Structure formation with scalar-tensor gravitational theories

Abstract

We study the evolution of linear density perturbations in a cosmological background described by scalar-tensor theories (STT) of gravity. The evolution of the density contrast δ is obtained using the Jeans formalism for an expanding Universe. Three classes of such theories are investigated: Brans-Dicke (BD) theory, which is the simplest possible STT: dynamical Λ theory, in which the function Λ([straight phi]) plays the role of a decaying cosmological constant; and a varying-ω theory, where the Brans-Dicke coupling function is no longer a constant. In general, theories with growing fluctuations admit, faster growth that, in conventional general relativity which may, in turn, allow for structure formation at, earlier times. However, there are solutions where growth is exponential, leading to conflicting ages for the Universe. There are also classes of theories with decaying and/or oscillatory modes which are incompatible with the paradigm of structure formation. The evolution of δ depends on ω, and this is shown to constrain the allowed values of the coupling function. We also find a possible connection between the ansatz a [straight phi] [superscript n] = constant (where a is the cosmic scale factor and [straight phi] is the scalar field of STT) and the weak field limit of BD theory.