solution has interesting features which might shed light on the character of exact nonlinear wave solutions to Einstein's equations. Additionally this solution may act as a template for higher dimensional ``brane-world'' model standing waves.   

A WKB-like approach to Unruh radiation

Unruh radiation is the thermal flux seen by an accelerated observer moving through Minkowski spacetime. In this article, we study Unruh radiation as tunneling through a barrier. We discuss the metric of the observer that constantly accelerates in vacuum, usually called the Rindler observer, and discuss some of its subtleties. To obtain the tunneling rate and the temperature of the Unruh radiation, we use a WKB-like method. This derivation should be accessible to advanced undergraduate students or beginning graduate students. In addition, this gravitational WKB method helps to highlight some fine points of the WKB method as usually applied in quantum mechanics. First, the tunneling rate strictly should be written as the closed path integral of the canonical momentum. Second, for the case of the gravitational WKB problem, there is a time-like contribution to the tunneling rate arising from an imaginary change of the time coordinate upon crossing the horizon. This temporal contribution to the tunneling rate has no analog in the ordinary quantum mechanical WKB calculation.   

New Perspective on the Cosmological Constant Problem

A multiverse approach to the Cosmological Constant Problem (CCP) is considered. It is assumed that each member of the multiverse ensemble has a characteristic scale $a$ that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with effective cosmological constant near the quantum filed theory value (of the order of the Planck vacuum energy density $\tilde\Lambda \approx 8 \pi$ in Planck units). For universes with characteristic scale of the order of the observed universe $a \approx 8\times 10^{60}$ the cosmological constant $\Lambda =\tilde\Lambda/a^2$ is within few orders of magnitude of the observed value.   

Quasilocal Energy in FRW Cosmology

I present a calculation of the quasilocal energy of a generic FRW model of the universe. The results have the correct behavior in the small-sphere limit and vanish for the empty Milne universe. Higher order corrections are found when comparing these results to classical calculations of cosmological energy. This case is different from others in the literature chiefly in that it involves a non-stationary spacetime. This fact can be used to differentiate between the various formulations of quasilocal energy. In particular, the formulation due to Brown and York is compared to that of Epp. Only one of these is seen to have the correct classical limit.   

Understanding Dark Energy

By careful analysis of the data from the WMAP satellite, scientists were surprised to determine that about 70\% of the matter in our universe is in some unknown form, and labeled it Dark Energy. Earlier, in 1998, two separate international groups of astronomers studying Ia supernovae were even more surprised to be forced to conclude that an amazing smooth transition occurred, from the expected slowing down of the expansion of our universe (due to normal positive gravitation) to an accelerating expansion of the universe that began at at a big bang age of the universe of about nine billion years. In 1918 Albert Einstein stated that his Lambda term in his theory of general relativity was ees,``the energy of empty space,'' and represented a negative pressure and thus a negative gravity force. However my 2004 ``Strong'' Magnetic Field model (SMF) for the origin of magnetic fields at Combination Time (Astro-ph0509223 and 0509222) in our big bang universe produces a unique topology for Superclusters, having almost all the mass, visible and invisible, i.e. from clusters of galaxies down to particles with mass, on the surface of an ellipsoid surrounding a growing very high vacuum. If I hypothesize, with Einstein, that there exists a constant ees force per unit volume, then, gradually, as the universe expands from Combination Time, two effects occur (a) the volume of the central high vacuum region increases, and (b) the density of positive gravity particles in the central region of each Supercluster in our universe decreases dramatically. Thus eventually Einstein's general relativity theory's repulsive gravity of the central very high vacuum region becomes larger than the positive gravitational attraction of all the clusters of galaxies, galaxies, quasars, stars and plasma on the Supercluster shell, and the observed accelerating expansion of our universe occurs. This assumes that our universe is made up mostly of such Superclusters. It is conceivable that the high vacuum region between Superclusters also plays a role in adding extra repulsive gravity force. Note that cosmologist Stephen Hawking comments on his website that ``There is no reason to rule out negative pressure. This is just tension.''