Solving the flatness and quasi-flatness problems in Brans-Dicke cosmologies with a varying light speed

We define the flatness and quasi-flatness problems in cosmological models. We seek solutions to both problems in homogeneous and isotropic Brans-Dicke cosmologies with a varying speed of light. We formulate this theory and find perturbative, non-perturbative and asymptotic solutions using both numerical and analytical methods. For a particular range of variations of the speed of light the flatness problem can be solved. Under other conditions there exists a late-time attractor with a constant value of Omega that is smaller than, but of the order of unity. Thus these theories may solve the quasi-flatness problem, a considerably more challenging problem than the flatness problem. We also discuss the related A and quasi-A problem in these theories. We conclude with an appraisal of the difficulties these theories may face.