Plasma cosmology

[
Hannes Alfvén suggested that, by scaling laboratory results by a factor of 10⁹, he could extrapolate magnetospheric conditions. Another scaling jump of 10⁹ was required to extrapolate to galactic conditions, and a third jump of 10⁹ was required to extrapolate to the Hubble distance. Hannes Alfvén, " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983Ap%26SS..89..313A&db_key=AST&data_type=HTML&format=&high=4521318e0206333 On hierarchical cosmology] " (1983) "Astrophysics and Space Science" (ISSN 0004-640X), vol. 89, no. 2, January 1983, p. 313-324.] ]

Plasma cosmology is a non-standard cosmologyIt is described as such by advocates and critics alike. In the February 1992 issue of "Sky & Telescope" ("Plasma Cosmology"), Anthony Peratt describes it as a "nonstandard picture". The open letter at [http://www.cosmologystatement.org/ www.cosmologystatement.org] – which has been signed by Peratt and Lerner – notes that "today, virtually all financial and experimental resources in cosmology are devoted to big bang studies". The ΛCDM model big bang picture is typically described as the "concordance model", "standard model" or "standard paradigm" of cosmology [http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+T+%22STANDARD+COSMOLOGICAL+MODEL%22 here] , and [http://lanl.arxiv.org/pdf/astro-ph/9505066 here] .] generally attributed to Nobel Prize winner Hannes Alfvén in the 1960s [Helge S. Kragh, "Cosmology and Controversy: The Historical Development of Two Theories of the Universe", 1996 Princeton University Press, 488 pages, ISBN 069100546X ( [http://books.google.com/books?id=f6p0AFgzeMsC&pg=PA384&dq=%22Plasma+Cosmology%22&sig=V2j6C8UTK3BCoBmQVWw6yVaCWrY#PPA383,M1 pp.482-483] )] that attempts to explain the development of the visible universe through the interaction of electromagnetic forces on astrophysical plasma. [Alfven, Hannes O. G., "Cosmology in the plasma universe - an introductory exposition", IEEE "Transactions on Plasma Science" (ISSN 0093-3813), vol. 18, Feb. 1990, p. 5-10.] Alfvén developed his cosmological ideas based on scaling of observations from terrestrial laboratories and in situ space physics experiments to cosmological scales orders-of-magnitude greater. His most famous cosmological proposal was that the universe was an ionized equal mixture of matter and anti-matter in the form of so-called ambiplasma that would naturally separate as annihilation reactions occurred accompanied by a tremendous release of energy.

Plasma cosmology contradicts the current consensus of astrophysicists that Einstein's Theory of general relativity explains the origin and evolution of the universe on its largest scales, relying instead on the further development of classical mechanics and electrodynamics in application to astrophysical plasmas. While in the late 1980s to early 1990s there was limited discussion over the merits of plasma cosmology, these ideas have generally been ignored by the mainstream cosmology community. [Plasma cosmology advocates Anthony Peratt and Eric Lerner, in an open letter cosigned by a total of 34 authors, state "An open exchange of ideas is lacking in most mainstream conferences", and "Today, virtually all financial and experimental resources in cosmology are devoted to big bang studies". [http://www.cosmologystatement.org/] ] [Tom Van Flandern writes in [http://metaresearch.org/cosmology/BB-top-30.asp "The Top 30 Problems with the Big Bang"] , "For the most part, these four alternative cosmologies [including Plasma Cosmology] are ignored by astronomers."]

Cosmic plasma

Hannes Alfvén devoted much of his professional career attempting to characterize plasmas for which he was awarded the Nobel Prize in Physics in 1970. However, while plasma physics is uncontroversially accepted to play an important role in many astrophysical phenomena due in part to plasma's ubiquity, Alfvén held to a few ideas which have not been accepted by the scientific consensus. Chief among these is the assertion that electromagnetic forces are equal in importance with gravitation on the largest scales. [H. Alfvén and C.-G. Falthammar, "Cosmic electrodynamics" (2nd edition, Clarendon press, Oxford, 1963). "The basic reason why electromagnetic phenomena are so important in cosmical physics is that there exist celestial magnetic fields which affect the motion of charged particles in space.... The strength of the interplanetary magnetic field is of the order of 10^-4 gauss (10 nanoteslas), which gives the [ratio of the magnetic force to the force of gravity] ≈ 10⁷. This illustrates the enormous importance of interplanetary and interstellar magnetic fields, compared to gravitation, as long as the matter is ionized." (p.2-3)] Alfvén came to this conclusion by extrapolating plasma phenomena from small scales to large scales.Fact|date=April 2007 While magnetic fields are considered of interest to modern astrophysics in many standard smaller-scale astrophysical structure formation models with magnetic braking speeding gravitational collapse by transferring angular momentum from the contracting objects, standard large-scale structure models do not normally consider the magnetic field large enough to aid in angular momentum transfer for virializing processes in clusters. [Colafrancesco, S. and Giordano, F. "The impact of magnetic field on the cluster M - T relation" Astronomy and Astrophysics, Volume 454, Issue 3, August II 2006, pp. L131-L134. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2006A%26A...454L.131C&db_key=AST&data_type=HTML&format=&high=453e529efc17118] recount: "Numerical simulations have shown that the wide-scale magnetic fields in massive clusters produce variations of the cluster mass at the level of ~ 5 − 10% of their unmagnetized value.... Such variations are not expected to produce strong variations in the relative [mass-temperature] relation for massive clusters."] Research in these issues is ongoing, but plasma processes are not considered in theoretical modeling to play a significant role in structure or galaxy formation. [See for example: Dekel, A. and Silk, J. "The origin of dwarf galaxies, cold dark matter, and biased galaxy formation" Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 303, April 1, 1986, p. 39-55. [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986ApJ...303...39D&db_key=AST&data_type=HTML&format=&high=453e529efc10253] where they model plasma processes in galaxy formation that is driven primarily by gravitation of cold dark matter.] Alfvén's models do not provide any predictions that can account for any cosmological observations including Hubble's law, the abundance of light elements, or the existence of the cosmic microwave background.

Examples of the highly speculative nature of Alfvén's conclusions include factually inaccurate explanations for star formation using Birkeland currents. [Alfvén, H.; Carlqvist, P., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1978Ap%26SS..55..487A&db_key=AST&data_type=HTML&format=&high=42ca922c9c30728 Interstellar clouds and the formation of stars] " "Astrophysics and Space Science", vol. 55, no. 2, May 1978, p. 487-509.] These plasma currents were held by Alfvén and his supporters to be responsible for many filamentary structures seen in astrophysical observations. However, there remains no direct observational evidence of such large scale plasma currentsFact|date=July 2007 and mainstream astrophysical explanations for large-scale phenomena preclude plasma current mechanisms.

Alfvén and Klein cosmologies

The conceptual origins of plasma cosmology were developed in 1965 by Alfvén in his book "Worlds-Antiworlds", basing some of his work on the ideas Kristian Birkeland first described at the turn of the century and Oskar Klein's earlier proposal that astrophysical plasmas played an important role in galaxy formation. In 1971, Klein would extend Alfvén's proposals and develop the "Alfvén-Klein model" of cosmology. Their cosmology relied on giant astrophysical explosions resulting from a hypothetical mixing of cosmic matter and antimatter that created the universe or "meta-galaxy" as they preferred to speculate (see the Shapley-Curtis debate for more on the history of distinguishing between the universe and the Milky Way galaxy). This hypothetical substance that spawned the universe was termed "ambiplasma" and took the forms of proton-antiprotons (heavy ambiplasma) and electrons-positrons (light ambiplasma). In Alfvén's cosmology, the universe contained "heavy" symmetric ambiplasma with protective "light" ambiplasma, separated by double layers. According to Alfvén, such an ambiplasma would be relatively long-lived as the component particles and antiparticles would be too hot and too low-density to annihilate with each other rapidly. Annihilation radiation would emanate from the double layers of plasma and antiplasma domains. The exploding double layer was also suggested by Alfvén as a possible mechanism for the generation of cosmic raysFact|date=February 2007, x-ray bursts and gamma-ray bursts. [Alfvén, H., " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986ITPS...14..779A&db_key=AST&data_type=HTML&format=&high=4521318e0221922 Double layers and circuits in astrophysics] ", (1986) IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 779-793. Based on the NASA sponsored conference " [http://ntrs.nasa.gov/search.jsp?R=13527&id=1&qs=Ntt%3Ddouble%252Blayers%26Ntk%3Dall%26Ntx%3Dmode%2520matchall%26N%3D32%26Ns%3DPublicationYear%257c1 Double Layers in Astrophysics] " (1986)]

Ambiplasma was proposed in part to explain the observed baryon asymmetry in the universe as being due to an initial condition of exact symmetry between matter and antimatter. [H. Alfvén and C.-G. Falthammar, "Cosmic electrodynamics" (Clarendon press, Oxford, 1963). H. Alfvén, "Worlds-antiworlds: antimatter in cosmology," (Freeman, 1966). O. Klein, "Arguments concerning relativity and cosmology," "Science" 171 (1971), 339.] According to Alfvén and Klein, ambiplasma would naturally form pockets of matter and pockets of antimatter that would expand outwards as annihilation between matter and antimatter occurred at the boundaries. Therefore, they concluded that we must happen to live in one of the pockets that was mostly baryons rather than antibaryons. The processes governing the evolution and characteristics of the universe at its largest scale would be governed mostly by this feature.

Alfvén postulated that the universe has always existed [Hannes Alfvén, "Has the Universe an Origin" (1988) "Trita-EPP", 1988, 07, p. 6. See also Anthony L. Peratt, " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1995Ap%26SS.227....3P&db_key=AST&data_type=HTML&format=&high=4521318e0229815 Introduction to Plasma Astrophysics and Cosmology] " (1995) "Astrophysics and Space Science", v. 227, p. 3-11: "issues now a hundred years old were debated including plasma cosmology's traditional refusal to claim any knowledge about an 'origin' of the universe (e.g., Alfvén, 1988).] due to causality arguments and rejection of "ex nihilo" models as a stealth form of creationism. [Alfvén, Hannes, " [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992ITPS...20..590A&db_key=AST&data_type=HTML&format=&high=4521318e0224666 Cosmology: Myth or Science?] " (1992) "IEEE Transactions on Plasma Science" (ISSN 0093-3813), vol. 20, no. 6, p. 590-600. See also [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1984JApA....5...79A] ] The cellular regions of exclusively matter or antimatter would appear to expand in regions local to annihilation, which Alfvén considered as a possible explanation for the observed apparent expansion of the universe as merely a local phase of a much larger history.

In 1993, theoretical cosmologist Jim Peebles criticized the cosmology of Klein (1971), and Alfvén's 1966 book, "Worlds-Antiworlds", writing that "there is no way that the results can be consistent with the isotropy of the cosmic microwave background radiation and X-ray backgrounds".P. J. E. Peebles, " [http://www.amazon.com/dp/0691074283 Principles of Physical Cosmology] ", (1993) Princeton University Press, p. 207, ISBN-13: 978-0691074283]

Further developments

While plasma cosmology has never had the support of most astronomers or physicists, a few researchers have continued to promote and develop the approach, and publish in the special issues of the IEEE Transactions on Plasma Science that are co-edited by plasma cosmology proponent Anthony Peratt. [(See IEEE Transactions on Plasma Science, issues in [http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PHY&sim_query=YES&ned_query=YES&aut_logic=OR&obj_logic=OR&author=&object=&start_mon=12&start_year=1986&end_mon=12&end_year=1986&ttl_logic=OR&title=&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&ref_stems=ITPS.&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1 1986] , [http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=1989&isnumber=928 1989] , [http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=1990&isnumber=1720 1990] , [http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=1992&isnumber=5186 1992] , [http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=2000&isnumber=19507 2000] , [http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=2003&isnumber=28301 2003] , and 2007 Announcement [http://plasmascience.net/ieeetps/SpecialIssuesUpcoming/SpacePlasmas.html 2007] here)] A few papers regarding plasma cosmology were published in other mainstream journals until the 1990s. Additionally, in 1991, Eric J. Lerner, an independent researcher in plasma physics and nuclear fusion, wrote a popular-level book supporting plasma cosmology called "The Big Bang Never Happened". At that time there was renewed interest in the subject among the cosmological community (along with other non-standard cosmologies). This was due to anomalous results reported in 1987 by Andrew Lange and Paul Richards of UC Berkeley and Toshio Matsumoto of Nagoya University that indicated the cosmic microwave background might not have a blackbody spectrum. However, the final announcement (in April 1992) of COBE satellite data corrected the earlier contradiction of the Big Bang; the level of interest in plasma cosmology has since fallen such that little research is now conducted.

Comparison to mainstream cosmology

Plasma cosmology has been developed in much less detail than mainstream cosmology and lacks many of the key predictions and features of the current models.Sean M. Carroll offers a direct critique of these alternatives on his blog "Preposterous Universe" http://preposterousuniverse.blogspot.com/2004/05/doubt-and-dissent-are-not-tolerated.html] In mainstream cosmology, detailed simulations of the correlation function of the universe, primordial nucleosynthesis, and fluctuations in the cosmic microwave background radiation, based on the principles of standard cosmology and a handful of free parameters, have been made and compared with observations, including non-trivial consistency checks. Plasma cosmology generally provides qualitative descriptions and no systematic explanation for the standard features of mainstream cosmological theories

For example, the standard hierarchical models of galaxy and structure formation rely on dark matter collecting into the superclusters, clusters, and galaxies seen in the universe today. The size and nature of structure are based on an initial condition from the primordial anisotropies seen in the power spectrum of the cosmic microwave background. [See "e.g." P. J. E. Peebles, "Large-scale structure of the universe" (Princeton, 1980).] Recent simulations show agreement between observations of galaxy surveys and "N"-body cosmological simulations of the Lambda-CDM model. [See, for example, the [http://www.mpa-garching.mpg.de/galform/virgo/vls/index.shtml Virgo Consortium's] large-scale simulation of "universes in boxes" with the largest voids reaching such sizes. See also F. Hoyle and M. S. Vogeley, Voids in the 2dF galaxy redshift survey, "Astrophys. J." 607, 751–764 (2004) arxiv|archive=astro-ph|id=0312533.] Most astrophysicists accept dark matter as a real phenomenon and a vital ingredient in structure formation, which cannot be explained by appeal to electromagnetic processes. The mass estimates of galaxy clusters using gravitational lensing also indicate that there is a large quantity of dark matter present, an observation not explained by plasma cosmology models. [See "e.g." M. Bartelmann and P. Schneider, Weak gravitational lensing, "Phys. Rept." 340 291–472 (2001) arxiv|archive=astro-ph|id=9912508.]

Mainstream studies also suggest that the universe is homogeneous on large scales without evidence of the very large scale structure required by plasma filamentation proposals. [P. J. E. Peebles, "Principles of Physical Cosmology" (Princeton, 1993). P. J. E. Peebles, "Large-scale structure of the universe" (Princeton, 1980).] The largest galaxy number count to date, the Sloan Digital Sky Survey, corresponds well to the mainstream picture. [M. Tegmark "et al." (SDSS collaboration), "The three-dimensional power spectrum of galaxies from the Sloan Digital Sky Survey", "Astrophysical J." 606 702–740 (2004). arxiv|archive=astro-ph|id=0310725 The failure of alternative structure formation models is clearly indicated by the deviation of the matter power spectrum from a power law at scales larger than 0.5 "h" Mpc^-1 (visible [http://space.mit.edu/home/tegmark/sdss.html here] ).The authors comment that their work has "thereby [driven] yet another nail into the coffin of the fractal universe hypothesis..."]

Light element production without Big Bang nucleosynthesis (as required in plasma cosmology) has been discussed in the mainstream literature and was determined to produce excessive x-rays and gamma rays beyond that observed. [J.Audouze "et al.', Big Bang Photosynthesis and Pregalactic Nucleosynthesis of Light Elements, 'Astrophysical Journal" 293:L53-L57, 1985 June 15 [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1985ApJ...293L..53A&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf] ] [Epstein "et al.", The origin of deuterium, "Nature", Vol. 263, September 16, 1976 point out that if proton fluxes with energies greater than 500 MeV were intense enough to produce the observed levels of deuterium, they would also produce about 1000 times more gamma rays than are observed.] This issue has not been completely addressed by plasma cosmology proponents in their proposals. [Ref. 10 in "Galactic Model of Element Formation" (Lerner, "IEEE Trans. Plasma Science Vol. 17, No. 2, April 1989 [http://www.health-freedom.info/pdf/Galactic%20Model%20of%20Element%20Formation.pdf] ) is J.Audouze and J.Silk, "Pregalactic Synthesis of Deuterium" in "Proc. ESO Workshop on "Primordial Helium", 1983, pp. 71-75 [http://adsabs.harvard.edu/abs/1983prhe.work...71A] Lerner includes a paragraph on "Gamma Rays from D Production" in which he claims that the expected gamma ray level is consistent with the observations. He cites neither Audouze nor Epstein in this context, and does not explain why his result contradicts theirs.] Additionally, from an observational point of view, the gamma rays emitted by even small amounts of matter/antimatter annihilation should be easily visible using gamma ray telescopes. However, such gamma rays have not been observed. This could be resolved by proposing, as Alfvén did, that the bubble of matter we are in is larger than the observable universe. In order to test such a model, some signature of the ambiplasma would have to be looked for in current observations, and this requires that the model be formalized to the point where detailed quantitative predictions can be made. This has not been accomplished.

No proposal based on plasma cosmology trying to explain the cosmic microwave background radiation has been published since COBE results were announced. Proposed explanations are relying on integrated starlight and do not provide any indication of how to explain that the observed angular anisotropies of CMB power spectrum is (so low as) one part in 10⁵. The sensitivity and resolution of the measurement of these anisotropies was greatly advanced by WMAP. The fact that the CMB was measured to be so isotropic, inline with the predictions of the big bang model, was subsequently heralded as a major confirmation of the Big Bang model to the detriment of alternatives. [D. N. Spergel "et al." (WMAP collaboration), "First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters", "Astrophys. J. Suppl." 148 (2003) 175.] These measurements showed the "acoustic peaks" were fit with high accuracy by the predictions of the Big Bang model and conditions of the early universe.

Plasma cosmology is not considered by the astronomical community to be a viable alternative to the Big Bang, and even its advocates agree the explanations it provides for phenomena are less detailed than those of conventional cosmology. As such, plasma cosmology has remained sidelined and viewed in the community as a proposal unworthy of serious consideration.

Notes

Further reading

* Alfvén, Hannes::*" [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1983Ap%26SS..89..313A On hierarchical cosmology] ", "Astrophysics and Space Science" (ISSN 0004-640X), vol. 89, no. 2, Jan. 1983, p. 313-324. (1983):*" [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1988LPB.....6..389A&db_key=AST&data_type=HTML&format=&high=45cce9d73311457 Cosmology in the plasma universe] ". (1988) "Laser and Particle Beams" (ISSN 0263-0346), vol. 6, Aug. 1988, p. 389-398. [http://public.lanl.gov/alp/plasma/downloads/CosmologyAlfven.pdf Full text] :*" [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986ITPS...14..629A&db_key=AST&data_type=HTML&format=&high=45cce9d73311457 Model of the plasma universe] ", "IEEE Transactions on Plasma Science" (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 629-638 [http://public.lanl.gov/alp/plasma/downloads/ModelOfTPU_Alfv%8En.pdf Full text] (PDF)
*Peratt, Anthony::*The [http://plasmauniverse.info/ Plasma Universe] (Website) overview and peer reviewed paper collection.:*" [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986ITPS...14..639P&db_key=AST&data_type=HTML&format=&high=45cce9d73311457 Evolution of the plasma universe. I - Double radio galaxies, quasars, and extragalactic jets] ", "IEEE Transactions on Plasma Science" (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 639-660. [http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-I.pdf Full text] (PDF):*" [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1986ITPS...14..763P&db_key=AST&data_type=HTML&format=&high=45cce9d73311457 Evolution of the plasma universe. II - The formation of systems of galaxies] ", "IEEE Transactions on Plasma Science" (ISSN 0093-3813), vol. PS-14, Dec. 1986, p. 763-778. [http://public.lanl.gov/alp/plasma/downloadsCosmo/Peratt86TPS-II.pdf Full text] (PDF):*" [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1988LPB.....6..471P&db_key=AST&data_type=HTML&format=&high=45cce9d73312115 The role of particle beams and electrical currents in the plasma universe] ", Peratt, Anthony L., Laser and Particle Beams (ISSN 0263-0346), vol. 6, Aug. 1988, p. 471-491 [http://public.lanl.gov/alp/plasma/downloads/Peratt_RolePartBeams.pdf Full text] (PDF)
* Wright, E. L. " [http://www.astro.ucla.edu/~wright/lerner_errors.html Errors in "The Big Bang Never Happened"] ". See also: Lerner, E. J. " [http://photoman.bizland.com/bbnh/p25.htm Dr. Wright is Wrong] ". Lerner's reply to the above.
* IEEE Xplore, " [http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=27 IEEE Transactions on Plasma Science] ", 18 issue 1 (1990), Special Issue on Plasma Cosmology including A. L. Peratt, "Plasma cosmology", "IEEE T. Plasma Sci." 18, 1-4 (1990).
*Various authors: " [http://adsabs.harvard.edu/abs/1995Ap%26SS.227....3P Introduction to Plasma Astrophysics and Cosmology] ", "Astrophysics and Space Science", v. 227 (1995) p. 3-11. Proceedings of the Second IEEE International Workshop on Plasma Astrophysics and Cosmology, held from 10 to 12 May 1993 in Princeton, New Jersey

Books

* H. Alfvén, "Worlds-antiworlds: antimatter in cosmology," (Freeman, 1966).
* H. Alfvén, "Cosmic Plasma" (Reidel, 1981) ISBN 90-277-1151-8
* E. J. Lerner, "The Big Bang Never Happened", (Vintage, 1992) ISBN 0-679-74049-X
* A. L. Peratt, "Physics of the Plasma Universe", (Springer, 1992) ISBN 0-387-97575-6