Is Dark Matter Dark Energy Pressure On Galaxies Or Conserving Energy From Scalar Expansion?
by Steven Gussman
Two models of dark matter are tested, (perhaps too) simply. First, is the gravitation associated with "dark matter" actually due to pressure placed on gravitationally stable galaxies by the space expanding around them? When the space in-between galaxies expands, it stands to reason that the pocket-galaxy in the middle of a sea of expanding space is being squeezed inward. Unless my physical intuition fails me, it seems that the acceleration associated with the Hubble parameter (in reality, there may be jerk involved) could then be used as an inward velocity on The Milky Way galaxy at the radius of the "dark matter" halo. If this acceleration were the same as that associated with a galaxy whose mass includes the major contribution of dark matter at that distance, then it would pass the first test.
Rather than using error bars / confidence intervals, I selected a small, medium, and large empirical value for each variable of interest (if I had only two empirical values, the medium value was their arithmetic mean). These values can all be seen at the top of the code, below. For the Hubble parameter, these were Hi = {69.8, 70, 74} (km/s)/Mpc.1 For the mass of the Milky Way: M[Milky Way]i = {(0.9e12)M☉, (1.28e12)M☉, (1.54e12)M☉} kg.2 And for the radius of the "dark matter" halo: R[Milky Way Halo]i = {9.02e21, 1.4e22, 1.8e22} m.3 The following is the C# code:4
/* Steven Gussman 9/22/23 12:24 AM (FRI)
* HubblePressure.cs is meant to test the hypothesis
* that the pressure of expanding space outside of gravitationally-bound galaxies
* accounts for the phenomenon called "dark matter". */
using System;
namespace HubblePressureHypothesis{
class HubblePressure{
// CONSTANTS
// Newton's universal gravitational constant
const double G = 6.67430e-11d; // Nm^2/kg^2
// Thruples are lower, mid, and higher-bounds on the value
// Solar mass
const double solarMass = 1.98847e30d; // kg
// Milky Way dark matter mass
// TO-DO: Why does Wikipedia list the wrong number with these citations?
// 0.9e12, 1.28e12, 1.54e12,
static double[] milkyWayMass = {0.9e12 * solarMass, 1.28e12 * solarMass,
1.54e12 * solarMass};
// Milky way dark matter halo radius // TO-DO: Wikpedia wrong again!?
// 9.02e21, 1.4e22, 1.8e22 m
static double[] milkyWayDarkMatterHaloRadius = {9.02e21d, 1.4e22d, 1.8e22d};
// Hubble parameter
static double[] H0 = {69.8d, 70d, 74d}; // (km/s)/Mpc
// Megaparsec in km
const double MEGA_PARSEC_IN_KILOMETERS = 1e6d * 3.09e13d; // km = 1 Mpc
// OUTPUTS
// Hubble acceleration
static double[] hubbleAcceleration = new double[3]; // m/s^2
// Dark matter acceleration
static double[] darkMatterAcceleration = new double[3]; // m/s^2
// Ratio of the Hubble acceleration to the dark matter acceleration
static double[] ratios = new double[3];
static void Main(string[] args){
Console.WriteLine("Hubble Pressure As Dark Matter Hypothesis " +
DateTime.Now.ToShortDateString() + " " +
DateTime.Now.ToShortTimeString() + "\n");
for(int i = 0; i < 3; i++){
// Calculate the Hubble acceleration
hubbleAcceleration[i] = AccelerationKinematic4(H0[i],
MEGA_PARSEC_IN_KILOMETERS) * 1_000d; // m/s^2
// Calculate the dark matter acceleration at the edge of the halo
darkMatterAcceleration[i] = AccelerationGravitation(milkyWayMass[i] *
0.1d, milkyWayDarkMatterHaloRadius[i]); // m/s
ratios[i] = hubbleAcceleration[i] / darkMatterAcceleration[i];
}
// Outputs
Console.WriteLine("Hubble Pressure Acceleration:\n" +
hubbleAcceleration[1] + " (" + hubbleAcceleration[0] + "-" +
hubbleAcceleration[2] + ") m/s^2.\n");
Console.WriteLine("Dark Matter Acceleration:\n" +
darkMatterAcceleration[1] + " (" + darkMatterAcceleration[0] + "-" +
darkMatterAcceleration[2] + ") m/s^2.\n");
Console.WriteLine("Ratios:\n" + ratios[1] + " (" + ratios[0] + "-" +
ratios[2] + ").");
}
// v^2 = v[0]^2 + 2ax
// a = (v^2 - v[0]^2) / 2x
// a = v^2 / 2x
static double AccelerationKinematic4(double velocity, double distance){
return (velocity * velocity) / (2d * distance);
}
// F = GMm/r^2 = ma
// a = GM/r^2
static double AccelerationGravitation(double mass, double distance){
return (G * mass) / (distance * distance);
}
}
}
Note that in the first output, around line 48 of the code calculates the acceleration at the edge of the halo distance based on 90% of the Milky Way's mass (that is, the "dark matter contribution"), whereas in the second output (as in the code printed above), 10% of the mass is used so as to compare the Hubble acceleration to the gravitation of visible matter at that distance. Barring a physical mistake with how to interpret the pressure that expanding spacetime would place on a stable pocket of it within, this would falsify the hypothesis that "dark matter" is the pressure dark energy's expansion of space around a galaxy places on it.
Another hypothesis that I attempted to explore has to do with the conservation of energy. In our present understanding of the expansion of the universe, energy is not conserved because the dark energy field is scalar (meaning that it maintains energy density despite expansion—implying more of it is created, proportionally). If we interpret this expansive anti-gravity force as being negative energy, then energy is in some sense being destroyed (this breaks the first law of thermodynamics all the same). The hypothesis is to ask whether all of the dark matter in the galaxies is the positive-mass equivalent to all of the (negative) dark energy created during expansion (which also predicts that dark matter is a dynamic value in which older / further galaxies should have less). The specific mechanism for the accounting is still missing from this idea, but it is a start.
For this hypothesis, the following variables pertaining to the observable universe are useful (prime variables pertain to values at present, as opposed to 13.8 Gy ago):5
R' = 4.4e26 m
V' = 3.566e80 m^3
R = 4.4e23 m
V = 3.6e71 m^3
pCritical = 0.85e-26 kg/m^3
pDark Energy' = pCritical × 0.683 = 5.8e-27 kg/m^3
MDark Energy' = pDark Energy' × V' = 2.1e54 kg
MDark Energy = 2.1e45 kg (meaning that roughly all of today's dark energy is "new")
MOrdinary' = 1.46e53 kg
MDark' = 8.1e53 kg
If the "dark matter" were a positive compensation for the creation of a lot of negative dark energy, then MDark' / MDark Energy' should be unity. Unfortunately, the ratio actually comes out to ~34% (meaning that there is a bout three times the mass contribution of dark energy as of dark matter). This, too, would then tend to be a falsified model. One interesting hail-Mary is that the dark energy pressure associated with the expansion of space is apparently three times the contribution to gravitation as the dark-energy-as-mass content itself.6 It is strange then that tripling the dark matter value would balance out the two (as 34% × 3 ≈ 100%). Alas, this does not really make sense, as the dark energy's positive contribution means the net effect is two times; and anyway, there is no reason to apply this to the dark matter variable except that it would "work".
Given the claim that the dark energy pressure is three times as strong as its energy density, one is tempted then to apply this 2-3× factor to the initial hypothesis; but this would only bring the acceleration value to ~20-30% of where it is needed (though it may bring it up to an order-of-magnitude match, reviving some hope for the dark-energy-pressure model).
Footnotes:
1. See "Hubble's Law" (Wikipedia) (accessed 9/25/23) (https://en.wikipedia.org/wiki/Hubble%27s_law) (though I have probably not read this full article); "The Hubble Constant, Explained" by Sasha Warren (UChicago News) (2021 / 2022) (https://news.uchicago.edu/explainer/hubble-constant-explained) (though I have not read this entire piece, I largely extracted values for H) (note that this is a tertiary source and I have not read the basic research in which the H values originate); "Parsec" (Wikipedia) (accessed Sep. 2023) (https://en.wikipedia.org/wiki/Parsec) (though I have not read this entire article); and "Expanding Universe" by Carl Rod Nave (HyperPhysics / Georgia State University) (1998) (http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/hubble.html) (though I have probably not read this entire page).
2. See "Milky Way" (Wikipedia) (accessed Sep. 2023) (https://en.wikipedia.org/wiki/Milky_Way) (though I have not read this entire article); "Kinematics Of The Stellar Halo And The Mass Distribution Of The Milky Way Using BHB Stars" by Prajwal R. Kafle et al. (The Astrophysical Journal / arxiv) (2012) (https://arxiv.org/abs/1210.7527) (though I have not read this paper); "Evidence For An Intermediate-Mass Milky Way From Gaia DR2 Halo Globular Cluster Motions" by Laura L. Watkins et al. (The Astrophysical Journal / arxiv) (2018 / 2019) (https://arxiv.org/abs/1804.11348) (though I have not read this paper); and "Solar Mass" (Wikipedia) (accessed Sep. 2023) (https://en.wikipedia.org/wiki/Solar_mass) (though I have not read this entry in its entirety) which further cites "Astronomical Constants" (The Astronomical Almanac) (2014) (https://web.archive.org/web/20131110215339/http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf) (though I have not read this entire source). Note that I appear to have mistakenly set the middle value to 1.28e12 instead of the proper mean, 1.22e12 (unless I have lost a source for an empirical 1.28e12 value). The discrepancy wouldn't change this analysis significantly.
3. See "Milky Way" which further cites "Astronomers Have Found The Edge Of The Milky Way At Last" by Ken Croswell (Science News) (2022) (https://www.sciencenews.org/article/astronomers-have-found-edge-milky-way-size) (though I have not read this article) which in turn cites "The Edge Of The Galaxy" by Alis J. Deason et al. (Monthly Notices Of The Royal Astronomical Society / arxiv) (2020) (https://arxiv.org/abs/2002.09497) (though I have not read this paper).
4. See "What Are The Kinematic Formulas?" (Khan Academy) (accessed Sep. 2023) (https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas) (though I probably haven't read this entire page); "The Science Of Balloons Part 1: Under Pressure" (Mathematics Of Waves And And Materials) (accessed Sep. 2023) (https://www.mwmresearchgroup.org/the-science-of-balloons-part-1.html) (I have read most, but not all of this page); and "Gravitational Constant" (Wikipedia) (accessed Sep. 2023) (https://en.wikipedia.org/wiki/Gravitational_constant) which further cites "2018 CODATA Value: Newtonian Constant Of Gravitation" (NIST) (2019) (https://physics.nist.gov/cgi-bin/cuu/Value?bg) (though I haven't read through this page).
5. See "Observable Universe" (Wikipedia) (accessed Sep. 2023) (https://en.wikipedia.org/wiki/Observable_universe) (though I have likely not read this entire entry) which further cites Extra Dimensions In Space And Time by Itzhak Bars and John Terning (Springer) (2009) (pp. 27) (https://books.google.com/books?id=fFSMatekilIC&pg=PA27#v=onepage&q&f=false) (though I have not read this book), WolframAlpha, and "Planck 2013 Results. XVI. Cosmological Parameters" by the Planck Collaboration (Astronomy & Astrophysics / arxiv) (2013 / 2014) (https://arxiv.org/abs/1303.5076) (though I have not read this paper).
6. See "Ask Ethan: Does Dark Energy Gravitate?" by Ethan Siegel (Forbes) (2020) (https://www.forbes.com/sites/startswithabang/2020/02/22/ask-ethan-does-dark-energy-gravitate/?sh=6d36d6f3fc19) (though I haven't read this entire piece) and the answer to "Could Gravity And Dark Matter Be Expressions Of Dark Energy?" by Stephen Perrenod (Quora) (~2020) (https://www.quora.com/Is-dark-energy-considered-more-powerful-than-cosmic-gravity) (which also explores a possible relationship between dark energy and dark matter, though I read this after most of the work on mine was done).
Change Log:
ReplyDelete9/26/23 12:35 AM
- Appended to footnote four the big-G citation(s).