Research ArticleOpen AccessGoogle Scholar indexed
Emergence of Friedmann Equation of Cosmology of a Flat Universe from the Time-Energy Uncertainty Principle
Department of Engineering Sciences, Uppsala University, Uppsala, Sweden
Karolinska Institute, Stockholm, Sweden
école polytechnique fédérale de Lausanne, Lausanne, Switzerland
- 1 Department of Engineering Sciences, Uppsala University, Uppsala, Sweden
- 2 Karolinska Institute, Stockholm, Sweden
- 3 école polytechnique fédérale de Lausanne, Lausanne, Switzerland
Journal of Modern Physics·Volume 08 (2017)·Pages 1979–1987·Published 9 November 2017·DOI10.4236/jmp.2017.812119
Copy link · social · email
Abstract
Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mechanics. In this paper, it is shown that the Friedmann equation pertinent to a homogeneous, isotropic and flat universe can also be obtained as a consequence of the energy balance in the expanding universe between the positive energy associated with vacuum and matter, and the negative gravitational energy. The results obtained here is a clear consequence of the fact that the surface area of the Hubble sphere is proportional to the total amount of information contained within it.
KeywordsFriedmann EquationExpansion of the UniverseVacuum EnergyDark EnergyTime-Energy Uncertainty PrincipleHolographic PrincipleHubble Sphere
- Hubble, E.P. (1929) Proceedings of the National Academy of Sciences of the United States of America, 15, 168. https://doi.org/10.1073/pnas.15.3.168
- Dodelson, S. (2003) Modern Cosmology. Academic Press, London.
- Bergström, L. and Goobar, A. (1999) Cosmology and Particle Physics. Wiley International, New York.
- Melia, F. (2007) Monthly Notices of the Royal Astronomical Society, 382, 1917-1921. https://doi.org/10.1111/j.1365-2966.2007.12499.x
- Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford.
- Friedmann, A. (1922) Zeitschrift für Physik, 10, 377-386. https://doi.org/10.1007/BF01332580
- Riess, A.G., et al. (1998) The Astronomical Journal, 116, 1009-1038. https://doi.org/10.1086/300499
- Perlmutter, S., et al. (1999) The Astronomical Journal, 517, 565-586. https://doi.org/10.1086/307221
- Cooray, V., Cooray, G. and Rachidi, F. An Alternative Approach to Estimate the Vacuum Energy Density of Free Space. https://www.preprints.org/manuscript/201707.0048/v1
- Misner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation. W.H. Freeman and Company, New York, USA.
- Hawking, S. (2002) The Theory of Everything. New Millennium, London.
- Tryon, E.P. (1973) Nature, 246, 396-397. https://doi.org/10.1038/246396a0
- Pasachoff, J.M. and Filippenko, A. (2001) The Cosmos: Astronomy in the New Millennium. Harcourt College Publishers, Texas.
- Berman, M.S. (2009) International Journal of Theoretical Physics, 48, 3278-3286. https://doi.org/10.1007/s10773-009-0125-8
- Cooperstock, F.I. and Israelit, M. (1995) Foundations of Physics, 25, 631-635. https://doi.org/10.1007/BF02059009
- Wichmann, E.H. (1971) Quantum Physics, Berkeley Physics Course, Volume 4. McGraw-Hill, New York. https://en.wikipedia.org/wiki/Scale_factor_(cosmology)
- Riess, A., et al. (2005) The Astrophysical Journal, 627, 579. https://doi.org/10.1086/430497
- Sandage, A., et al. (2006) The Astrophysical Journal, 653, 843. https://doi.org/10.1086/508853
- Komatsu, E., et al. (2011) The Astrophysical Journal Supplement Series, 192, 18. https://doi.org/10.1088/0067-0049/192/2/18