Dynamics of cosmological perturbations in modified Brans-Dicke cosmology with matter-scalar field interaction

In this work we focus on a novel completion of the well-known Brans-Dicke theory that introduces an interaction between the dark energy and dark matter sectors, known as complete Brans-Dicke (CBD) theory. We obtain viable cosmological accelerating solutions that fit Supernovae observations with great precision without any scalar potential $V(\phi)$. We use these solutions to explore the impact of the CBD theory on the large scale structure by studying the dynamics of its linear perturbations. We observe a growing behavior of the lensing potential $\Phi_{+}$ at late-times, while the growth rate is actually suppressed relatively to $\Lambda$CDM, which allows the CBD theory to provide a competitive fit to current RSD measurements of $f\sigma_{8}$. However, we also observe that the theory exhibits a pathological change of sign in the effective gravitational constant concerning the perturbations on sub-horizon scales that could pose a challenge to its validity.