Particle Horizons in Cosmology

K. Purnachandra Rao

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia.

DOI: 10.4236/jmp.2013.49162                

Abstract

The importance of investigating particle horizons in order to interpret a cosmological solution of Einstein’s field equations has been described. We have presented the formula and studied the particle horizons in some of the cosmological models presented in our earlier papers. It is well known that the Friedman-Robertson-Walker (F-R-W) models, the energy density of the free gravitational field denoted by ε, equivalently denoted by MacCallum parameter ξ, vanishes but the particle horizons exist and thus the former has no bearing on the latter. However, we have shown in our models presented herein that ε is related with particle horizons. Further, it is shown that as ε grows, the segment of the corresponding particle horizon decreases and thus the radius of the corresponding visible universe decreases.

Keywords

In Homogeneity; Anisotropy; Cosmology; Particle Horizon

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. C. Tolman, Proceedings of the National Academy of Sciences of USA, Vol. 20, 1934, p. 69.
[2]	G. C. Omer, The Astrophysical Journal, Vol. 109, 1949, p. 164.
[3]	H. Bondi, Monthly Notices of the Royal Astronomical Society, Vol. 107, 1947, p. 410.
[4]	J. Krishna Rao, Current Science, Vol. 35, 1966, p. 389.
[5]	J. Krishna Rao, General Relativity and Gravitation, Vol. 2, 1971, pp. 385-386. http://dx.doi.org/10.1007/BF00758157
[6]	J. Krishna Rao, Journal of Physics (London), Vol. A5, 1972, p. 479.
[7]	J. Krishna Rao, General Relativity and Gravitation, Vol. 2, 1973, p. 351. doi:10.1007/BF00771004
[8]	J. Krishna Rao, Pramana: Journal of Physics, Vol. 34, 1990, p. 423.
[9]	J. Krishna Rao, Journal of the Institute of Mathematics, Vol. 51, 1995, p. 57.
[10]	K. Purnachandra Rao, Unpublished Ph.D. Thesis, Bhavnagar University, Bhavnagar, 1997.
[11]	K. Purnachandra Rao, et al., Mathematics Today, Vol. 16, 1998, p. 25.
[12]	K. Purnachandra Rao, Mathematics Today, Vol. 17, 1999, p. 29.
[13]	K. Purnachandra Rao, Mathematics Today, Vol. 21, 2005, p. 31.
[14]	K. Purnachandra Rao, Mathematics Today, Vol. 24, 2008, p. 17.
[15]	K. Purnachandra Rao, Mathematics Today, Vol. 25, 2009, p. 34.
[16]	K. Purnachandra Rao, Mathematics Today, Vol. 27, 2011, p. 54.
[17]	M. A. H. MacCallum, In: V. D. Sabbata, Ed., The Origin and Evolution of Galaxies, World Scientific Pub. Co., 1982.
[18]	M. A. H. MacCallum, In: B. R. Iyer, A. Kembhavi, J. V. Narliker and C. V. Vishveshwara, Eds., Highlights in Gravitation and Cosmology, University Press, Cambridge, 1988.
[19]	A. K. Raychaudhuri, Physical Review, Vol. 98, 1955, pp. 1123-1126. doi:10.1103/PhysRev.98.1123
[20]	W. Rindler, Monthly Notices of the Royal Astronomical Society, Vol. 116, 1956, p. 662.
[21]	W. Rindler, “Essential Relativity: Special, General and Cosmological,” Springer-Verlag, 1977.