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The Universe in Expansion

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Lecture Notes in Cosmology

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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).

Oras ubicumque locaris extremas, quaeram: quid telo denique fiet?

(wherever you shall set the boundaries, I will ask: what will then happen to the arrow?)

Lucretius, De Rerum Natura

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Notes

  1. 1.

    This means that they possess 6 Killing vectors, i.e. there are six transformations which leave the spatial metric invariant (Weinberg 1972).

  2. 2.

    See also Lemaître (1997) for a recent republication and translation of Lemaître’s 1933 paper.

  3. 3.

    Pretty much the same happens with the redshift. A certain source has redshift z which, actually, is not a constant but varies slowly. This is called redshift drift and it was first considered by Sandage (1962) and McVittie (1962). Applications of the redshift drift phenomenon to gravitational lensing are proposed in Piattella and Giani (2017).

References

  • Ade, P.A.R., et al.: Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016)

    Article  Google Scholar 

  • Avelino, A., Kirshner, R.P.: The dimensionless age of the universe: a riddle for our time. Astrophys. J. 828(1), 35 (2016)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  MathSciNet  Google Scholar 

  • Bonometto, S.: Cosmologia & Cosmologie. Zanichelli (2008)

    Google Scholar 

  • 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 

  • de Sitter, W.: Einstein’s theory of gravitation and its astronomical consequences. Third paper. Mon. Not. R. Astron. Soc. 78, 3–28 (1918a)

    Article  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • de Sitter, W.: On the curvature of space. Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 20, 229–243 (1918c)

    ADS  Google Scholar 

  • Etherington, I.M.H.: On the definition of distance in general relativity. Philos. Mag. 15 (1933)

    Google Scholar 

  • Fabris, J.C., Velten, H.: Neo-Newtonian cosmology: an intermediate step towards general relativity. RBEF 4302 (2012)

    Google Scholar 

  • Friedmann, A.: Ueber die Kruemmung des Raumes. Z. Phys. 10, 377–386 (1922)

    Article  ADS  Google Scholar 

  • Friedmann, A.: Ueber die Moeglichkeit einer Welt mit konstanter negativer Kruemmung des Raumes. Z. Phys. 21, 326–332 (1924)

    Article  ADS  Google Scholar 

  • Giblin, J.T., Mertens, J.B., Starkman, G.D.: Observable deviations from homogeneity in an inhomogeneous universe. Astrophys. J. 833(2), 247 (2016)

    Article  ADS  Google Scholar 

  • Harrison, E.R.: Cosmology without general relativity. Ann. Phys. 35, 437–446 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  • Hogg, D.W.: Distance measures in cosmology (1999)

    Google Scholar 

  • Hwang, J.-C., Noh, H.: Newtonian hydrodynamics with general relativistic pressure. JCAP 1310, 054 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  • Lemaitre, G.: The expanding universe. Mon. Not. R. Astron. Soc. 91, 490–501 (1931)

    Article  ADS  Google Scholar 

  • Lemaître, G.: The expanding universe. Gen. Rel. Gravit. 29, 641–680 (1997)

    Article  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Maartens, R.: Causal thermodynamics in relativity (1996)

    Google Scholar 

  • McCrea, W.H., Milne, E.A.: Newtonian Universes and the curvature of space. Q. J. Math. 5 (1934)

    Google Scholar 

  • McCrea, W.H.: Relativity theory and the creation of matter. Proc. R. Soc. Lond. Ser. A 206, 562–575 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Milne, E.A.: A Newtonian expanding Universe. Q. J. Math. 5 (1934)

    Google Scholar 

  • Milne, E.A.: Relativity, gravitation and world-structure. The Clarendon Press, Oxford (1935)

    MATH  Google Scholar 

  • Perlmutter, S., et al.: Measurements of omega and lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999)

    Article  ADS  Google Scholar 

  • Piattella, O.F., Giani, L.: Redshift drift of gravitational lensing. Phys. Rev. D 95(10), 101301 (2017)

    Article  ADS  Google Scholar 

  • Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)

    Article  ADS  Google Scholar 

  • Robertson, H.P.: Kinematics and world-structure. Astrophys. J. 82, 284 (1935)

    Article  ADS  Google Scholar 

  • Robertson, H.P.: Kinematics and world-structure III. Astrophys. J. 83, 257 (1936)

    Article  ADS  Google Scholar 

  • Ryden, B.: Introduction to Cosmology, 244 p. Addison-Wesley, San Francisco (2003)

    Google Scholar 

  • Sandage, A.: The change of redshift and apparent luminosity of galaxies due to the deceleration of selected expanding universes. Astrophys. J. 136, 319 (1962)

    Article  ADS  Google Scholar 

  • 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)

    Article  ADS  Google Scholar 

  • Schutz, B.F.: A First Course In General Relativity. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  • 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 

  • Walker, A.G.: On milne’s theory of world-structure. Proc. Lond. Math. Soc. 2(1), 90–127 (1937)

    Article  MathSciNet  Google Scholar 

  • Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)

    Google Scholar 

  • Wu, K.K.S., Lahav, O., Rees, M.J.: The large-scale smoothness of the universe. Nature 397, 225–230 (1999). (19 (1998))

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Núcleo Cosmo-UFES and Department of Physics, Federal University of Espírito Santo, Vitória, Espírito Santo, Brazil

    Oliver Piattella

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  1. Oliver Piattella
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Correspondence to Oliver Piattella .

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Piattella, O. (2018). The Universe in Expansion. In: Lecture Notes in Cosmology. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-95570-4_2

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