Flat Friedmann-Lemaitre-Robertson-Walker Cosmological Model with Time-Dependent Cosmological Constant in Brans-Dicke Theory of Gravity

Abstract

Recently, there has been much interest in investigating outstanding problems of cosmology with modified theories of gravity. The Brans-Dicke theory of gravity is one such theory developed by Brans and Dicke absorbing Mach’s principle into the General Theory of Relativity. In Brans-Dicke theory, gravity couples with a time-dependent scalar field ϕ through a coupling parameter ω. This theory reduces to the General Theory of Relativity if the scalar field ϕ is constant and the coupling parameter ω →∞. In this paper, we consider a flat Friedmann-Lemaıtre-Robertson-Walker (FLRW) universe with a time-dependent cosmological constant in Brans-Dicke theory of gravity. Exact solutions of the field equations are obtained by using a power law relation between the scale factor and the Brans-Dicke scalar field ϕ and by taking the Hubble parameter H to be a hyperbolic function of the cosmic time t. We study the cosmological dynamics of our model by graphically representing some important cosmological parameters such as the deceleration parameter, energy density parameter, equation of state parameter, jerk parameter, snap parameter, lerk parameter etc. The statefinder diagnostic pair of the model is also obtained and the validity of the four energy conditions, viz. the Strong energy condition (SEC), Weak energy condition (WEC), Dominant energy condition (DEC) and Null energy condition (NEC), is examined. We find that the universe corresponding to our model is expanding throughout its evolution and exhibits late time cosmic acceleration, which is in agreement with the current observational data.

Keywords

• Brans-Dicke theory
• Friedmann-Lemaˆıtre-Robertson-Walker universe
• Cosmological constant
• Hubble parameter
• Deceleration parameter