Universe evolution in the Einstein frame of Jordan–Brans–Dicke theory

Cosmological models of the Universe in the framework of Jordan-Brans-Dicke theory in the Einstein frame in the case of scalar field domination as well as in the presence of cosmological constant $\Lambda$ with matter, which is described by barometric equation of state $P=\alpha\varepsilon$ ($P$ is the pressure, $\varepsilon$ is the energy density of matter), are considered. The analysis of obtained results in the light of observational data are done. It is shown that the contribution of the scalar field and $\Lambda$-member ($\Lambda>0$ ) in the case of $q=-1/2$ ($q$ is the "decelerating" parameter) compensate each other. In addition, the situation leads to Einstein’s theory.