Basic Elements of Cosmology

Shapiro, Ilya L.

doi:10.1007/978-3-030-26895-4_16

Ilya L. Shapiro⁸

Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

2476 Accesses

Abstract

According to modern scientific understanding, at the large scale, our universe is an expanding, homogeneous, and isotropic space, approximately 14 billion years (14 bi) old. The size of the universe is defined by the distance which light can cover in this time period, which is quite big. We are learning more about the history of the universe every year. One of the most interesting questions is that how we can explore and understand such an old and gigantic universe, if the region of space where the observations are performed is confined primarily to a small part of our Solar System, which has almost negligible size even compared to the typical distances in our galaxy. The time interval of our observations is also restricted to just a few thousands of years, and of scientific instrumental observations to much less than that. The answer to this question is that there are many qualitatively different observables and methods of observations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

1.
The reader can read about the anomaly, e.g., in [15], when this problem was solved. The solution does not require understanding of the quantum aspects of the problem.
2.
This historically interesting issue is described in the paper [17].
3.
The reader can see the papers [13, 20] for the details of the solution.

References

S. Dodelson, Modern Cosmology (Academic Press, Cambridge, 2003)
Google Scholar
V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Cambridge, 2005)
Book Google Scholar
D.S. Gorbunov, V.A. Rubakov, Introduction to the Theory of the Early Universe: Vol. I. Hot Big Bang Theory; Vol. II. Cosmological Perturbations and Inflationary Theory (World Scientific Publishing, Singapore, 2011)
Book Google Scholar
S. Weinberg, Cosmology (Oxford University Press, Oxford, 2008)
MATH Google Scholar
Ph.J.E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993)
Google Scholar
P. Peter, J.-Ph Uzan, Primordial Cosmology (Oxford University Press, Oxford, 2013)
Google Scholar
S. Weinberg, Gravitation and Cosmology (Wiley, Hoboken, 1972)
Google Scholar
S.W. Hawking, G.F.R. Ellis, The large scale structure of space-time (Cambridge University Press, Cambridge, 1973)
Book Google Scholar
L.D. Landau, E.M. Lifshits, The Classical Theory of Fields - Course of Theoretical Physics, vol. 2 (Butterworth-Heinemann, Oxford, 1987)
Google Scholar
A.T. Fomenko, S.P. Novikov, B.A. Dubrovin, Modern Geometry-Methods and Applications, Part I: The Geometry of Surfaces, Transformation Groups, and Fields (Springer, Berlin, 1992)
MATH Google Scholar
F. J\(\ddot{\rm u}\)ttner, Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Ann. der Phys. Bd 116, S. 145 (1911)
Google Scholar
A.D. Sakharov, The initial stage of an expanding universe and the appearance of a nonuniform distribution of matter. Zh. Eksp. Teor. Fiz. 49(1), 345 [Sov. Phys. JETP 22 (1966) 241]. See also L.P. Grishchuk, Cosmological Sakharov oscillations and quantum mechanics of the early universe. arXiv:1106.5205
G. de Berredo-Peixoto, I.L. Shapiro, F. Sobreira, Simple cosmological model with relativistic gas. Mod. Phys. Lett. A 20, 2723 (2005)
Article ADS Google Scholar
A.M. Pelinson, I.L. Shapiro, On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field. Phys. Lett. B 694, 467 (2011)
Article ADS Google Scholar
M.V. Fischetti, J.B. Hartle, B.L. Hu, Quantum effects in the early universe. 1. Influence of trace anomalies on homogeneous, isotropic, classical geometries. Phys. Rev. D20, 1757 (1979)
ADS MathSciNet Google Scholar
I.L. Shapiro, Effective action of vacuum: Semiclassical approach. Class. Quant. Grav. 25, 103001 (2008). arXiv:0801.0216
Article ADS MathSciNet Google Scholar
E. Bianchi, C. Rovelli, Why all these prejudices against a constant? Unpublished. arXiv:1002.3966
L. Bergstrom, Non-baryonic dark matter: Observational evidence and detection methods. Rep. Prog. Phys. 63, 793 (2000). hep-ph/0002126
Article ADS Google Scholar
Y. Akrami, and others, Planck 2018 results. I. Overview and the cosmological legacy of Planck, Planck Collaboration (2018). arXiv:1807.06205. N. Aghanim, and others, Planck 2018 results. VI. Cosmological parameters, Planck Collaboration (2018). arXiv:1807.06209
J.C. Fabris, I.L. Shapiro, F. Sobreira, DM particles: how warm they can be? JCAP 02, 001 (2009). arXiv:0806.1969
Article ADS Google Scholar

Download references

Author information

Authors and Affiliations

Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil
Ilya L. Shapiro

Authors

Ilya L. Shapiro
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilya L. Shapiro .

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Shapiro, I.L. (2019). Basic Elements of Cosmology. In: A Primer in Tensor Analysis and Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26895-4_16

Download citation

DOI: https://doi.org/10.1007/978-3-030-26895-4_16
Published: 30 August 2019
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26894-7
Online ISBN: 978-3-030-26895-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics