Tag Archives: Gravity

Unified Physics including Dark Matter and Dark Energy

Dark matter keeps escaping direct detection, whether it might be in the form of WIMPs, or primordial black holes, or axions. Perhaps it is a phantom and general relativity is inaccurate for very low accelerations. Or perhaps we need a new framework for particle physics other than what the Standard Model and supersymmetry provide.

We are pleased to present a guest post from Dr. Thomas J. Buckholtz. He introduces us to a theoretical framework referred to as CUSP, that results in four dozen sets of elementary particles. Only one of these sets is ordinary matter, and the framework appears to reproduce the known fundamental particles. CUSP posits ensembles that we call dark matter and dark energy. In particular, it results in the approximate 5:1 ratio observed for the density of dark matter relative to ordinary matter at the scales of galaxies and clusters of galaxies. (If interested, after reading this post, you can read more at his blog linked to his name just below).

Thomas J. Buckholtz

My research suggests descriptions for dark matter, dark energy, and other phenomena. The work suggests explanations for ratios of dark matter density to ordinary matter density and for other observations. I would like to thank Stephen Perrenod for providing this opportunity to discuss the work. I use the term CUSP – concepts uniting some physics – to refer to the work. (A book, Some Physics United: With Predictions and Models for Much, provides details.)

CUSP suggests that the universe includes 48 sets of elementary-particle Standard Model elementary particles and composite particles. (Known composite particles include the proton and neutron.) The sets are essentially (for purposes of this blog) identical. I call each instance an ensemble. Each ensemble includes its own photon, Higgs boson, electron, proton, and so forth. Elementary particle masses do not vary by ensemble. (Weak interaction handedness might vary by ensemble.)

One ensemble correlates with ordinary matter, 5 ensembles correlate with dark matter, and 42 ensembles contribute to dark energy densities. CUSP suggests interactions via which people might be able to detect directly (as opposed to infer indirectly) dark matter ensemble elementary particles or composite particles. (One such interaction theoretically correlates directly with Larmor precession but not as directly with charge or nominal magnetic dipole moment. I welcome the prospect that people will estimate when, if not now, experimental techniques might have adequate sensitivity to make such detections.)


This explanation may describe (much of) dark matter and explain (at least approximately some) ratios of dark matter density to ordinary matter density. You may be curious as to how I arrive at suggestions CUSP makes. (In addition, there are some subtleties.)

Historically regarding astrophysics, the progression ‘motion to forces to objects’ pertains. For example, Kepler’s work replaced epicycles with ellipses before Newton suggested gravity. CUSP takes a somewhat reverse path. CUSP models elementary particles and forces before considering motion. The work regarding particles and forces matches known elementary particles and forces and extrapolates to predict other elementary particles and forces. (In case you are curious, the mathematics basis features solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators.)

I (in effect) add motion by extending CUSP to embrace symmetries associated with special relativity. In traditional physics, each of conservation of angular momentum, conservation of momentum, and boost correlates with a spatial symmetry correlating with the mathematics group SU(2). (If you would like to learn more, search online for “conservation law symmetry,” “Noether’s theorem,” “special unitary group,” and “Poincare group.”) CUSP modeling principles point to a need to add to temporal symmetry and, thereby, to extend a symmetry correlating with conservation of energy to correlate with the group SU(7). The number of generators of a group SU(n) is n2−1. SU(7) has 48 generators. CUSP suggests that each SU(7) generator correlates with a unique ensemble. (In case you are curious, the number 48 pertains also for modeling based on either Newtonian physics or general relativity.)

CUSP math suggests that the universe includes 8 (not 1 and not 48) instances of traditional gravity. Each instance of gravity interacts with 6 ensembles.

The ensemble correlating with people (and with all things people see) connects, via our instance of gravity, with 5 other ensembles. CUSP proposes a definitive concept – stuff made from any of those 5 ensembles – for (much of) dark matter and explains (approximately) ratios of dark matter density to ordinary matter density for the universe and for galaxy clusters. (Let me not herein do more than allude to other inferably dark matter based on CUSP-predicted ordinary matter ensemble composite particles; to observations that suggest that, for some galaxies, the dark matter to ordinary matter ratio is about 4 to 1, not 5 to 1; and other related phenomena with which CUSP seems to comport.)

CUSP suggests that interactions between dark matter plus ordinary matter and the seven peer combinations, each comprised of 1 instance of gravity and 6 ensembles, is non-zero but small. Inferred ratios of density of dark energy to density of dark matter plus ordinary matter ‘grow’ from zero for observations pertaining to somewhat after the big bang to 2+ for observations pertaining to approximately now. CUSP comports with such ‘growth.’ (In case you are curious, CUSP provides a nearly completely separate explanation for dark energy forces that govern the rate of expansion of the universe.)

Relationships between ensembles are reciprocal. For each of two different ensembles, the second ensemble is either part of the first ensemble’s dark matter or part of the first ensemble’s dark energy. Look around you. See what you see. Assuming that non-ordinary-matter ensembles include adequately physics-savvy beings, you are looking at someone else’s dark matter and yet someone else’s dark energy stuff. Assuming these aspects of CUSP comport with nature, people might say that dark matter and dark-energy stuff are, in effect, quite familiar.

Copyright © 2018 Thomas J. Buckholtz



Distant Galaxy Rotation Curves Appear Newtonian

One of the main ways in which dark matter was postulated, primarily in the 1970s, by Vera Rubin (recently deceased) and others, was by looking at the rotation curves for spiral galaxies in their outer regions. Although that was not the first apparent dark matter discovery, which was by Fritz Zwicky from observations of galaxy motion in the Coma cluster of galaxies during the 1930s.

Most investigations of spiral galaxies and star-forming galaxies have been relatively nearby, at low redshift, because of the difficulty in measuring these accurately at high redshift. For what is now a very large sample of hundreds of nearby galaxies, there is a consistent pattern. Galaxy rotation curves flatten out.


M64, image credit: NASA, ESA, and the Hubble Heritage Team (AURA/STScI)

If there were only ordinary matter one would expect the velocities to drop off as one observes the curve far from a galaxy’s center. This is virtually never seen at low redshifts, the rotation curves consistently flatten out. There are only two possible explanations: dark matter, or modification to the law of gravity at very low accelerations (dark gravity).

Dark matter, unseen matter, would case rotational velocities to be higher than otherwise expected. Dark, or modified gravity, additional gravity beyond Newtonian (or general relativity) would do the same.

Now a team of astronomers (Genzel et al. 2017) have measured the rotation curves of six individual galaxies at moderately high redshifts ranging from about 0.9 to 2.4.

Furthermore, as presented in a companion paper, they have stacked a sample of 97 galaxies with redshifts from 0.6 to 2.6  to derive an average high-redshift rotation curve (P. Lang et al. 2017). While individually they cannot produce sufficiently high quality rotation curves, they are able to produce a mean normalized curve for the sample as a whole with sufficiently good statistics.

In both cases the results show rotation curves that fall off with increasing distance from the galaxy center, and in a manner consistent with little or no dark matter contribution (Keplerian or Newtonian style behavior).

In the paper with rotation curves of 6 galaxies they go on to explain their falling rotation curves as due to “first, a large fraction of the massive high-redshift galaxy population was strongly baryon-dominated, with dark matter playing a smaller part than in the local Universe; and second, the large velocity dispersion in high-redshift disks introduces a substantial pressure term that leads to a decrease in rotation velocity with increasing radius.” 

So in essence they are saying that the central regions of galaxies were relatively more dominated in the past by baryons (ordinary matter), and that since they are measuring Hydrogen alpha emission from gas clouds in this study that they must also take into account the turbulent gas cloud behavior, and this is generally seen to be larger at higher redshifts.

Stacy McGaugh, a Modified Newtonian Dynamics (MOND) proponent, criticizes their work saying that their rotation curves just don’t go far enough out from the galaxy centers to be meaningful. But his criticism of their submission of their first paper to Nature (sometimes considered ‘lightweight’ for astronomy research results) is unfounded since the second paper with the sample of 97 galaxies has been sent to the Astrophysical Journal and is highly detailed in its observational analysis.

The father of MOND, Mordehai Milgrom, takes a more pragmatic view in his commentary. Milgrom calculates that the observed accelerations at the edge of these galaxies are several times higher than the value at which rotation curves should flatten. In addition to this criticism he notes that half of the galaxies have low inclinations, which make the observations less certain, and that the velocity dispersion of gas in galaxies that provides pressure support and allows for lower rotational velocities, is difficult to correct for.

As in MOND, in Erik Verlinde’s emergent gravity there is an extra acceleration (only apparent when the ordinary Newtonian acceleration is very low) of order. This spoofs the behavior of dark matter, but there is no dark matter. The extra ‘dark gravity’ is given by:

g _D = sqrt  {(a_0 \cdot g_B / 6 )}

In this equation a0 = c*H, where H is the Hubble parameter and gB is the usual Newtonian acceleration from the ordinary matter (baryons). Fundamentally, though, Verlinde derives this as the interaction between dark energy, which is an elastic, unequilibrated medium, and baryonic matter.

One could consider that this dark gravity effect might be weaker at high redshifts. One possibility is that density of dark energy evolves with time, although at present no such evolution is observed.

Verlinde assumes a dark energy dominated de Sitter model universe for which the cosmological constant is much larger than the matter contribution and approaches unity, Λ = 1 in units of the critical density. Our universe does not yet fully meet that criteria, but has Λ about 0.68, so it is a reasonable approximation.

At redshifts around z = 1 and 2 this approximation would be much less appropriate. We do not yet have a Verlindean cosmology, so it is not clear how to compute the expected dark gravity in such a case, but it may be less than today, or greater than today. Verlinde’s extra acceleration goes as the square root of the Hubble parameter. That was greater in the past and would imply more dark gravity. But  in reality the effect is due to dark energy, so it may go with the one-fourth power  of an unvarying cosmological constant and not change with time (there is a relationship that goes as H² ∝ Λ in the de Sitter model) or change very slowly.

At very large redshifts matter would completely dominate over the dark energy and the dark gravity effect might be of no consequence, unlike today. As usual we await more observations, both at higher redshifts, and further out from the galaxy centers at moderate redshifts.


R. Genzel et al. 2017, “Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago”, Nature 543, 397–401,

P. Lang et al. 2017, “Falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS^3D and SINS/ZC-SINF”

Stacy McGaugh 2017,

Mordehai Milgrom 2017, “High redshift rotation curves and MOND”

Erik Verlinde 2016, “Emergent Gravity and the Dark Universe” https;//