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.
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Notes
- 1.
Generally considering scales larger than 100 Mpc.
- 2.
It states that the radial velocities of recession of galaxies are directly proportional to their distances from us, i.e., \(v=H_0 d\) where \(H_0\) is the constant of proportionality known as the Hubble constant. It was the first observational evidence that our Universe is expanding.
- 3.
The metric in Eq. (1.1) bears the signature (−,\(+\),\(+\),\(+\)) which is in fact the most widely used in the literature. However, it can also be derived with the signature (\(+\),−,−,−),
- 4.
For a simple proof, see p. 162 of T. Padmanabhan, Theoretical Astrophysics Volume III: Galaxies and Cosmology, Cambridge University Press (2002).
- 5.
The proper distance or the true distance is determined by multiplying the scale factor a(t) to the comoving distance.
- 6.
The redshift parameter z is connected to the scale factor by the relation \(a=\frac{1}{1+z}\).
- 7.
This equation is also known in the literature as the Raychaudhuri equation.
- 8.
For an extensive discussion on its physical reality and its relevance in Cosmology, the readers may see the recent paper by Melia (2018).
- 9.
I suggest the readers to go through the first three chapters of the book by E. Poisson (2004) to have a basic understanding of Differential Geometry and related concepts which are relevant to this book.
- 10.
The term “dark energy” was coined by Michael Turner in 1998 motivated by Fritz Zwicky’s “dark matter” from the 1930s.
- 11.
Dark matter is an exotic, invisible substance which interacts neither with baryonic matter nor with electromagnetic radiation, thereby making it impossible to detect with current instruments. Its existence can be understood by the gravitational effects it appears to have on galaxies and galaxy clusters and also by the effects of gravitational lensing.
- 12.
A negative cosmological constant (\(\varLambda <0\)) leads to anti de Sitter (AdS) spacetime. Such a spacetime is possible only for \(k=-1\).
- 13.
The matter era should have dominated for a sufficient amount of time so as to allow structure formation which means that the DE could not have begun to dominate very early. The fact that it is relevant exactly at the present time is what we have already referred to as the cosmic coincidence problem (in Sect. 1.6.1) and is one of the greatest mysteries of contemporary Cosmology.
- 14.
Generally, a cutoff is referred to as a threshold value for a physical quantity such as energy, momentum, or length. Cutoffs are introduced in order to prevent singularities from appearing during calculations. Note that, in the context of HDE, the traditional terms “infrared” and “ultraviolet” do not literally refer to specific regions of the spectrum.
- 15.
This ratio is a constant if Hubble radius is chosen as the IR cutoff.
- 16.
See Sect. 1.7 for explanation.
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Suggested Further Reading
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.
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.
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.
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.
Energy Conditions: Poisson, E., 2004. Arelativist’s toolkit – The mathematics of black hole mechanics. Cambridge University Press.
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.
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.
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.
Dark, Holographic, and Energy: Wang, S., Y. Wang, and M. Li. 2017. Holographic dark energy. Physics Reports 696: 1.
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.
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Saha, S. (2018). Fundamentals of Relativistic Cosmology. In: Elements of Cosmological Thermodynamics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-74706-4_1
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