“GRAVITATIONAL TIME DILATION EXPLAINS HOW
RELATIVISTICALLY ACCUMULATED DARK MASS EQUIVALENT CURVES SPACETIME AROUND GALACTIC SCALE STRUCTURES”
by Jose Gregorio Baquero
In a similar way of how relativistic length contraction explain electromagnetism, relativistic effects explain the observations evidencing the existence unaccounted gravity attributed to Dark Matter around galaxies and galaxy clusters. When all forms of traveling energy quanta get closer to galaxies get delayed due to gravitational time dilations. Ultimately the accumulative effect is a substantial increase in energy density when seen from a frame of reference far from the center of galaxies in an Density Wave like mechanism. That increased energy density is imperceptible for an observer within the galaxy’s inner frames of reference. The higher concentration of travelling energy around galaxies in effect has an equivalent relativistic mass that is creating extra gravitational distortion in spacetime. This extra gravity is at least a substantial part of the unaccounted gravity attributed to Dark Matter.
From the beginning of existence all forms of energy’s own movement created and still is creating new fabric of spacetime. Every unit of volume of space in the universe is being crossed from all possible spatial directions by traveling energy quanta in the form of neutrinos, electromagnetic waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of waves and particles yet to be discovered. The lines traced by each quantum of energy (world lines) can be seen as fibers that intersect themselves in a way that they weave spacetime fabric. The “fibers” of this Energy Felt get denser around galaxies and galaxy clusters. Any field studied by quantum mechanics is a manifestation of the Energy Felt in a particular range of frequencies of the energy spectrum.
Using a thought experiment this document proves that traveling energy quanta (neutrinos, electromagnetic waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of energy and particles yet to be discovered) are getting relativistically accumulated around galaxies and galaxy clusters and must be considered as an important factor on the total gravity around cosmic structures.
Explaining “Observed” Dark Matter using General Relativity
Let’s imagine two identical laser pointers, Pa and Pb. Pa is going to be pointing in that way that its emitted photons (A) will pass parallel to Andromeda Galaxy galactic plane, at a minimum distance of one radius of Andromeda (Ra). Similarly Pb is pointing perfectly parallel to Pa in a way that its emitted photons (B) will pass at a minimum distance of 10 times Andromeda Radius (10Ra), for simplicity let’s omit gravitational lensing distortion. We set two light detectors, Da and Db at the other side of the galaxy in order to catch the photons emitted by Pa and Pb respectively.
General Relativity tells us that there is a different gravitational time dilation on the two different frames of reference; the frame of reference at Ra distance to the galactic plane and the frame of reference at 10Ra. For a rough calculation let’s use Andromeda’s mass including Dark Matter and calculate time for the two frames of reference at the moment when each photon gets to its closest point to the galaxy’s center.
There is a gravitational time dilation ratio (Ta/Tb) of 100.002% at the instant when the photons are closest to the center of the galaxy.
If time dilation for photons emitted by Pa were to remain constant along the 220.000 light years across the galaxy the photons hitting Da would take 161 days more than the photons hitting Db as measured by a clock on Db , but this is not the case. The gravitational field varies through the photons voyage.For all photons traveling on a plane parallel to the galaxy disk at Ra distance the ratio (Ta/Tb) decreases when the photons are farther away from the center of the galaxy depending on the actual mass-energy distribution of the galaxy. This is better visualized by a tridimensional distribution curved surface.Generalizing the time dilation ratio for two different radii (r, Ȓ) we can have:
Average Time of Relativistic Accumulation for a Static Frame of Reference at R
To calculate an average of time dilation ratio as measured on a static frame of reference we will integrate spherical surfaces (onion layers) multiplied by time dilation ratio while the radius varies and our product will be divided by the volume for Ȓ. Our approximation will use mass including Dark Matter as if it were inside an hypothetical black hole our integral will be calculated starting at Schwarzschild radius (rs) all the way to a non orbital (static) radius (Ȓ ).
The average time of relativistic accumulation for a sphere with r=Ȓ as measured on a static frame of reference:This means that on average a traveling photon (boson or any relativistic particle) will stay at least 27 days longer inside the sphere with the radius of the galaxy as measured on a static frame of reference at R
Average Time of Relativistic Accumulation for an Orbiting Frame of Reference
If we calculate the average of time dilation ratio as measured from a orbiting star (frame of reference orbiting the galaxy) we will have to use the time dilation for a circular orbit for a given orbital radius (R ), a constant, as our denominator and for our numerator we will have the integral from the Schwarzschild radius to orbital radius ( R) of all spherical surfaces (onion layers) multiplied by time dilation ratio (non rotational) while the radius varies. The result will be divided by the volume for R. This approximation also will use mass including Dark Matter as if it were inside an hypothetical black hole.
For mathematical model and testing with rotation curves:
This means that on average a traveling photon (boson or any relativistic particle) will stay about 1.76 seconds longer inside the sphere with the radius of the galaxy as measured on a orbiting frame of reference at R
Energy Felt Density Needed to Account for Dark Matter
Let’s imagine the Volume of Accumulation (U) by multiplying the surface of the sphere with radius (R ) times the distance a photon travels in the time of accumulation. The before mentioned Volume will need to have an Energy equivalent mass equal to the “observed” Dark Matter mass calculated for that particular orbital radius (R ) using the orbital velocity (V). Therefore the Energy Felt Density ( ) will be calculated by dividing the energy equivalent for Dark Matter Mass by the Volume of Accumulation.
Energy Felt Density calculated for a static frame of reference:
For mathematical model and testing with rotation curves:
Gravitational Lensing and Rotation Curve Discrepancies
When an observer on Earth calculates Dark Matter mass by measuring the bending of light caused by Gravitational Lensing there is a discrepancy with the calculated Dark Matter mass calculated from rotation velocities. While the rotation velocities calculation uses the orbiting probe at radius R (stars, dwarf galaxies, etc) frame of reference time dilation; the calculation from gravitational lensing uses the observer’s orbing frame of reference time dilation. This is needed since the observer becomes a part of the system (e.g. moving observer-rainbow system).
Discussion and Conclusion
The Dark Matter phenomenon explained as the Relativistic Accumulation of Mass-Energy allows us to mathematically calculate an approximation to Energy Felt density for a first time. No other phenomenon had given us the most remote chance to observe a quantifiable manifestation of this energy. Current Vacuum Energy Density (10^-9 joules/cubic meter ), calculated from universe expansion observations, differs greatly with predictions from quantum electrodynamics (QED) and stochastic electrodynamics (SED) where it is required a value 120 orders of magnitude larger (10^113 joules/cubic meter). Our calculated Energy Felt Density values indicate that there is a much higher energy density across the universe and that the observed values correspond only to the resultant of positive and negative (e.g. potential, gravitational) energy density interactions.
Cosmologists agree on being an inflationary period in the early universe where similar energy (in nature but not in magnitude) to that of observed Vacuum Energy rapidly inflated the universe exponentially in a very short period of time. It is currently believed that most of the inflaton field energy got transformed into other types of radiation and matter particles which density were diluted by further expansion of the universe. It is not completely ruled out that the remnant of that energy is still been created across the universe in ways that are very difficult to measure experimentally although Casimir Effect experiments have demonstrated the existence of such energy. Some cosmologists believe that a small oscillation on the current Vacuum Energy value could be responsible for the creation of Dark Matter.
As an analogy, we could think of the universe as the proverbial inflating balloon whose surface represents our spatial dimensions. Our balloon now is a special one; it is made out of latex fibers that when stretched won’t break. Rather, the fiber will separate slightly allowing the air to escape through the miniscule holes. With an initial colossal air pressure the balloon started inflating at an exponentially accelerated rate while all the air was contained (when energy density was so high that that energy acted, effectively, onto itself). During the inflation period there was very little cooling in the universe since all new space created had new intrinsic energy created with it. There was matter formation; that is there was creation of elementary particles but they rapidly decayed back to energy because of the high temperature and continuous energy bombardment. There is the point when the balloon latex fibers got stretched and very little air started to escape. The universe started to cool down at a greater rate allowing for a big part of the remnant energy to transform into elementary particles like neutrinos and electrons. Cooling allowed quarks to form and after it photons were able to travel through space. The balloon rapidly slowed its inflation since not only the air pressure diminished but at the same time the remnant pressure was less effective at inflating it. This analogy illustrates how nowadays the universe can have a higher vacuum energy density than that calculated from current universe expansion rates.
Also, it is currently accepted by the scientific community that neutrinos, specially primordial neutrinos, make out at least 10% of Dark Matter (Hot Dark Matter). This estimate is not taking into account the mechanism described on this paper. A bigger contribution has been ruled out because neutrinos are traveling at relativistic speeds; that is higher speed than any escape velocity (at any possible orbit). The phenomenon here described- Relativistically Accumulated Mass-Energy- can easily explain a significant accumulation of Hot Dark Matter not previously accounted by any calculation previously performed.
A star orbiting at Ȓ distance from the center of the galaxy will “feel” the combined effect of the gravity generated by the baryonic mass and the relativistically accumulated mass-energy inside that sphere. All the mass (baryonic and relativistically accumulated mass-energy) located outside that sphere is also “felt” but its gravitational net effect cancels out. This is similar to calculations for an object falling through a hole towards the center of a planet where its acceleration only depends on the mass of a sphere with a radius equal to the object distance to the center of that planet. Furthermore, we do not have observations of the gravitational effects of Dark Matter taken outside of the Milky Way and time in our frame of reference is dilated differently to time at a point far away from the Milky Way. Our observations therefore should show differences with those of an observer outside our galaxy.
In the space between galaxies energy density gets higher than that of the surrounding space because of both galaxies’ gravity compounded effect. These structures connect galaxies and galaxy clusters together forming the Cosmic Web. Dark Matter concentration ratio is different for different galaxies and galaxy clusters, not only because differences in mass distribution but also because galaxies have different masses. In addition, younger galaxies do have less Dark Matter in proportion to regular matter since the mass-energy relativistic accumulation has a compounding effect over time: The higher the energy density ratio; the more mass-energy relativistic accumulation, the more mass-energy relativistic accumulation; the more gravity, the more gravity; the more mass-energy relativistic accumulation. Even though in the early universe energy density was higher, that density was more uniformly distributed. That means that the further away we look to younger galaxies, the less Dark Matter we should find. What causes the mass-energy relativistic accumulation is the difference in energy density close to the galaxies in comparison with that of the galaxies’ surrounding space.
Traveling Energy particles and waves that come from outside the galaxy are not rotating with the galaxy. They will pass by if unobstructed. The time dilation on the frames of reference when close to the galaxy is greater specially if compared with orbiting frames of reference at a greater distance . Similarly to how relativity (length contraction) explains electromagnetism, relativistic particle and waves density is higher in the frames of reference closer to the galaxy than those far from the galaxy. In a way, there is a reservoir of traveling energy around galaxies that is constantly renewed with new energy.
It is this paper conclusion that there is no need for particularly special particles forming Dark Matter substance or even parallel universes’ escaped gravity to account for the extra gravity existing around cosmic structures. In a way, Dark Matter is just traveling energy. The purpose of this paper is to demonstrate the mechanism for mass-energy relativistic accumulation around galaxies and calculation for actual Dark Matter accumulated by this phenomenon will need to be performed using more precise models. Einstein was right and his findings continue to enlighten our understanding of the universe.
- Zwicky (1933). “Die Rotverschiebung von extragalaktischen Nebeln”. Helvetica Physica Acta. 6: 110–127.
- Zwicky (1937). “On the Masses of Nebulae and of Clusters of Nebulae”. The Astrophysical Journal. 86: 217.
- Freese,(May 2014). “The Cosmic Cocktail: Three Parts Dark Matter”. Princeton University Press. ISBN978-1-4008-5007-5.
- Babcock, (1939), “The rotation of the Andromeda Nebula“, Lick Observatory bulletin ; no. 498
- Overbye(December 27, 2016). “Vera Rubin, 88, Dies; Opened Doors in Astronomy, and for Women”. New York Times. Retrieved December 27, 2016.
- First observational evidence of dark matter. Darkmatterphysics.com. Retrieved 6 August 2013.
- Rubin, W. Ford, Jr.(February 1970). “Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions”. The Astrophysical Journal. 159: 379–403.
- Bosma, (1978). “The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types”(Ph.D. Thesis). Rijksuniversiteit Groningen.
- Rubin (1980). “Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii from NGC 4605 (R = 4kpc) to UGC 2885 (R = 122kpc)”. The Astrophysical Journal. 238: 471.
- (May 1966). “A High-Resolution 21-cm Hydrogen-Line Survey of the Andromeda Nebula”. The Astrophysical Journal.
- Gottesman, (1966). “A neutral hydrogen survey of the southern regions of the Andromeda nebula”. Monthly Notices of the Royal Astronomical Society. 133 (4): 359–387.
- Rogstad, (September 1972). “Gross Properties of Five Scd Galaxies as Determined from 21-centimeter Observations”. The Astrophysical Journal. 176: 315–321.
- “Planck Publications: Planck 2015 Results”. European Space Agency. (February 2015).
- Weiss, “Big Bang Nucleosynthesis: Cooking up the first light elements” in: Einstein Online Vol. 2 (2006), 1017
- Raine,T. Thomas (2001). “An Introduction to the Science of Cosmology”. IOP Publishing. p. 30.
- Tisserand (2007). “Limits on the Macho content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds”. Astronomy and Astrophysics. 469 (2): 387–404.
- Graff, (1996). “Analysis of a Hubble Space Telescope Search for Red Dwarfs: Limits on Baryonic Matter in the Galactic Halo”. The Astrophysical Journal. 456: L49.
- Najita (2000). “From Stars to Superplanets: The Low‐Mass Initial Mass Function in the Young Cluster IC 348”. The Astrophysical Journal. 541 (2): 977–1003.
- Wyrzykowski, (2011) “The OGLE view of microlensing towards the Magellanic Clouds”– IV. OGLE-III SMC data and final conclusions on MACHOs,” MNRAS, 416, 2949.
- Freese, (2000). “Death of Stellar Baryonic Dark Matter Candidates”.
- Freese, , (2000). “Death of Stellar Baryonic Dark Matter”. The First Stars. ESO Astrophysics Symposia. p. 18.
- Canetti, L.M.Drewes, M. Shaposhnikov (2012). “Matter and Antimatter in the Universe”. New J.Phys. 14: 095012
- Peter (2012). “Dark Matter: A Brief Review”.
- Jungman, (March 1996). “Supersymmetric dark matter”. Physics Reports. 267 (5–6): 195–373.
- “Neutrinos as Dark Matter”. Astro.ucla.edu. 21 September 1998. Retrieved 6 January 2011.
- Gaitskell, (2004). “Direct Detection of Dark Matter”. Annual Review of Nuclear and Particle Science. 54: 315–359.
- “Neutralino Dark Matter”. Retrieved 26 December 2011. Griest, Kim. “WIMPs and MACHOs”(. Retrieved 26 December 2011.
- McGaugh (April 10, 2007). “The rotation velocity attributable to dark matter at intermediate radii in disk galaxies”. The Astrophysical Journal. 659: 149–161
- McGaugh (Feb 20, 2003). “A limit on the cosmological mass density and power spectrum from the rotation curves of low surface brightness galaxies”. The Astrophysical Journal. 584: 566–576.
- de Blok (2009). “The core-cusp problem”. Advances in Astronomy. 2010: 1–14.
- Del Popolo, (Mar 2017) “Small scale problems of the ΛCDM model: a short review”
- Navarro (December 1996). “The cores of dwarf galaxy haloes”. MNRAS. 283 (3): L72–L78.
- Milgrom (1983). “A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis”. Astrophysical Journal. 270: 365–370.
- Milgrom (1983). “A modification of the Newtonian dynamics – Implications for galaxies”. Astrophysical Journal. 270: 371–389.
- McGaugh (2014). “A Tale of Two Paradigms: the Mutual Incommensurability of LCDM and MOND”. Canadian Journal of Physics. 93: 250–259
- Bekenstein (2004). “Relativistic gravitation theory for the MOND paradigm”. Phys. Rev. D70 (8): 83509.
- Clifton, (2011), “Modified Gravity and Cosmology”
- Capozziello, (October 2012). “The dark matter problem from f(R) gravity viewpoint”. Annalen der Physik. 524 (9–10).
- Mannheim (April 2006). “Alternatives to Dark Matter and Dark Energy”. Progress in Particle and Nuclear Physics. 56 (2). arXiv:astro-ph/0505266.
- Joyce (Mar 2015). “Beyond the Cosmological Standard Model”. Physics Reports. 568.
- Markevitch (Jul 2006). “Dark Matter and the Bullet Cluster”. 36th COSPAR Scientific Assembly. Beijing, China. Abstract only
- Douglas(2006). “A Direct Empirical Proof of the Existence of Dark Matter”. The Astrophysical Journal Letters. 648 (2): L109–L113. Bibcode:2006ApJ…648L.109C. arXiv:astro-ph/0608407 . doi:10.1086/508162.
- “Verlinde’s new theory of gravity passes first test”. December 16, 2016.
- Brouwer (Dec 2016). “First test of Verlinde’s theory of Emergent Gravity using Weak Gravitational Lensing measurements”. Monthly Notices of the Royal Astronomical Society. 2547–2559.
- “First test of rival to Einstein’s gravity kills off dark matter”. December 2016. Retrieved 20 February 2017.
- McCulloch (Jul 2017) ”Galaxy rotations from quantised inertia and visible matter only”
- Robert,R. Davé, K. Nagamine (Sep 2015). “The rise and fall of a challenger: the Bullet Cluster in Lambda cold dark matter simulations”. Monthly Notices of the Royal Astronomical Society. 452: 3030–3037.
- Angus, (Sep 2006). “Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry”. Mon. Not. R. Astron. Soc. 371 (1): 138–146.
- Einstein (1916), ”Die Grundlage der allgemeinen Relativitatsteorie” Ann. d. Phys. 49 769–822. Engl. transl. in: The Principle of Relativity, New York, Dover, 1952, p. 109
- Einstein (1905).”Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?”, Annalen der Physik, 18: 639–643.
- O’Connor (1996), “General relativity”. Mathematical Physics index, School of Mathematics and Statistics, University of St. Andrews, Scotland. Retrieved 2015-02-04.
- Jürgen(1973), “Survey of general relativity theory”, in Israel, Werner, Relativity, Astrophysics and Cosmology, D. Reidel, pp. 1–125,
- Friedman(1922). “Über die Krümmung des Raumes”. Z. Phys. (in German). 10 (1): 377–386 The original Russian manuscript of this paper is preserved in the Ehrenfest archive.
- Friedman(1924). “Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes”. Z. Phys. (in German). 21 (1): 326–332.
- “Universe 101”. NASA. Retrieved September 9, 2015. The actual density of atoms is equivalent to roughly 1 proton per 4 cubic meters.
- Weinberg “The cosmological constant problem”, Review of Modern Physics 61 (1989), 1-23.
- Zel’dovich (1967) ‘Cosmological Constant and Elementary Particles’ JETP letters 6, 316-317 and ‘The Cosmological Constant and the Theory of Elementary Particles’ Soviet Physics Uspekhi 11 (1968), 381-393.
- Rugh, (2002). “The quantum vacuum and the cosmological constant problem”. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 33 (4): 663–705. doi:10.1016/S1355-2198(02)00033-3.
- Leffert, “ Resolution of the Vacuum Energy Problem”. https://arxiv.org/ftp/astro-ph/papers/0308/0308014.pdf
- Margan,”Estimating the Vacuum Energy Density”.
- Einstein “Relativity : the Special and General Theory by Albert Einstein”. Project Gutenberg.
- Schwarzschild, K. (1916). “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften. 7: 189–196 For translation, see S. Antoci,A. Loinger, A. (1999). “On the gravitational field of a mass point according to Einstein’s theory”.
- Eddington, “Mathematical Theory of Relativity”, Cambridge UP 1922 (2nd ed.1924, repr.1960), at page 85and page 93.
- Buchdah(1985). “Isotropic coordinates and Schwarzschild metric”. International Journal of Theoretical Physics. 24 (7): 731–739.
- Tipler (2008), “Physics for Scientists and Engineers – with Modern Physics” (6th Edition),
- Shapiro (1964). “Fourth Test of General Relativity”. Physical Review Letters. 13 (26): 789–791.
- Shapiro (1968). “Fourth Test of General Relativity: Preliminary Results”. Physical Review Letters. 20 (22): 1265–1269.
- Desai, (Aug 2017) “Galactic Shapiro Delay to the Crab Pulsar and limit on Einstein’s Equivalence Principle Violation” https://arxiv.org/pdf/1612.02532.pdf
- .Lin, (1964). “On the spiral structure of disk galaxies”. Astrophysical Journal. 140: 646–655.
- Carignan, (April 2005). “Extended Hi Rotation Curve and Mass Distribution of M31”APJ Letters. arXiv:astro-ph/0603143
- Oman, (Jul 2015) “The unexpected diversity of dwarf galaxy rotation curves” arXiv:1504.01437v2
- Sofue (Aug 2016) “Rotation and Mass in the Milky Way and Spiral Galaxies”
- Shan (August 2010) “Mass discrepancy in galaxy clusters as a result of the offset between dark matter and baryon distributions” arxiv.org/abs/1006.3484
- Bradac, (March 2008) “Dark Matter and Baryouns in the Most X-Ray Lumious and Merging Galaxy Cluster” RX J1347.5−1145 http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-13191.pdf
- Rev. Astron. Astrophys. (1999). 37: 127-189 1999 “The X-ray/Lensing Mass Discrepancy” https://ned.ipac.caltech.edu/level5/March03/Mellier/Mellier3.html
- Wu, T. (1998) “A comparison of different cluster mass estimates: consistency or discrepancy?” http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle
- Soucail (January 2012)”Dark matter distribution in the merging cluster Abell 2163”
- Newton, Optice: Sive de Reflexionibus, Refractionibus, Inflexionibus & Coloribus Lucis Libri Tres,Propositio II, Experimentum VII, edition 1740:Ex quo clarissime apparet, lumina variorum colorum varia esset refrangibilitate : idque eo ordine, ut color ruber omnium minime refrangibilis sit, reliqui autem colores, aureus, flavus, viridis, cæruleus, indicus, violaceus, gradatim & ex ordine magis magisque refrangibiles.
- Newton(1704). Opticks.
- Oh, (May 2015). “High-resolution Mass Models of Dwarf Galaxies from Little Things”. The Astronomical Journal. 149 (6): 180.
- Genina, (Jul 2017) “The core-cusp problem: a matter of perspective”. arXiv:1707.06303
- White (3 February 2001). “The mass of a halo”. Astronomy and Astrophysics. 367 (1): 27–32.
- Kirshner (2002). “The Extravagant Universe: Exploding Stars, Dark Energy and the Accelerating Cosmos”. Princeton University Press. p. 71.
- Carroll (Jul 2013). “An Introduction to Modern Astrophysics (International ed.). Pearson”. pp. 1173–1174.
- Epps(March 2017). “The weak-lensing masses of filaments between luminous red galaxies”, Monthly Notices of the Royal Astronomical Society. https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stx517
- Geller; (1989). “Mapping the universe.”. Science. 246 (4932): 897–903. 10.1126/science.246.4932.897.
- Okabe (Mar 2017)“Strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago” 10.1038/nature21685 arXiv:1703.04310
- Lang (Mar 2017) “Falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS^3D and SINS/ZC-SINF” 10.3847/1538-4357/aa6d82 or arXiv:1703.05491v1
- Wuyts (Aug 2016) “KMOS^3D: Dynamical constraints on the mass budget in early star-forming disks”
- Übler (Jun 2017)”The evolution of the Tully-Fisher relation between z~2.3 and z~0.9 with KMOS^3D” 10.3847/1538-4357/aa7558 arXiv:1703.04321v2
- Ringermacher (October 2014) “Model –Independent Plotting of the Cosmological Scale Factor of the Cosmological Scale a Function of Look Back Time”
- I. Ringermacher (March 2015) “Observation of Discrete Oscillations In a Model-Independent Plot of Cosmological Scale Factor Versus Lookback Time and Scalar Field Model”
- Eisenstein, D. J. (2005). “Dark energy and cosmic sound”. New Astronomy Reviews. 49 (7–9): 360. Bibcode:2005NewAR..49..360E. doi:10.1016/j.newar.2005.08.005.
- Eisenstein (2005). “Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies”. The Astrophysical Journal. 633 (2): 560. Bibcode:2005ApJ…633..560E. arXiv:astro-ph/0501171 .
- Dodelson,(2003). Modern Cosmology. Academic Press. ISBN978-0122191411.
- Gannon (December 21, 2012). “New ‘Baby Picture’ of Universe Unveiled”. Space.com. Retrieved December 21, 2012.
- Bennett (2012). “Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results”. arXiv:1212.5225
- Zao, (14 May 2013). “Casimir forces on a silicon micromechanical chip”. Nature Communications. 4: 1845
- Sparnaay (1957). “Attractive Forces between Flat Plates”. Nature. 180 (4581): 334
- Sparnaay (1958). “Measurements of attractive forces between flat plates”. Physica. 24 (6–10): 751.
- Lamoreaux, (1997). “Demonstration of the Casimir Force in the 0.6 to 6 μm Range”. Physical Review Letters. 78
- Mohideen (1998). “Precision Measurement of the Casimir Force from 0.1 to 0.9 µm”. Physical Review Letters. 81 (21): 4549
- G, Bressi (2002). “Measurement of the Casimir Force between Parallel Metallic Surfaces”. Physical Review Letters. 88 (4): 041804.
- Nemiroff, (17 December 2006). “Photo of ball attracted to a plate by Casimir effect”. Astronomy Picture of the Day. NASA.
- Genet (2004). “Electromagnetic vacuum fluctuations, Casimir and Van der Waals forces”. Annales de la Fondation Louis de Broglie. 29 (1–2): 311–328.
- “The Force of Empty Space”, Physical Review Focus, 3 December 1998
- Lambrecht, “The Casimir effect: a force from nothing”, Physics World, September 2002.
- American Institute of Physics News Note 1996
- Jaffe (2005). “Casimir effect and the quantum vacuum”. Physical Review D. 72 (2): 021301.
- “The Casimir effect: a force from nothing”. Physics World. 1 September 2002. Retrieved 17 July 2009. http://wwwf9.ijs.si/~margan/Articles/vacuum_energy_density.pdf