The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time

Author(s)
Xiaochun Mei

ABSTRACT

The true meaning of the constant in the Robertson-Walker metric is discussed when the scalar factor s the function of time. By strict calculation based on the Riemannian geometry, it is proved that the spatial curvature of the R-W metric is K=(κ-R^{2})/R^{2} . The result indicates that the R-W metric has no constant curvature when R(t)≠0 and κ is not spatial curvature factor. We can only consider κ as an adjustable parameter with κ≠0 in general situations. The result is completely different from the current understanding which is based on the precondition that the scalar factor R(t) is fixed. Due to this result, many conclusions in the current cosmology such as the densities of dark material and dark energy should be re-estimated. In this way, we may overcome the current puzzling situation of cosmology thoroughly.

The true meaning of the constant in the Robertson-Walker metric is discussed when the scalar factor s the function of time. By strict calculation based on the Riemannian geometry, it is proved that the spatial curvature of the R-W metric is K=(κ-R

KEYWORDS

Cosmology, General Relativity, R-W Metric, Riemannian Geometry, Space-Time Curvature, Dark Material, Dark Energy, Hubble Constant

Cosmology, General Relativity, R-W Metric, Riemannian Geometry, Space-Time Curvature, Dark Material, Dark Energy, Hubble Constant

Cite this paper

nullX. Mei, "The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time,"*International Journal of Astronomy and Astrophysics*, Vol. 1 No. 4, 2011, pp. 177-182. doi: 10.4236/ijaa.2011.14023.

nullX. Mei, "The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time,"

References

[1] S. Weinberg, “Gravitation and Cosmology,” Science Pub- lishing Company, 1984, p. 441.

[2] S. Zhiming, “Tensor in Physics,” Beijing Normal University Publishing Company, Beijing, 1985, p.180.

[3] P. de Bernardis, et al., “A High Spatial Resolution Analy- sis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data,” Nature, Vol. 404, 2000, pp. 955-959. doi:10.1038/35010035

[4] C. L. Merriment, et al., “Wilkinson Microwave Anisot- ropy Probe (WMAP), Observations: Temperature-Pola- rization Correlation, Astrophysical Journal Supplement Series, Vol. 148, No. 1, 2003, pp. 195-211.

[5] J. H. Oort, “In La Struccture et Evolution de Univers, Institute International de Physique Solvay,” R. Stoops, Brussles, 1958, p. 58.

[6] R. G. Carlberg, et al., “Galaxy Cluster Virial Masses and Omega,” Astrophysical Journal, 1996, Vol. 462, pp. 32- 49. doi:10.1086/177125

[7] D. N. Schramm, M. S. Furner, “Big-Bang Nucleosynthesis Enters the Precision Era,” Reviews of Modern Physics, Vol. 70, No. 1, 1998, pp. 303-318. doi:10.1103/RevModPhys.70.303

[1] S. Weinberg, “Gravitation and Cosmology,” Science Pub- lishing Company, 1984, p. 441.

[2] S. Zhiming, “Tensor in Physics,” Beijing Normal University Publishing Company, Beijing, 1985, p.180.

[3] P. de Bernardis, et al., “A High Spatial Resolution Analy- sis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data,” Nature, Vol. 404, 2000, pp. 955-959. doi:10.1038/35010035

[4] C. L. Merriment, et al., “Wilkinson Microwave Anisot- ropy Probe (WMAP), Observations: Temperature-Pola- rization Correlation, Astrophysical Journal Supplement Series, Vol. 148, No. 1, 2003, pp. 195-211.

[5] J. H. Oort, “In La Struccture et Evolution de Univers, Institute International de Physique Solvay,” R. Stoops, Brussles, 1958, p. 58.

[6] R. G. Carlberg, et al., “Galaxy Cluster Virial Masses and Omega,” Astrophysical Journal, 1996, Vol. 462, pp. 32- 49. doi:10.1086/177125

[7] D. N. Schramm, M. S. Furner, “Big-Bang Nucleosynthesis Enters the Precision Era,” Reviews of Modern Physics, Vol. 70, No. 1, 1998, pp. 303-318. doi:10.1103/RevModPhys.70.303