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We examine homogeneous but anisotropic cosmologies in scalar-tensor gravity theories, including Brans-Dicke gravity. We present a method for deriving solutions for any isotropic perfect fluid with a barotropic equation of state ($pproptorho$) in a spatially flat (Bianchi type~I) cosmology. These models approach an isotropic, general relativistic solution as the expansion becomes dominated by the barotropic fluid. All models that approach general relativity isotropize except for the case of a maximally stiff fluid. For stiff fluid or radiation or in vacuum we are able to give solutions for arbitrary scalar-tensor theories in a number of anisotropic Bianchi and Kantowski-Sachs metrics. We show how this approach can also be used to derive solutions from the low-energy string effective action. We discuss the nature, and possibly avoidance of, the initial singularity where both shear and non-Einstein behavior is important.
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Scalar-tensor theories are frequently only consistent with fifth force constraints in the presence of a screening mechanism, namely in order to suppress an otherwise unacceptably large coupling between the scalar and ordinary matter. Here we investigate precisely which subsets of Horndeski theories do not give rise to and/or require such a screening mechanism. We investigate these subsets in detail, deriving their form and discussing how they are restricted upon imposing additional bounds from the speed of gravitational waves, solar system tests and cosmological observables. Finally, we also identify what subsets of scalar-tensor theories precisely recover the predictions of standard (linearised) $Lambdatext{CDM}$ cosmologies in the quasi-static limit.
We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fre, Sagnotti and Sorin (Nuclear Physics textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state $p^{(m)} = w, rho^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.
The possibility of a connection between dark energy and gravity through a direct coupling in the Lagrangian of the underlying theory has acquired an increasing interest due to the recently discovered capability of the extended quintessence model to encompass the fine-tuning problem of the cosmological constant. The gravity induced R-boost mechanism is indeed responsible for an early, enhanced scalar field dynamics, by virtue of which the residual imprint of a wide set of initial field values is cancelled out. The initial conditions problem is particularly relevant, as the most recent observations indicate that the dark energy equation of state approaches, at the present time, the cosmological constant value, wDE = -1; if confirmed, such observational evidence would cancel the advantage of a standard, minimally coupled scalar field as a Dark Energy candidate instead of the cosmological constant, because of the huge fine tuning it would require. We give here a general classification of the scalar-tensor gravity theories admitting R-boost solutions scaling as a power of the cosmological redshift, outlining those behaving as an attractor for the quintessence field. In particular, we show that all the R-boost solutions with the dark energy density scaling as the relativistic matter or shallower represent attractors. This analysis is exhaustive as for the classification of the couplings which admit R-boost and the subsequent enlargement of the basin of attraction enclosing the initial scalar field values.
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