FIZIKA B 19 (2010) 4 , 269-282

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Department of Nuclear Engineering, Cheju National University, Ara-dong 1, Jeju 690-756, South Korea
College of Mathematics and Information Sciences, Neijiang Normal University,
Neijiang 641112, Sichuan, China       E-mail address:

Received 4 October 2010;     Revised manuscript received 26 March 2011
Accepted 9 February 2011     Online 6 May 2011

Two of the greatest problems in theoretical physics today are the accelerated expansion of the universe and the singularity problem at the origin of time. This crisis has been attacked head on, but no convincing, well-developed and well-motivated solutions have emerged. While much work in literature has focused on the search for new matter sources that yield accelerating solutions, and to avoid concurrently the initial singularity, more recently complementary approach of examining whether alternative theories of gravity might be responsible for cosmic acceleration and whether the singularity problem may be avoided was developed. The work done in this paper is just a kind of the simple modified gravitational physics to solve both problems simultaneously. In the present work, we analyze all kinematic expressions for a closed but effectively flat universe when the cosmological constant and the matter density decays, respectively, like Λ = C/a and ρ(a)=βG−1(a)a−2/(8π), where C and β are real positive parameters, a(a) is the scale factor and G is the gravitational coupling constant which is assumed to depend on the scale factor as predicted by several models. It is found for some constrained parameters that the universe is closed but effectively flat, free from the initial singularity, dominated by dark energy and is accelerated in time. Expressions for some observable quantities were derived and are found to be compatible with available recent astrophysical findings.

PACS numbers: 04.50.+h, 11.25.Yb, 98.80.Es, 95.36.+x
UDC 524.83

Keywords: higher-dimensional cosmology, decaying lambda, decaying density of matter, non-singular cosmology, dark energy

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