Born-Infeld gravity with a Brans-Dicke scalar
AbstractRecently proposed Born-Infeld (BI) theories of gravity assume a constant BI parameter (κ). However, no clear consensus exists on the sign and value of κ. Recalling the Brans-Dicke (BD) approach, where a scalar field was used to generate the gravitational constant G, we suggest an extension of Born-Infeld gravity with a similar Brans-Dicke flavor. Thus, a new action, with κ elevated to a spacetime dependent real scalar field, is proposed. We illustrate this new theory in a cosmological setting with pressureless dust and radiation as matter. Assuming a functional form of κ(t), we numerically obtain the scale factor evolution and other details of the background cosmology. It is known that BI gravity differs from general relativity (GR) in the strong-field regime but reduces to GR for intermediate and weak fields. Our studies in cosmology demonstrate how, with this new, scalar-tensor BI gravity, deviations from GR, as well as usual BI gravity, may arise in the weak-field regime too. For example, we note a late-time acceleration without any dark energy contribution. Apart from such qualitative differences, we note that fixing the sign and value of κ is no longer a necessity in this theory, though the origin of the BD scalar does remain an open question.