Advertisement

The Universe in Expansion

  • Oliver PiattellaEmail author
Chapter
  • 960 Downloads
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

We introduce in this chapter the geometric basis of cosmology and the expansion of the universe. A part from the technical treatment, historical, theological and mythological introductions to cosmology can be found in Ryden (Introduction to Cosmology, Addison-Wesley, San Francisco, 244 p 2003) and Bonometto (Cosmologia & Cosmologie, Zanichelli 2008).

References

  1. Ade, P.A.R., et al.: Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016)CrossRefGoogle Scholar
  2. Avelino, A., Kirshner, R.P.: The dimensionless age of the universe: a riddle for our time. Astrophys. J. 828(1), 35 (2016)ADSCrossRefGoogle Scholar
  3. Baqui, P.O., Fabris, J.C., Piattella, O.F.: Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure. JCAP 1604(04), 034 (2016)ADSMathSciNetCrossRefGoogle Scholar
  4. Bonometto, S.: Cosmologia & Cosmologie. Zanichelli (2008)Google Scholar
  5. de Sitter, W.: On the relativity of inertia. Remarks concerning Einstein’s latest hypothesis. Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 19, 1217–1225 (1917)Google Scholar
  6. de Sitter, W.: Einstein’s theory of gravitation and its astronomical consequences. Third paper. Mon. Not. R. Astron. Soc. 78, 3–28 (1918a)CrossRefGoogle Scholar
  7. de Sitter, W.: Further remarks on the solutions of the field-equations of the Einstein’s theory of gravitation. Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 20, 1309–1312 (1918b)ADSGoogle Scholar
  8. de Sitter, W.: On the curvature of space. Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 20, 229–243 (1918c)ADSGoogle Scholar
  9. Etherington, I.M.H.: On the definition of distance in general relativity. Philos. Mag. 15 (1933)Google Scholar
  10. Fabris, J.C., Velten, H.: Neo-Newtonian cosmology: an intermediate step towards general relativity. RBEF 4302 (2012)Google Scholar
  11. Friedmann, A.: Ueber die Kruemmung des Raumes. Z. Phys. 10, 377–386 (1922)ADSCrossRefGoogle Scholar
  12. Friedmann, A.: Ueber die Moeglichkeit einer Welt mit konstanter negativer Kruemmung des Raumes. Z. Phys. 21, 326–332 (1924)ADSCrossRefGoogle Scholar
  13. Giblin, J.T., Mertens, J.B., Starkman, G.D.: Observable deviations from homogeneity in an inhomogeneous universe. Astrophys. J. 833(2), 247 (2016)ADSCrossRefGoogle Scholar
  14. Harrison, E.R.: Cosmology without general relativity. Ann. Phys. 35, 437–446 (1965)ADSMathSciNetCrossRefGoogle Scholar
  15. Hogg, D.W.: Distance measures in cosmology (1999)Google Scholar
  16. Hwang, J.-C., Noh, H.: Newtonian hydrodynamics with general relativistic pressure. JCAP 1310, 054 (2013)ADSMathSciNetCrossRefGoogle Scholar
  17. Lemaitre, G.: The expanding universe. Mon. Not. R. Astron. Soc. 91, 490–501 (1931)ADSCrossRefGoogle Scholar
  18. Lemaître, G.: The expanding universe. Gen. Rel. Gravit. 29, 641–680 (1997)CrossRefGoogle Scholar
  19. Lima, J.A.S., Zanchin, V., Brandenberger, R.H.: On the Newtonian cosmology equations with pressure. Mon. Not. R. Astron. Soc. 291, L1–L4 (1997)ADSCrossRefGoogle Scholar
  20. Maartens, R.: Causal thermodynamics in relativity (1996)Google Scholar
  21. McCrea, W.H., Milne, E.A.: Newtonian Universes and the curvature of space. Q. J. Math. 5 (1934)Google Scholar
  22. McCrea, W.H.: Relativity theory and the creation of matter. Proc. R. Soc. Lond. Ser. A 206, 562–575 (1951)ADSMathSciNetCrossRefGoogle Scholar
  23. McVittie, G.C.: Appendix to the change of redshift and apparent luminosity of galaxies due to the deceleration of selected expanding universes. Astrophys. J. 136, 334 (1962)ADSGoogle Scholar
  24. Milne, E.A.: A Newtonian expanding Universe. Q. J. Math. 5 (1934)Google Scholar
  25. Milne, E.A.: Relativity, gravitation and world-structure. The Clarendon Press, Oxford (1935)zbMATHGoogle Scholar
  26. Perlmutter, S., et al.: Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999)ADSCrossRefGoogle Scholar
  27. Piattella, O.F., Giani, L.: Redshift drift of gravitational lensing. Phys. Rev. D 95(10), 101301 (2017)ADSCrossRefGoogle Scholar
  28. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)ADSCrossRefGoogle Scholar
  29. Robertson, H.P.: Kinematics and world-structure. Astrophys. J. 82, 284 (1935)ADSCrossRefGoogle Scholar
  30. Robertson, H.P.: Kinematics and world-structure III. Astrophys. J. 83, 257 (1936)ADSCrossRefGoogle Scholar
  31. Ryden, B.: Introduction to Cosmology, 244 p. Addison-Wesley, San Francisco (2003)Google Scholar
  32. Sandage, A.: The change of redshift and apparent luminosity of galaxies due to the deceleration of selected expanding universes. Astrophys. J. 136, 319 (1962)ADSCrossRefGoogle Scholar
  33. Sarkar, S., Pandey, B.: An information theory based search for homogeneity on the largest accessible scale. Mon. Not. R. Astron. Soc. 463(1), L12–L16 (2016)ADSCrossRefGoogle Scholar
  34. Schutz, B.F.: A First Course In General Relativity. Cambridge University Press, Cambridge (1985)Google Scholar
  35. Velten, H.E.S., vom Marttens, R.F., Zimdahl, W.: Aspects of the cosmological coincidence problem. Eur. Phys. J. C 74(11), 3160 (2014)Google Scholar
  36. Walker, A.G.: On milne’s theory of world-structure. Proc. Lond. Math. Soc. 2(1), 90–127 (1937)MathSciNetCrossRefGoogle Scholar
  37. Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)Google Scholar
  38. Wu, K.K.S., Lahav, O., Rees, M.J.: The large-scale smoothness of the universe. Nature 397, 225–230 (1999). (19 (1998))ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Núcleo Cosmo-UFES and Department of PhysicsFederal University of Espírito SantoVitóriaBrazil

Personalised recommendations