Brans-Dicke theory, or sometimes called Jordan-Brans-Dicke theory, is a competitor to Albert Einstein's general theory of relativity.
Brans-Dicke theory is a scalar-tensor theory of gravity, where the gravitational interaction is mediated by a scalar field, as well as the tensor field of general relativity.
Robert H. Dicke
Carl H. Brans
Robert Dicke and Carl Brans in 1961 give us this theory, building on the 1959 work of Pascual Jordan.
At the present moment, both general relativity and Brans-Dicke theory are in agreement with observation.
Brans-Dicke theory, however, represents a minority viewpoint in physics.
Both Brans-Dicke theory and general relativity are examples of a class of relativistic classical theories of gravitation, known as 'metric theories.' In both these theories, spacetime is equipped with a metric tensor, and the gravitational field is represented by the Riemannian curvature tensor, which is actually determined by the metric tensor.
All metric theories satisfy the Equivalence principle of Albert Einstein. Thus, all the laws of physics known in special relativity, are valid in local Lorentz frames. Thus, all metric theories exhibit the gravitational redshift effect.