A Brief Analysis of de Sitter Universe in Relativistic Cosmology

Mohajan, Haradhan (2017): A Brief Analysis of de Sitter Universe in Relativistic Cosmology. Published in: Journal of Scientific Achievements , Vol. 2, No. 11 (30 November 2017): pp. 1-17.

Abstract

The de Sitter universe is the second model of the universe just after the publications of the Einstein’s static and closed model. In 1917, Wilhelm de Sitter has developed this model which is a maximally symmetric solution of the Einstein field equation with zero density. The geometry of the de Sitter universe is theoretically more complicated than that of the Einstein universe. The model does not contain matter or radiation. But, it predicts that there is a redshift. This article tries to describe the de Sitter model in some detail but easier mathematical calculations. In this study an attempt has been taken to provide a brief discussion of de Sitter model to the common readers.

• Item Type: MPRA Paper
• Language: English
• Keywords: de Sitter space-time, empty matter universe, redshifts
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General

References

Anninos, D.; Ng, G.S. and Strominger, A. (2012), Future Boundary Conditions in de Sitter Space, arXiv:1106.1175 [hep-th].

Barata, J.C.A.; Jäkel, C.D. and Mund, J. (2017), Interacting Quantum Fields on de Sitter Space. arXiv:1607.02265v2 [math-ph] 12 Jun 2017.

Bartelmann, M. (2012), Development of Cosmology: From a Static Universe to Accelerated Expansion, In: B. Falkenburg, W. Rhode (Eds.), From Ultra Rays to Astroparticles, Springer.

Carroll, S.M. (2004), Spacetime and Geometry: An Introduction to General Relativity, San Francisco: Addison-Wesley.

Chavanis, P.-H. (2012), Models of Universe with a Polytropic Equation of State, arXiv:1208.0797v1 [astro-ph.CO].

de Sitter, W. (1917a), On Einstein’s Theory of Gravitation and its Astronomical Consequences, Monthly Notices of the Royal Astronomical Society, 78: 3–28.

de Sitter, W. (1917b), On the Relativity of Inertia. Remarks Concerning Einstein’s Latest Hypothesis, Proceedings of the Royal Academy of Sciences at Amsterdam (KNAW), 19(II): 1217–1225.

Duerbeck, H.W. and Seitter, W.C. (2001), In Hubble’s Shadow: Early Research on the Expansion of the Universe, In Miklos Konkoly Thege (1842–1916), 100 Years of Observational Astronomy and Astrophysics; A Collection of Papers on the History of Observational Astrophysics, C. Sterken and J. B. Hearnshaw (Eds.), pp. 231–254, Brussels: VUB Press.

Einstein, A. (1915), The Field Equations of Gravitation (in German), König, Preuss, Akad, Wiss, (Berlin) Sitzungsberichte, 844–847.

Einstein, A. (1917), Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsber, Preuss, Akad, Wiss, Berlin: 142–152.

Hannabuss, K.C. (1971), The Localizability of Particles in de Sitter Space, Proceedings of the Cambridge Philosophical Society, 70: 283–302.

Harvey, A. and Schucking, E. (2000), Einstein’s Mistake and the Cosmological Constant, American Journal of Physics, 68(8): 723–727.

Hawking, S.W. and Ellis, G.F.R. (1973), The Large Scale Structure of Space-time, Cambridge University Press, Cambridge.

Hofbaur, T. (2014), On the Stability of a de Sitter Universe with Self-interacting Massive Particles, PhD Thesis, Sigill University, Maximilians, München,

Inomata, A. (1968), The de Sitter Universe and Mach’s Principle, Progress of Theoretical Physics, 39(5): 1370–1372.

Islam, J.N. (2002), An Introduction to Mathematical Cosmology, 2nd Ed., Cambridge University Press, Cambridge.

Joshi, P.S. (1996), Global Aspects in Gravitation and Cosmology, 2nd Ed., Clarendon Press, Oxford.

Joshi, P.S. (2008), Gravitational Collapse and Spacetime Singularities, Cambridge University Press, Cambridge.

Lemaître, G. (1925), Note on de Sitter’s Universe, Journal of Mathematical Physics, 4: 188–192.

Lord, E.A. (1973), Geometry of the de-Sitter Universe, International Journal of Theoretical Physics, 9(2): 117–127.

Mohajan, H.K. (2017a), Space-Time Singularities in Gravitational Cosmology and Age of the Universe, Book to Appear.

Mohajan, H.K. (2017b), Development of Einstein’s Static Cosmological Model of the Universe, Journal of Scientific Achievements, 2(7): 18–30.

Penrose, R. (1968), Structure of Space-Time, in Batelle Rencontres, Lectures in Mathematics and Physics. In: C. M. DeWitt and J. A. Wheeler (Eds.), pp. 121–235, Benjamin, New York.

Penrose, R. (1970), Gravitational Collapse: The Role of General Relativity, General Relativity and Gravitation, 34(7): 1141–1165.

Perlmutter, S.; Aldring, G.; Goldhaber, G.; Knop. R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S. Goobar,A.; Groom, D.E.; Hook, I.M.; Kim, A.G.; Kim, M.Y.; Lee, J.C.; Nunes, N.J. et al. (1999), Measurements of Ω and Λ from 42 High-Redshift Supernovae, The Astrophysical Journal, 517(2): 565–586.

Schmidt, H.J. (1993), On the de Sitter Space-Time–The Geometric Foundation of Inflationary Cosmology, Fortschritte der Physik, 41(3): 179–199.

Strominger, A. (2001), The dS/CFT Correspondence, JHEP 0110, 034, [arXiv:hep-th/0106113].

Tolman, R.C. (1939), Static Solution of Einstein’s Field Equation for Spheres of Fluid, Physical Review, 55(4): 364–373.

Tolman, R.C. (1969), Relativity, Thermodynamics and Cosmology, Clarendon Press, Oxford.

Wikipedia (2017), Wikipedia, the Free Encyclopedia.