A Type of Holographic Scalar Field Model and Coincidence Problem

One of the main problems in cosmology is to resolve the problem of accelerating expansion and cosmological coincidence problem of the late universe. Many models, such as the cosmological constant model, the scalar field model, and the holographic model proposed in Einstein’s tensor gravity theory, have solved many problems in explaining these problems. The Brans-Dicke (BD) scalar-tensor theory, proposed by Brans and Dicke in 1961, is a generalization of Einstein’s tensor theory of gravity. In this theory, the scalar field can be combined with gravity, and many scalar field models have been proposed, since the observational constraints of the coupling parameters are not clear. In general formalism for scalar fields, parameterization may be relevant in some sense. For example, parameterization of parameters such as dark matter-dark energy interaction coefficient, equation of state parameter, and holographic constant, which have been proposed to solve the problem of cosmological coincidence problem, has some significance. Therefore, in this paper, we have applied the well-known Jassal-Bagular-Padmanabhann (JBP) parameterization in cosmology to the scalar field to construct a holographic scalar field model, perform cosmological verification, and consider the problem of late cosmic acceleration expansion and cosmological coincidence problem. The model parameters obtained by minimizing the chi-square function have nonzero values, and the current values of the transition red shift, equation of state parameter, deceleration parameter, and coincidence parameter are in good agreement with previous studies. We also confirmed the validity of the model and finally obtained a limit on the rate of change of the gravitational constant.