Abstract
From the four types of interactions present in our world, only electromagnetism and gravity are long-range interactions. The weak and the strong interactions are so short-ranged that they cannot be responsible for the large-scale behaviour of our universe. However, despite its long range character, electromagnetism cannot be the dominant force in an electrically neutral universe. The only long range interaction that remains is gravity, whose source is energy density. Thus, a theory of the cosmos must be based on a theory of gravity. The best gravitational theory we have so far is Einstein’s theory of General Relativity [9, 10]. In contrast to the Standard Model, which is a quantum field theory, General Relativity is a classical field theory. Aside from this, the distinctive feature of gravity compared to the other fundamental interactions is that it is not a theory defined on space-time, but a theory of space-time itself. The physical foundation of General Relativity is the equivalence principle, which states that gravity uniformly couples to all kind of energy density. Mathematically, space-time is described by a pseudo-Riemannian manifold \(\mathcal{M}\) and the gravitational field by the metric field \(g_{\mu \nu }(x)\) on \(\mathcal{M}\). The gravitational interaction manifests itself geometrically as curvature of space-time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We use the sign convention: signature \((-1,1,1,1),+\!R^{\alpha }_{\;\;\beta \gamma \delta }=\Gamma ^{\alpha }_{\;\;\beta \delta ,\gamma }-\ldots \) and \(R^{\sigma }_{\;\;\mu \sigma \nu }= +\!R_{\mu \nu }\).
- 2.
A globally hyperbolic manifold is equivalent to the existence of a Cauchy surface, i.e. given some initial data on a 3-hypersurface \(\Sigma _{t}\), the evolution is uniquely determined by the equations of motion. There are also theoretical attempts to investigate whether our universe has a different topology, e.g. a torus, on the basis of experimental data, see e.g. [3, 6, 7, 18].
- 3.
If \(V(\varphi )\) was the Higgs potential of the Standard Model, the inflaton would settle in the electroweak vacuum, generating the mass of gauge bosons and fermions.
- 4.
The density and pressure fluctuations contained in \(\delta T_{\mu \nu }\) are scalar perturbations.
References
Albrecht, A., Steinhardt, P.J.: Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys. Rev. Lett. 48, 1220 (1982)
Arnowitt, R., Deser, S., Misner, C.W.: The dynamics of general relativity. In: Witten, L. (ed.) Gravitation: An Introduction to Current Research, pp. 227–265. Wiley, New York (1962)
Aurich, R., Lustig, S., Steiner, F.: CMB anisotropy of the Poincaré dodecahedron. Class Quantum Gravity 22, 2061 (2005)
Baumann, D.: TASI lectures on inflation. http://arxiv.org/abs/0907.5424 (2009) [160 pages] (cited on 19 Dec 2011)
Bunch, T., Davies, P.: Quantum field theory in de Sitter space: renormalization by point splitting. Proc. Roy. Soc. Lond. A 360, 117 (1978)
Copi, C.J., Huterer, D., Schwarz, D.J., Starkman, G.D.: Large-angle anomalies in the CMB. Adv. Astron. 2010, 847541 (2010)
Cornish, N.J., Spergel, D.N., Starkman, G.D., Komatsu, E.: Constraining the topology of the Universe. Phys. Rev. Lett. 92, 201302 (2004)
Davies, P.C.W.: Scalar particle production in Schwarzschild and Rindler metrics. J. Phys. A 8, 609 (1975)
Einstein, A.: Die Feldgleichungen der Gravitation. Sitzber. kgl.-preuß. Akad. Wiss. Berlin, Sitzung der phys.-math. Klasse, XLVIII, 844 (1915)
Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. (Berlin), 4th series, 49, 769 (1916)
Fulling, S.A.: Nonuniqueness of canonical field quantization in Riemannian space-time. Phys. Rev. D 7, 2850 (1973)
Guth, A.: Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981)
Guth, A.H., Pi, S.Y.: Fluctuations in the new inflationary universe. Phys. Rev. Lett. 49, 1110 (1982)
Hawking, S.W.: The development of irregularities in a single bubble inflationary universe. Phys. Lett. B 115, 295 (1982)
Kiefer, C., Lohmar, I., Polarski, D., Starobinsky, A.A.: Origin of classical structure in the universe. J. Phys. Conf. Ser. 67, 012023 (2007)
Kiefer, C., Lohmar, I., Polarski, D., Starobinsky, A.A.: Pointer states for primordial fluctuations in inflationary cosmology. Class Quantum Gravity 24, 1699 (2007)
Kiefer, C., Polarski, D., Starobinsky, A.A.: Quantum-to-classical transition for fluctuations in the early universe. Int. J. Mod. Phys. D 7, 455 (1998)
Lachièze-Rey, M., Luminet, J.-P.: Cosmic topology. Phys. Rep. 254, 135 (1995)
Linde, A.D.: A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B 108, 389 (1982)
Maldacena, J.M.: Non-gaussian features of primordial fluctuations in single field inflationary models. J. High Energy Phys. 05, 013 (2003)
Mukhanov, V.F., Chibisov, G.V.: Quantum fluctuation and a nonsingular universe. JETP Lett. 33, 532 (1981). (In Russian)
Mukhanov, V.F., Feldman, H.A., Brandenberger, R.H.: Theory of cosmological perturbations. Phys. Rep. 215, 203 (1992)
Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21, 562 (1968)
Parker, L.: Quantized fields and particle creation in expanding universes. I. Phys. Rev. 183, 1057 (1969)
Perlmutter, S., et al. (Supernova Cosmology Project): Measurements of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999)
Peter, P., Uzan, J.-P.: Primordial Cosmology. Oxford University Press, New York (2009)
Starobinsky, A.A.: Spectrum of relict gravitational radiation and early state of the universe. JETP Lett. 30, 682 (1979)
Starobinsky, A.A.: Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations. Phys. Lett. B 117, 175 (1982)
Straumann, N.: From primordial quantum fluctuations to the anisotropies of the cosmic microwave background radiation. Ann. Phys. (Leipzig) 15, 701 (2006)
Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976)
Will, C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Steinwachs, C.F. (2014). Cosmology. In: Non-minimal Higgs Inflation and Frame Dependence in Cosmology. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01842-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-01842-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01841-6
Online ISBN: 978-3-319-01842-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)