Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

Sanjay Oli

doi:10.1155/2014/874739

Abstract

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

Highlights

The observational analysis of High-Redshift Type Ia Supernova and Supernova Cosmological Project [1,2,3,4,5] provided a wealth of information about our universe
The field of cosmology has been highly enriched by the Kaluza-Klein theory [7, 8], in which they have shown that gravitation and electromagnetism could be unified in a single geometrical structure
Chodos and Detweiler obtained a higher-dimensional cosmological model in which an extra dimension contracts and indicates that this contraction of extra dimension is a consequence of cosmological evolution

Summary

Introduction

The observational analysis of High-Redshift Type Ia Supernova and Supernova Cosmological Project [1,2,3,4,5] provided a wealth of information about our universe. A number of authors [12,13,14,15,16,17,18,19,20,21,22] obtained the solutions of Einstein’s field equations for higherdimensional space-times containing a variety of matter fields In their analysis, some authors have shown that there is an expansion of the four-dimensional space-times while the fifth dimension contracts or remains constant. A limited number of authors studied cosmological models in higher-dimensional space-time with variable gravitational constant “G” and cosmological constant “Λ” [25,26,27,28,29]. We solve Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ

Einstein’s Field Equations for Kaluza-Klein Space-Times

Solutions of Field Equations

Conclusion