An Uneven Vacuum Energy Fluid as Λ, Dark Matter, MOND and Lens
HongSheng Zhao
Abstract and summary · read the original at the source · none found
In one page
HongSheng Zhao reviews a family of gravity theories — Jacob Bekenstein’s TeVeS and its relatives — that do something readers of this site will recognise. They drop dark matter as a particle and replace the cosmological constant with a vacuum energy that is allowed to be uneven. Zhao’s argument is that these are not really modified gravity at all: written in a single physical metric they sit inside ordinary general relativity, with one non-uniform vector field standing in for dark energy and dark matter together. He works the analogy out in detail. The galaxy equation takes the form of electrostatics with a polarisation term, the effective gravitational constant behaves like a dielectric, and the vacuum’s energy density varies from place to place the way it does between Casimir plates. He then runs the sanity checks — rotation curves of dwarf and spiral galaxies, lensing across about fifty CASTLES systems, solar-system limits — and names the measurement that would separate an uneven dark-energy fluid from a real halo.
Why it matters hereChapter 5 treats the vacuum as a fluid with structure, and this is a mainstream astrophysics review doing exactly that at galaxy scale: the same zero-point energy density that fills a Casimir gap, allowed to vary from place to place, and asked to carry the work that dark matter and dark energy do. Chapter 13 needs that bridge, because the site’s one adjustable quantity has to account for cosmology as well as for the bench.
What it claims
01On galaxy scales the gravity attributed to dark matter and the gravity of the known matter are tied together by a single empirical relation — the dark gravity is roughly the geometric mean of the known gravity and a fixed acceleration a0 of about one angstrom per second squared — and that relation fits the rotation curves of both faint and bright spiral galaxies.Section 1.1, equation 1, with the fits in Figure 1 (arXiv:0802.1775v3)
Published and peer-reviewed02The acceleration scale where dark matter effects appear, the square root of the cosmological constant, and the product of the speed of light with the Hubble constant are all the same number. Zhao writes that these empirical facts should not be treated as random coincidences of the fundamental parameters of the universe.Section 1.1, equation 2 (arXiv:0802.1775v3)
What to watch03Light can be bent by the vacuum itself, because the vacuum is not empty and can be a fluid with an energy density — and that density is measurable in the laboratory. Zhao notes that the Casimir pressure between two neutral plates one hundredth of a centimetre apart is about ten to the minus ten erg per cubic centimetre, the same order as the cosmological constant’s energy density, although the cosmic value sits a factor of ten to the twelve below current Casimir sensitivity.Section 2, opening paragraphs and the paragraph on gravitational energy density (arXiv:0802.1775v3)
Published and peer-reviewed04Any spatial variation in the vacuum energy density curves some patches of spacetime more than others and so produces a dark-matter-like effect. Zhao expresses it as an effective gravitational coupling that varies with place and time, a dielectric-like parameter, and proposes measuring it with a table-top Cavendish torsion experiment carried out at different depths in the gravitational environment — on Earth, at the edge of the solar system, and in the void between galaxies.Section 2, the Gedanken experiment paragraphs, and Section 3 (arXiv:0802.1775v3)
Designed, not yet built05TeVeS-like theories are single-metric theories that can be recast entirely inside the standard general-relativity framework, with the cosmological constant replaced by a non-trivial non-uniform vacuum energy. The vector field then contributes a Maxwell-like term, and the galaxy equation becomes electrostatics with a polarisation field whose susceptibility depends on field strength and on a characteristic column density comparable to that of a sheet of paper.Section 3, equation 4, and Section 4.1, equations 8 to 12 (arXiv:0802.1775v3)
Published and peer-reviewed06An uneven dark-energy fluid and a real dark-matter halo can be told apart by observation. For an edge-on razor-thin Kuzmin disk the two produce the same rotation curve but different lensing convergence — a ratio of one over the square root of two at an impact parameter equal to the disk scale — so a combined lensing and kinematics study of a single lens decides between them, and the smaller convergence would also allow a larger Hubble constant to fit the same time-delay data.Section 6, equations 33 to 37 (arXiv:0802.1775v3)
What to watch
Read it · abstract
Abstract
Various TeVeS-inspired and f(R)-inspired theories of gravity have added an interesting twist to the search for dark matter and vacuum energy, modifying the landscape of astrophysics day by day. These theories can be together called a Non-uniform Dark Energy fluid (a Nu-Lambda fluid or a VΛ fluid); a common thread of these theories, according of an up-to-date summary by HZL1, is a non-uniform vector field, describing an uneven vacuum energy fluid. The so-called "alternative" gravity theories are in fact in the standard GR gravity framework except that the cosmological "constant" is replaced by a nontrivial non-uniform vacuum energy, which couples the effects of Dark Matter and Dark Energy together by a single field. Built initially bottom-up rather than top-down as most gravity theories, TeVeS-inspired theories are healthily rooted on empirical facts. Here we attempt a review of some sanity checks of these fast-developing theories from galaxy rotation curves, solar system constraints, and gravitational lensing. We will also discuss some theoretical aspects of these theories related to the vacuum energy, and point out some analogies with electromagnetism and the Casimir effect.
HongSheng Zhao, An Uneven Vacuum Energy Fluid as Λ, Dark Matter, MOND and Lens, Modern Physics Letters A 23 (2008), World Scientific. Published paper at doi.org/10.1142/s021773230802656x; the author’s preprint, read in full for this page, is at arxiv.org/abs/0802.1775.
(Abstract only — no further text of the paper is reproduced here; see the rights note above. Companion sheets on this site: Grigory Volovik’s superfluid vacuum in /library/stm-6ee45bd8be, Rugh and Zinkernagel on the quantum vacuum and the cosmological constant problem at /library/stm-bea1f2cb9c, Meinert and Hofmann’s axial anomaly account of the dark universe at /library/stm-b06591e288, dark matter as a superfluid at /library/stm-25005f2061 and /library/stm-395f34ea17, Verlinde’s emergent gravity at /library/stm-601c8315b2, and the DESI DR2 dark-energy measurement at /library/stm-15541611e8.)
The way in
https://doi.org/10.1142/s021773230802656xLICENCE. Published by World Scientific under DOI 10.1142/S021773230802656X, Modern Physics Letters A volume 23 (2008); Crossref records no Creative Commons statement and the site’s own fetch record returns a null licence, so only the published abstract is reproduced here. SOURCE READ. The author’s preprint, arXiv:0802.1775v3 dated 3 March 2008, was downloaded and read in full for this page, and every locator below cites that preprint’s section, equation and figure numbers. The preprint is posted under arXiv’s non-exclusive distribution licence, which is not a Creative Commons licence, so it too is summarised rather than reproduced. Two small differences are worth recording for anyone comparing the two: the preprint is typeset for International Journal of Modern Physics D, and its abstract closes on ‘galaxy rotation curves, gravitational lensing and cosmic acceleration’ where the published abstract reproduced below reads ‘galaxy rotation curves, solar system constraints, and gravitational lensing’. The preprint also writes the review in the first person singular. AUTHOR AFFILIATIONS as printed: HongSheng Zhao, National Astronomical Observatories, Chinese Academy of Sciences, Datun Road, Chaoyang district, Beijing; and SUPA, School of Physics and Astronomy, University of St Andrews, Fife. The paper is based on lectures at the Lensing Winter School, Sicily 2006, and an invited talk at Fundamental Physics From Quantum to Cosmology, Washington DC 2006. RELATED PAGES on this site: Grigory Volovik’s superfluid-vacuum programme at /library/stm-6ee45bd8be, Rugh and Zinkernagel on the quantum vacuum and the cosmological constant problem at /library/stm-bea1f2cb9c, Meinert and Hofmann on the axial anomaly in galaxies at /library/stm-b06591e288, the dark-matter-superfluidity papers at /library/stm-25005f2061 and /library/stm-395f34ea17, Verlinde’s emergent gravity at /library/stm-601c8315b2, and the DESI DR2 dark-energy measurement at /library/stm-15541611e8.
How to cite it
HongSheng Zhao (2008) An Uneven Vacuum Energy Fluid as Λ, Dark Matter, MOND and Lens. doi:10.1142/s021773230802656x
Where it sits in the curriculum
The unified pictureWhat the vacuum isThe vacuum as a quantum fluidThe evidence ladder