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Fundamentals of Relativistic Cosmology

  • Subhajit SahaEmail author
Chapter
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

This chapter provides a concise introduction to the basic notions of Cosmology. Starting from the Cosmological Principle, the Weyl’s Postulate, and the Einstein’s equations, this chapter goes on to explain the relevant concepts of Cosmology required to gain the necessary insights into the subject of cosmological thermodynamics. It gives a brief, yet an effective description of the Friedmann–Lemaitre–Robertson–Walker metric, the observational parameters, the cosmological horizons, particularly, the apparent, event, and particle horizons, and the inexplicable dark energy.

Keywords

Cosmology Cosmological principle Weyl’s postulate Einstein’s field equations FLRW metric Friedmann equation Raychaudhuri equation Hubble parameter Dark energy Cosmological constant 

References

  1. Amendola, L., and S. Tsujikawa. 2010. Dark energy – Theory and observations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  2. Amendola, L., F. Finelli, C. Burigana, and D. Carturan. 2003. WMAP and the generalized Chaplygin gas. Journal of Cosmology and Astroparticle Physics 07: 005.ADSCrossRefGoogle Scholar
  3. Amendola, L., M. Gasperini, and F. Piazza. 2006. SNLS data are consistent with acceleration at \(z=3\). Physical Review D 74: 127302.ADSCrossRefGoogle Scholar
  4. Bedran, M.L., V. Soares, and M.E. Araujo. 2008. Temperature evolution of the FRW universe filled with modified Chaplygin gas. Physics Letters B 659: 462.ADSCrossRefGoogle Scholar
  5. Benaoum, H.B. 2002. Accelerated Universe from modified Chaplygin gas and Tachyonic fluid. arXiv:hep-th/0205140.
  6. Bento, M.C., O. Bertolami, and A.A. Sen. 2002. Generalized Chaplygin gas, accelerated expansion and dark energy-matter unification. Physical Review D 66: 043507.ADSCrossRefGoogle Scholar
  7. Carroll, S.M. 2001. The cosmological constant. Living Reviews in Relativity 4: 1.ADSMathSciNetCrossRefGoogle Scholar
  8. Carroll, S.M. 2004. Spacetime and geometry – An introduction to general relativity. San Francisco: Pearson Education.zbMATHGoogle Scholar
  9. Carroll, S.M., M. Hoffman, and M. Trodden. 2003. Can the dark energy equation-of-state parameter \(w\) be less than \(-1\)? Physical Review D 68: 023509.ADSCrossRefGoogle Scholar
  10. Cheng, T.P. 2005. Relativity, gravitation and cosmology – A basic introduction. Oxford: Oxford University Press.zbMATHGoogle Scholar
  11. Cohen, A., D. Kaplan, and A. Nelson. 1999. Effective field theory, black holes, and the cosmological constant. Physical Review Letters 82: 4971.ADSMathSciNetCrossRefGoogle Scholar
  12. Copeland, E.J., M. Sami, and S. Tsujikawa. 2006. Dynamics of dark energy. International Journal of Modern Physics D 15: 1753.ADSMathSciNetCrossRefGoogle Scholar
  13. Costa, S., M. Ujevic, and A.F. dos Santos. 2008. A mathematical analysis of the evolution of perturbations in a modified Chaplygin gas model. General Relativity and Gravitation 40: 1683.ADSMathSciNetCrossRefGoogle Scholar
  14. Das, S., P.S. Corasaniti, and J. Khoury. 2006. Super-acceleration as signature of dark sector interaction. Physical Review D 73: 083509.ADSCrossRefGoogle Scholar
  15. de Bernardis, P., et al. 2000. A flat Universe from high-resolution maps of the cosmic microwave background radiation. Nature (London) 404: 955.ADSCrossRefGoogle Scholar
  16. Debnath, U., and S. Chakraborty. 2008. Role of modified Chaplygin gas as a dark energy model in collapsing spherically symmetric cloud. International Journal of Theoretical Physics 47: 2663.ADSMathSciNetCrossRefGoogle Scholar
  17. Debnath, U., A. Banerjee, and S. Chakraborty. 2004. Role of modified Chaplygin gas in accelerated universe. Classical and Quantum Gravity 21: 5609.ADSMathSciNetCrossRefGoogle Scholar
  18. del Campo, S., R. Herrera, and D. Pavón. 2009. Interacting models may be key to solve the cosmic coincidence problem. Journal of Cosmology and Astroparticle Physics 01: 020.CrossRefGoogle Scholar
  19. d’Inverno, R.A. 1998. Introducing Einstein’s relativity. Oxford: Oxford University Press.zbMATHGoogle Scholar
  20. Faraoni, V. 2011. Cosmological apparent and trapping horizons. Physical Review D 84: 024003.ADSCrossRefGoogle Scholar
  21. Frieman, J.A., M.S. Turner, and D. Huterer. 2008. Dark energy and the accelerating universe. Annual Review of Astronomy and Astrophysics 46: 385.ADSCrossRefGoogle Scholar
  22. Guth, A. 1981. Inflationary universe: A possible solution to the horizon and flatness problems. Physical Review D 23: 347.ADSCrossRefGoogle Scholar
  23. Hsu, S.D.H. 2004. Entropy bounds and dark energy. Physics Letters B 594: 13.ADSCrossRefGoogle Scholar
  24. Kamenshchik, A.Y., U. Moschella, and V. Pasquier. 2001. An alternative to quintessence. Physics Letters B 511: 265.ADSCrossRefGoogle Scholar
  25. Li, M. 2004. A model of holographic dark energy. Physics Letters B 603: 1.ADSMathSciNetCrossRefGoogle Scholar
  26. Liddle, A. 2003. An introduction to modern cosmology. New York: Wiley.Google Scholar
  27. Matarrese, S., M. Colpi, V. Gorini, and U. Moschella (eds.). 2011. Dark matter and dark energy – A challenge for modern cosmology. Berlin: Springer.zbMATHGoogle Scholar
  28. Melia, F. 2018. The apparent (gravitational) horizon in cosmology. American Journal of Physics 86: 585.ADSCrossRefGoogle Scholar
  29. Mukhanov, V. 2005. Physical foundations of cosmology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  30. Padmanabhan, T. 2002. Theoretical astrophysics volume III: Galaxies and cosmology. Cambridge: Cambridge University Press.Google Scholar
  31. Padmanabhan, T. 2003. Cosmological constant - The weight of the vacuum. Physics Reports 380: 235.ADSMathSciNetCrossRefGoogle Scholar
  32. Peebles, P.J.E., and B. Ratra. 2003. The cosmological constant and dark energy. Reviews of Modern Physics 75: 559.ADSMathSciNetCrossRefGoogle Scholar
  33. Ryden, B. 2002. Introduction to cosmology. Reading: Addison-Wesley.Google Scholar
  34. Sahni, V. 2004. Dark matter and dark energy. Lecture Notes in Physics 653: 141.ADSCrossRefGoogle Scholar
  35. Spergel, D.N., et al. 2003. First year Wilkinson microwave anisotropy probe (WMAP) observations: Determination of cosmological parameters. The Astrophysical Journal Supplement Series 148: 175.ADSCrossRefGoogle Scholar
  36. Trodden, M., and Carroll, S.M. 2004. TASI lectures: Introduction to cosmology. arXiv:astro-ph/0401547.CrossRefGoogle Scholar
  37. Wang, B., Y. Gong, and E. Abdalla. 2005. Transition of the dark energy equation of state in an interacting holographic dark energy model. Physics Letters B 624: 141.ADSCrossRefGoogle Scholar
  38. Wu, Y., S. Li, J. Lu, and X. Yang. 2007. The modified Chaplygin gas as a unified dark sector model. Modern Physics Letters A 22: 783.ADSCrossRefGoogle Scholar

Suggested Further Reading

  1. General Relativity: Schutz, B. 2009. A first course in general relativity. Cambridge: Cambridge University Press; Carroll, S.M. 2004. Spacetime and geometry — An introduction to general relativity. Pearson Education; d’Inverno, R. 1992. Introducing Einstein’s relativity. Oxford University Press; Padmanabhan, T. 2010. Gravitation: Foundations and frontiers. Cambridge University Press.Google Scholar
  2. Cosmological Horizons: Faraoni, V. 2015. Cosmological and black hole apparent horizons. Springer; Wald, R.M. 1984. General relativity. The University of Chicago Press; Ashtekar, A. 2004. Isolated and dynamical horizons and their applications. Living Reviews in Relativity 7: 10; Date, G. 2000. Notes on isolated horizons. Classical and Quantum Gravity 17: 5025; Ashtekar, A., C. Beetle, and S. Fairhurst. 2000. Mechanics of isolated horizons. Classical and Quantum Gravity 17: 253; Melia, F. 2018. The apparent (gravitational) horizon in cosmology. American Journal of Physics 86: 585.CrossRefGoogle Scholar
  3. Cosmology: Trodden, M., and S.M. Carroll. TASI lectures: Introduction to cosmology. arXiv:astro-ph/0401547; Liddle, A. 2003. An introduction to modern cosmology. Wiley; Mukhanov, V. 2005. Physical foundations of cosmology. Cambridge University Press; Ryden, B. 2016. Introduction to cosmology. Cambridge University Press; Narlikar, J.V., and T. Padmanabhan. 2001. Standard cosmology and alternatives: A critical appraisal. Annual Review of Astronomy and Astrophysics 39: 211.ADSCrossRefGoogle Scholar
  4. Cosmic Inflation: Kinney, W.H. TASI lectures on inflation. arXiv:0509.1529 [astro-ph.CO]; Liddle, A.R., and D.H. Lyth. 2000. Cosmological inflation and large-scale structure. Cambridge University Press.
  5. Energy Conditions: Poisson, E., 2004. Arelativist’s toolkit – The mathematics of black hole mechanics. Cambridge University Press.Google Scholar
  6. Holographic Principle: Bousso, R. 2002. The holographic principle. Reviews of Modern Physics 74: 825; Bigatti, D., and L. Susskind. TASI lectures on the holographic principle. arXiv:hep-th/0002044.
  7. Dark Energy: Copeland, E., M. Sami, and S. Tsujikawa. 2006. Dynamics of dark energy. International Journal of Modern Physics D 15: 1753; Amendola, L., and S. Tsujikawa. 2010. Dark energy — Theory and observations. Cambridge University Press; Matarrese, S., M. Colpi, V. Gorini, and U. Moschella (eds.). 2011. Dark matter and dark energy — A challenge for modern cosmology. Springer.Google Scholar
  8. Cosmological Constant: Padmanabhan, T. 2003. Cosmological constant: The weight of the vacuum. Physics Reports 380: 235; Carroll, S.M. 2001. The cosmological constant. Living Reviews in Relativity 4: 1.MathSciNetCrossRefGoogle Scholar
  9. Dark, Holographic, and Energy: Wang, S., Y. Wang, and M. Li. 2017. Holographic dark energy. Physics Reports 696: 1.Google Scholar
  10. Gravity, Modified, and Theories: Papantonopoulos, E. 2015. Modifications of Einstein’s theory of gravity at large distances. Springer; Nojiri, S., S.D. Odintsov, and V.K. Oikonomou. 2017. Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution. Physics Reports 692: 1; Clifton, T., P.G. Ferreira, A. Padilla, and C. Skordis. 2012. Modified gravity and cosmology. Physics Reports 513: 1.Google Scholar

Copyright information

© The Author(s), under exclusive licence to Switzerland AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsPanihati MahavidyalayaKolkataIndia

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