Appendix/Ramblings/DarkMatterMusings

Musings Regarding Dark Matter and Dark Energy

[Joel E. Tohline recollection on 3/8/2015] It was during my first year (July 1978 - June 1979) as a J. Willard Gibbs Instructor in the Astronomy Department at Yale University that I started wondering whether the nearly ubiquitous display of "flat rotation curves" in disk galaxies might be explained, not via the dark matter hypothesis, but by invoking a $1/r$ force-law for gravity at large distances. My reasoning was simple:

1. I was uncomfortable with the "dark matter" hypothesis, which smelled to me like the story of aether, all over again.
2. If Isaac Newton had been handed Vera Rubin's observations — which showed that orbital velocities were approximately constant with distance — instead of Kepler's observations — which showed that orbital velocities behaved as $v\propto r^{-1/2}$ — he likely would have hypothesized that the gravitational acceleration due to a central point mass is proportional to $r^{-1}$ instead of $r^{-2}$.

While I put quite a lot of thought into this idea in the late '70s and early '80s — and I still give it some thought from time to time because I consider the astrophysics community's fundamental understanding of "dark matter" and now, too, "dark energy" to be weak — I produced only two publications on the topic, neither of which was in a refereed archival journal:

• Stabilizing a Cold Disk with a $1/r$ Force Law.
• Does Gravity Exhibit a $1/r$ force on the Scale of Galaxies?

From time to time, I plan to post here some of the research notes that I have generated on this topic over the years, as well as recollections of discussions of the topic that I have had with professional colleagues. I begin by posting a scanned copy of one of my most cherished possessions from my time at Yale.

• Notes from Beatrice Tinsley showing that she, too, had given some thought to the implications of a $1/r$ force-law for gravity in 1978.
• Early interactions with Vera Rubin.
• Attraction associated with a uniform-density sphere — my derivation in the early '80s, with the kind assistance of LSU Professor Attipat K. Rajagopal.
• Remarks on Christodoulou & Kazanas (2015).
• Radial Dependence of the Strong Nuclear Force

[Joel E. Tohline on 24 October 2022] Today I stumbled on the following interesting paper:

• C. Lu, Z.-W. Li, S.-F. Yuan, Z. Wan, S.-H. Qin, K. Zhu, & Y. Xie (2014), Research in Astronomy and Astrophysics, Vol. 14, No. 10, pp. 1301 - 1306:   Preliminary Limits on a Logarithmic Correction to the Newtonian Gravitational Potential in Binary Pulsars. They "estimate the upper limit of the Tohline-Kuhn-Kruglyak parameter λ …" They, in turn, refer to the following …
  • J. P. Mücket & H.-J. Treder (1977, Astronomische Nachrichten, Vol. 298, Issue 2, p. 65) <-- First to consider The Perihelion Advance according to a Post-Newtonian Gravitational Law with Logarithmic Correction Term in the context of planets.
  • T. Clifton, P. G. Ferreira, A. Padilla, & C. Skordis (2012, Physics Reports, Vol. 513, Issue 1, pp. 1 - 189) <-- recent review titled, Modified Gravity and Cosmology.

See Also