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 , w _ { DE } = -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 .