ApproachingΛwithout fine-tuning

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Abstract
We address the fine-tuning problem of dark energy cosmologies which arises when the dark energy density needs to initially lie in a narrow range in order for its present value to be consistent with observations. As recently noticed, this problem becomes particularly severe in canonical quintessence scenarios, when trying to reproduce the behavior of a cosmological constant, i.e., when the dark energy equation of state wQ approaches -1: these models may be reconciled with a large basin of attraction only by requiring a rapid evolution of wQ at low redshifts, which is in conflict with the most recent estimates from type Ia Supernovae discovered by Hubble space telescope. Next, we focus on scalar-tensor theories of gravity, discussing the implications of a coupling between the quintessence scalar field and the Ricci scalar (“extended quintessence”). We show that, even if the equation of state today is very close to -1, by virtue of the scalar-tensor coupling the quintessence trajectories still possess the attractive feature which allows to reach the present level of cosmic acceleration starting by a set of initial conditions which covers tens of orders of magnitude; this effect, entirely of gravitational origin, represents a new important consequence of the possible coupling between dark energy and gravity. We illustrate this effect in typical extended quintessence scenarios