Ya B Zeldovich's ideas and modern Brans – Dicke cosmology

We compare Ya B Zeldovich's ideas about Brans–Dicke theory and Mach's principles, contained in now-classical books, with modern results in this field. Our recent results on the Brans–Dicke cosmology with the cosmological term are presented. The Friedmann–Brans–Dicke equations are written for the flat Universe. The initial conditions for the model are provided by the presently observed Hubble constant, its first time derivative (the deceleration parameter), and matter density. The cosmological scenario with the scale factor not vanishing in the past, corresponding to the absence of the cosmological singularity, is analytically calculated. Instead of the singularity, the scale factor experiences a ‘bounce’ and demonstrates regular behavior at all times. Some ideas related to Mach's principle are also discussed.