Scaling solutions in scalar–tensor cosmologies

Abstract

The possibility of a connection between dark energy and gravity through a direct couplingin the Lagrangian of the underlying theory has acquired an increasing interestdue to the recently discovered capability of the extended quintessence model toencompass 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 virtueof which the residual imprint of a wide set of initial field values is cancelled out. The initialconditions problem is particularly relevant, as the most recent observations indicate that thedark 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 astandard, minimally coupled scalar field as a dark energy candidate instead ofthe cosmological constant, because of the huge fine tuning it would require. Wegive here a general classification of the scalar–tensor gravity theories admittingR-boost solutions scaling as a power of the cosmological redshift, outlining thosebehaving as an attractor for the quintessence field. In particular, we show that all theR-boost solutions with the dark energy density scaling as the relativistic matter or shallower representattractors. This analysis is exhaustive as for the classification of the couplings which admitR-boost and the subsequent enlargement of the basin of attraction enclosing the initial scalarfield values.