On the consequences of a cosmological model with a time-dependent cosmological «constant» and the relationship between Einstein equivalence principle, Mach's principle and dirac's principle

Abstract

Within the framework of a cosmological model with a time-dependent cosmological constant Λ, we examine the evolutionary behaviour of the Universe during the radiation-dominated and matter-dominated eras. The smallness of the cosmological constant and the origin of galaxy formation are explained. For a dust-filled universe withp≃0, the model yields a cosmological solutionk=−1,R∼t. The relationship among Einstein equivalence principle, Mach's principle and Dirac's principle is also elucidated through the time-dependent Λ. It is shown that these principles are compatible, and Mach's principle and Dirac's principle can be viewed as an initial-value condition and a dynamic consequence of Einstein's equations (satisfying Einstein equivalence principle), respectively.