
The bigravity theory: a bimetric cosmological model
The bigravity theory is a bimetric cosmological model with two CPTsymmetric universes interacting through gravitation, including joint variations of the speed of light and all physical constants through time. The model is based on two coupled Einstein field equations, and the geometrical support is a Riemannian manifold with two conjugated metrics having their own geodesics.
The developments of this model led to various papers published in academic journals through peer review and specialized international meetings since 1977. It is described with classical yet powerful tools ranging from Newtonian cosmology, though General relativity, to group theory. This web site, bigravitytheory.com, is a professional place to find, download and study related preprints and published papers about the theory (see footnotes) and some popular initiation courses to standard and twin cosmologies as well as group theory (coming soon).
The bigravity theory represents an alternative to the standard model. Both share the same basic physical laws (the general relativity for example) but the bimetric model describes several obervational data otherwise, and can propose explanations to problems the standard model cannot answer. For example the bimetric model explains the apparent absence of primordial antimatter and describes what could be the physical expression of the "time reversal" of a particle. The acceleration of the cosmic expansion, classically charged to a negative pressure "cosmological constant" or another kind of exotic "dark energy" whose nature remains unknown, is due to the repulsive effect of the twin universe on ours. There is also no need to resort to any "dark matter": the invisible repulsive "twin matter" in the twin universe gives gravitational lensing effects; 2D bigravity computer simulations with joint gravitational instabilities showed the selfformation of a lacunar largescale structure, with twin matter conglomerates located inside giant hollow cells. They also showed the selfformation of barred spiral structures, stable on great numbers of turns, which could explain the abnormal flatness of the galaxy rotation curve by a twin confinment effect, preventing galaxies from bursting under the effect of their high centrifugal force, with no need to add any ingredient as "cold dark matter" nor ad hoc local adjustements of parameters. The same twin matter halos would also explain the "Pioneer anomaly" i.e. robotic spacecrafts decelerating while they approach such an antigravitational barrier surrounding the outer solar system. The model also proposes a working principle for the mysterious quasars. Finally, due to the joint variations of physical constants in the RadiationDominated Era of the universe and with high local energy densities, the model offers an alternative explanation for redshift and apparent farthest "dwarf galaxies". It also suggests a "hyperspace transfer" transient mechanism for neutron stars reaching their critical limit (alternative to the "frozen" black hole theory) where a hypertoric bridge would briefly link the geodesics of the two metrics, through which the matter in excess would escape before a quick closure of the spacetime surgery.
Author's career in astrophysics
Perhaps some readers know that, before publishing in the theoretical field of astrophysics and cosmology from 1987, I had a 15 years long activity in experimental research about magnetohydrodynamics (MHD) from which I published various papers (if you want more information about this subject you can browse the web site MHDprospects.com devoted to my MHD career). Initially I was indeed a specialist in fluid dynamics, graduated from Supaero (French National Higher School of Aeronautics and Space). I worked seven years at the Marseille Institute of Fluid Mechanics, France, between 1965 and 1972.
In 1972 I defended my EngD thesis,^{1} whose subject linked both engineering and astrophysical aspects of ionized gases in two parts: at first, a presentation of the basis for the kinetic theory of nonequilibrium plasmas, and thereafter its application to galactic dynamics (there I resumed the work from the astrophysicist Subrahmanyan Chandrasekhar, with a more compact matrix rewriting). I integrated the French National Center for Scientific Research (CNRS) as an astophysicist at the Marseille Observatory, where I worked until retirement in 2003. At that time galactic dynamics was precisely my first applied work following my thesis, where I made the Friedmann equations emerge from an elliptic solution of the Vlasov equation coupled with Poisson's equation. At the very begining in this field, I published a rewriting of the Newtonian cosmology using my kinetic theory of nonequilibrium plasmas, resuming the work made by Arthur Milne and William McCrea (1934). This solution besides allowed to recover the rotating universe of Otto Heckmann and Engelbert Schücking.^{2}
In 1977, I published two papers of what would then become my main work: the construction of a cosmological model with not only one universe, but two universes born from the same initial Big bang singularity: the twin universe theory.^{3,}^{4} This model intended at the beginning to propose an answer to the complete absence of primordial antimatter from the Big bang and the apparent baryon assymetry of the universe. In this idea, matter and antimatter would have mainly populated two different, parallel universes. The twin universe with its antiparallel arrow of time would be the Tsymmetric of our universe. It would be also enantiomorph (Psymmetry) and mainly populated by antimatter (Csymmetry) because its CPviolation would be opposite. So the two metrics would present each other as a complete CPT symmetry, and considering them as a whole, the universe would globally keep an unviolated parity. In 1984 I discovered Andrei Sakharov's scientific work for the first time, collected outside USSR in a book.^{5} I had the surprise to learn he also published the same idea before.^{6,7,8,9 }Alas Sakharov died before we could meet and discuss about it.
In 1988, I was the first to introduce a variable speed of light (VSL) cosmology,^{10,11,12,13} with joint variations of all physical constants, as an alternative to the cosmic inflation theory. Unlike other preceding authors who tried to vary the gravitational constant G without changing the speed of light c, and unlike other following authors who introduced a variable speed of light without touching anything else, the model I propose preserves the Lorentz invariance and the energy. In the RadiationDominated Era of the universe, the time varies like the conformal time log t, and the metric is conformally flat. The joint variations of all physical constants are combined to space and time scale factors changes, so that all equations and measurements of these constants remain unchanged through the evolution of the universe. The only true "absolute constant" is the ratio G/c^{2}, as stipulated by Einstein's constant in the Einstein field equation.
From 1995 I published for the first time these parameters within a mature twin universe model, which approached its modern form.^{15}
Since that time the bigravity theory is developed from a mathematical physics underlying ground. The model is now fully geometrized, for example with the description of the twin matter naturally arising from the group theory using a method invented in 1974 by the mathematician JeanMarie Souriau.^{16} I produced a series of preprints between 1996 and 1998 on these grounds.^{17,18,19,20,21}
Using this work I presented the most complete synthesis of the bimetric cosmological model at an international meeting on astrophysics and cosmology in 2001.^{31}
For years, the great majority of cosmologists did not understand the model cause of quite difficult topological and chronological concepts, or did not take the time to evaluate it. Except for Andrei Sakharov who easily handled Tsymmetric topologies and proposed the first bimetric CPTsymmetric cosmological model (but without bigravity), we can cite Michael Green and John Henry Schwarz, Robert Foot and Ray Volkas, NimaArkani Ahmed, Savas Dimopoulos and Georgi Dvali, as well as the Nobel laureate Abdus Salam, who pushed towards descriptions of multiple universes interacting through gravitation (but wihout any Tsymmetry). As to other VSL theories, they change the speed of light through time but do not jointly modify other physical constants through a gauge process, so they break Lorentz invariance and do not preserve energy. One can say although its great proposals, the bigravity theory has not successfully interested the cosmological community yet. But in 2007, I incorporated a very selective club made of the best mathematicians and geometers, working in the field of mathematical physics through functional analysis. An international meeting took place in August 2007. There, I could finally talk to an assembly made of specialists who not only were aware of the basis involved, but were also for the first time firing questions after questions, being strongly interested in the model thanks to its mathematical physics basis and its links with observational data.^{32,33,34,35,36,37}
In 2008 I was invited at Imperial College London to present my work about variable speed of light cosmology, at Physical Interpretations of Relativity Theory conference.^{38}
Thanks to this good professional contact with the world of geometers, future developments are coming. Among other things we plan to finally make bigravity 3D computer simulations with powerful modern CPUs. We also hope to interest some clever scientists in Englishspeaking parts of the world, who are working on exciting new ideas such as LQG (Loop Quantum Gravity). We do not think the superstring theory could ever bring any concrete improvement in our knowledge of the universe. Not only asphyxiating other alternative theories, it has above all divorced long ago with true Popper's falsifiability, betraying one of the most fundamental principle of scientific research.
You can read and study the bigravity theory with documents to download as PDF files below. The most complete description of this bimetric model to date is presented in the summary from 2001,^{31} and in the paper series from 2007.^{32,33,34,35,36,37}



References
^{1} J.P. Petit (1972). "Applications of the kinetic theory of gases to plasma physics and galactic dynamics". Doctor of Engineering thesis, AixMarseille University, France.
^{2} J.P. Petit (16–20 Septembrer, 1974). "Proceedings" in International meeting on spiral glaxies dynamics. Institut des Hautes Études Scientifiques (IHES), BuressurYvette, France.
^{3} J.P. Petit (May 23, 1977). "Enantiomorphic universes with opposite time arrows". Comptes rendus de l'Académie des Sciences 263: 1315–1318. Paris: French Academy of Sciences.
^{4} J.P. Petit (June 6, 1977). "Universes interacting with their opposite timearrow fold". Comptes rendus de l'Académie des Sciences 284: 1413–1416. Paris: French Academy of Sciences.
^{5} A.D. Sakharov (1982). "Collected Scientific Works" (tr. D. Ter Haar, D. V. Chudnovsky et al.). Marcel Dekker, NY. ISBN 0824717147.
^{5} A.D. Sakharov (1984). "Œuvres scientifiques" (in French, tr. L. Michel, L.A. Rioual). Anthropos (Economica), Paris. ISBN 2715710909.
^{6} A.D. Sakharov (1967). "CP violation and baryonic asymmetry of the Universe". ZhETF Pis'ma 5 (Tr. JETP Lett. 5, 24–27) (5): 32–35.
^{7} A.D. Sakharov (1970). "A multisheet Cosmological model". preprint. Moscow, Russia: Institute of Applied Mathematics.
^{8} A.D. Sakharov (1972). "Topological structure of elementary particles and CPT asymmetry". Problems in theoretical physics, dedicated to the memory of I.E. Tamm. Nauka, Moscow, Russia.
^{9} A.D. Sakharov (1980). "Cosmological model of the Universe with a time vector inversion". ZhETF (Tr. JETP 52, 349351) (79): 689–693.
^{10} J.P. Petit (1988). An interpretation of cosmological model with variable light velocity. Modern Physics Letters A, 3 (16): 1527.
^{11} J.P. Petit (1988). Cosmological model with variable light velocity: the interpretation of red shifts. Modern Physics Letters A, 3 (18): 1733.
^{12} J.P. Petit; M. Viton (1989). Gauge cosmological model with variable light velocity: Comparizon with QSO observational data. Modern Physics Letters A, 4 (23): 2201–2210.
^{13} P. Midy; J.P. Petit (June 1989). Scale invariant cosmology. The International Journal of Modern Physics D, 8: 271–280.
^{14} J.P. Petit (July 1994). The missing mass problem. Il Nuovo Cimento B, 109: 697–710.
^{15} J.P. Petit (1995). Twin Universes Cosmology. Astrophysics and Space Science (226): 273–307.
^{16} J.M. Souriau (1997). "Structure of dynamical systems". Birkhäuser. ISBN 0817636951.
^{16} J.M. Souriau (1970). Structure des systèmes dynamiques (in French, free download). Dunod. ISSN 07502435.
^{17} J.P.Petit; P. Midy (1998). Geometrization of matter and antimatter through coadjoint action of a group on its momentum space. 1: Charges as additional scalar components of the momentum of a group acting on a 10Dspace. Geometrical definition of antimatter. Preprint.
^{18} J.P. Petit; P. Midy (1998). Geometrization of matter and antimatter through coadjoint action of a group on its momentum space. 2: Geometrical description of Dirac's antimatter. Preprint.
^{19} J.P. Petit; P. Midy (1998). Geometrization of matter and antimatter through coadjoint action of a group on its momentum space. 3: Geometrical description of Dirac's antimatter. A first geometrical interpretation of antimatter after Feynmann and socalled CPTtheorem. Preprint.
^{20} J.P. Petit; P. Midy (1998). Geometrization of matter and antimatter through coadjoint action of a group on its momentum space. 4: The twin group. Geometrical description of Dirac's antimatter. Geometrical interpretation of antimatter after Feynmann and socalled CPTtheorem. Preprint.
^{21} F. HenryCouannier; G. d'Agostini, J.P. Petit (2005). I Matter, antimatter and geometry. II The twin universe model: a solution to the problem of negative energy particles. III The twin universe model plus electric charges and matterantimatter symmetry. Preprint. arXiv:0712.0067
^{22} J.P. Petit; P. Midy (1998). "Repulsive dark matter". Preprint.
^{23} J.P. Petit; P. Midy (1998). "Matter ghost matter astrophysics. 1: The geometrical framework. The matter era and Newtonian approximation". Preprint.
^{24} J.P. Petit; P. Midy (1998). "Matter ghost matter astrophysics. 2: Conjugated steady state metrics. Exact solutions". Preprint.
^{25 }J.P. Petit; P. Midy (1998). "Matter ghostmatter astrophysics. 3: The radiative era : The problem of the "origin" of the universe. The problem of the homogeneity of the early universe". Preprint.
^{26} J.P. Petit; P. Midy (1998). "Matter ghost matter astrophysics. 4: Joint gravitational instabilities". Preprint.
^{27} J.P. Petit; P. Midy, F. Landsheat (1998). "Matter ghost matter astrophysics. 5: Results of numerical 2d simulations. VLS. About a possible schema for galaxies' formation". Preprint.
^{28} J.P.Petit; F.Landsheat (1998). "Matter ghost matter astrophysics. 6: Spiral structure". Preprint.
^{29} J.P. Petit; P. Midy (1998). "Matterghost matter astrophysics. 7: Confinment of spheroidal galaxies by surounding ghost matter". Preprint.
^{30} J.P. Petit; P. Midy (1998). "Questionable black hole". Preprint.
^{31} J.P. Petit; P. Midy, F. Landsheat (June 2001). Twin matter against dark matter in International Meeting on Atrophysics and Cosmology. "Where is the matter?", Marseille, France.
^{32} J.P. Petit; G. d'Agostini (August 2007). Bigravity as an interpretation of the cosmic acceleration. Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques. arXiv:0712.0067
^{33} J.P. Petit; G. d'Agostini (August 2007). Bigravity: a bimetric model of the Universe. Exact nonlinear solutions. Positive and negative gravitational lensings. Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques. arXiv:0801.1477
^{34} J.P. Petit; G. d'Agostini (August 2007). Bigravity: a bimetric model of the Universe with variable constants, inluding VSL (variable speed of light). Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques. arXiv:0803.1362
^{35} J.P. Petit; G. d'Agostini (August 2007). "Bigravity: Bimetric model of the universe. Very large structure". Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques.
^{36} J.P. Petit; G. d'Agostini (August 2007). "Bigravity: Bimetric model of the universe. Joint gravitational instabilities". Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques.
^{37} J.P. Petit; G. d'Agostini (August 2007). "Bigravity: spiral structure". Colloque International sur les Techniques Variationnelles CITV, tr. International Meeting on Variational Techniques.
^{38} J.P. Petit; G. d'Agostini (1215 September 2008). Bigravity Variable Constants Model (A bimetric model of the Universe. Interpretation of the cosmic acceleration. In early time a symmetry breaking goes with a variable speed of light era, explaining the homogeneity of the early Universe. The c(R) law is derived from a generalized gauge process evolution). 11^{th} international conference on Physical Interpretations of Relativity Theory (PIRT XI), Imperial College, London.

