The Hubble Flow and Cosmological Considerations

A repelling force has obvious applicability toward observational cosmology. If we consider a dust filled universe, with no density gradients in or , we ought to be able to approximate the observed Hubble flow in a simple fashion. The repelling field on a shell of material, due to the presence of interior to the shell, will be:

$$\tilde{g}(r) = \frac{\pi^{2}}{2} \tilde{G}\tau \vec{r}\ ,$$ (9)

where $\tau$ is the 4-dimensional volume density of the . (This result follows from the fact that the hyper-volume of the sphere of is: $\frac{\pi^{2}}{2}r^{4}$). Thus, our interaction superficially has the same effect as the cosmological constant, whereby:

$$\frac{\pi^{2}}{2} \tilde{G} \tau = \frac{1}{3}\Lambda .$$ (10)

Using the results of Perlmutter et al. (1999) and Riess et al. (1998), we set $\Omega_{\Lambda} \equiv \Lambda/3H_0^2=0.7$, and therefore find (with $H_0=70km/s/Mpc$) : $\tau \approx 10^{-57} g/cm^{4}$. We are now afforded another consistency check with regard to our original assumption of equal mass distributions of M and over 100 Mpc. Using the 4 dimensional volume for , we find that $\approx 10^{50}$ g. If we assume that the average 3-D density of real matter is given by $\rho \approx 3 \cdot 10^{-31}\ g/cm^{3}$ for the M (i.e. there is no ``dark" matter), we get $M \approx 3 \cdot 10^{49}$ g. However, since the cosmological principle implies that expansion proceeds in the same way for all shells, we see that $\tau / \rho \propto 1/a$, where $a$ is the scale factor for the expansion. Thus, the repulsive stress is diluted over time (unlike the stress due to a $\Lambda$ term), and therefore the acceleration may end at some time in the future, thereby avoiding the problems that a vacuum dominated, eternally accelerating universe faces (see Barrow, Bean and Magueijo, 2000).

We would like to thank Tad Pryor, Jerry Sellwood, Jim Peebles, John Conway, Arthur Kosowsky, Tina Kahniashvili, Stu Kurtz, Libby Maljian and Stacy McGaugh for stimulating discussions, and Patty Gulyas for help in the manuscript preparation.