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For well over 50 years astrophysicists have been struggling with the apparent mass discrepancies that seem to exist in large scale structures throughout the universe (Zwicky 1937). The discovery of asymptotically flat galactic rotation curves at large distances from the core (Bosma 1978) started an avalanche of ``dark" matter (DM) ideas in an effort to explain the growing body of data. Interestingly, it seems that many current versions of DM run into serious difficulties when compared with observed properties of galaxies (Sellwood 2000). Moreover, with the discovery of the likelihood of a global acceleration to the Hubble flow (Perlmutter et al. 1999; Riess et al. 1998), it would seem that the time is ripe for a fundamentally new approach, one which might have the possibility of explaining many disparate observational problems. To this end, we postulate an additional mode for gravitational interaction in which the field associated with a hypothetical particle is everywhere repelling. For simplicity, we call the mass associated with this field $\tilde{M}$, to distinguish it from ``ordinary" matter, M. If the repelling field is inverse-square in nature, the combined gravitational and anti-gravitational force between the M and $\ensuremath{\tilde{M}}$ will be independent of separation, and thus merely implies a change in the magnitude of G.

However, a potential of the form $\Phi_{\ensuremath{\tilde{M}}} \propto \frac{1}{r^{2}}$ has several interesting aspects that we will investigate here:

A) Although repelling by nature, it can substantially enhance the gravitational acceleration in the limit of large distances from the center of the potential, as well as yield standard Newtonian dynamics as r $\rightarrow$ 0.

B) It suggests a force acting over a 4 dimensional, real spatial manifold.

An obvious characteristic of the superposition of an inverse-cube repelling force with an inverse-square attracting force is that it establishes and requires a length scale to be invoked. Only at one particular separation of an $M-\ensuremath{\tilde{M}}$ pair will the magnitudes of the field strengths be equal. Thus, if this separation of an isolated M-$\tilde{M}$ pair is given as $R_{0}$, any perturbation of either particle tends toward equilibrium. (By equilibrium, we mean here that the absolute value of the two fields are equal). If the separation is increased, the inverse-square attractive term dominates (thereby decreasing the separation ), while if the separation is decreased, the inverse-cube repelling term dominates (thereby sending the system back toward larger values of the separation).

At equilibrium, we have:

\tilde{g} \equiv \left\vert\frac{\tilde{G}\tilde{M}}{R^{3}_{...
...ght\vert = \left\vert\frac{GM}{R^{2}_{0}} \right\vert
\equiv g
\end{displaymath} (1)

So, for the case of M=$\tilde{M}$, it follows that $\frac{\tilde{G}}
{G} = R_{0}$. Since we invoke ``equilibrium'' (M=$\tilde{M}$) at the limit of large R, it seems natural to choose $R_{o} \approx 100$ Mpc, which is the putative lower bound of true global homogeneity (Tucker, Lin & Shectman 1999). With this value,

\frac{\tilde{G}}{G} \approx 3 \cdot 10^{26} cm \ \ \mbox{and...
...s} \ \
\tilde{G} \approx 2 \cdot 10^{19} cgs \ \ \mbox{units}
\end{displaymath} (2)

Note that this distance scale is merely a currently observed quantity, and as such, does not in principle depend on the time history of the Universe. If the Universe is flat or open, this scale length can exist at all epochs. Thus, we don't necessarily need to invoke time variability of fundamental constants. If the Universe is closed, there will be an epoch where the scale factor implies global distances smaller than 100 Mpc, but this still does not rule out anything that follows here. In any event, we bear in mind that this value is just a working hypothesis, and has no real effect on our conclusions for dynamics, since the product of $\tilde{G}$ and \ensuremath{\tilde{M}} is all that appears in every calculation. However, we shall see in section 3 that our ``guess" is apparently quite close to a value that redefines the Planck scales in a strikingly reasonable way, and also (in section 4) that this provides a natural value of the density of \ensuremath{\tilde{M}} to explain the apparent acceleration of the Hubble flow. In this regard, it is useful to point out, that as a repelling field, it will will be smooth over large distances, being characterized as a fluid with some density $\tau$. We consider this idea below.

next up previous
Next: Dynamics in the Fourth Up: Toward a Symmetrization of Previous: Toward a Symmetrization of
Terry Matilsky