Abstract
We study the cosmological evolution of an induced gravity model with a self-interacting scalar field σ and in the presence of matter and radiation. Such model leads to Einstein gravity plus a cosmological constant as a stable attractor among homogeneous cosmologies and is therefore a viable dark-energy (DE) model for a wide range of scalar field initial conditions and values for its positive γ coupling to the Ricci curvature γσ2R.
Highlights
Several years ago a model for a varying gravitational coupling was introduced by Brans and Dicke [1]
The model has a stable attractor towards Einstein Gravity (EG) plus Λ and can be very similar to the ΛCDM model for the homogeneous mode, on taking into account the Solar system constraints quoted in [6, 7, 8]
Interacting for the equivalent Brans-Dicke model) the model has an attractor towards EG plus Λ, very differently from the case of a massless scalar - i.e. λ = 0, for which there is no mechanism of attraction towards EG
Summary
Several years ago a model for a varying gravitational coupling was introduced by Brans and Dicke [1]. In order to reduce such a strong time dependence in a cosmological setting, while retaining the Brans-Dicke results in the weak field limit, several years ago a simple model for induced gravity [2, 3] involving a scalar field σ and a quartic λσ4/4 potential was introduced. This model was globally scale invariant (that is did not include any dimensional parameter) and the spontaneous breaking of scale invariance in such a context led to both the gravitational constant and inflation, through a nonzero cosmological constant [4]. In an EG framework quadratic or quartic potentials for canonical scalar fields are consistent with DE only with
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