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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 w_Q approaches -1: these models may be reconciled with a large basin of attraction only by requiring a rapid evolution of w_Q at low reshifts, 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 investigate the $H_0$ tension in a range of extended model frameworks beyond the standard $Lambda$CDM without the data from cosmic microwave background (CMB). Specifically, we adopt the data from baryon acoustic oscillation, big bang nucleosynthes
Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dy
The form of the inflationary potential is severely restricted if one requires that it be natural in the technical sense, i.e. terms of unrelated origin are not required to be correlated. We determine the constraints on observables that are implied in
Discrepant measurements of the Universes expansion rate ($H_0$) may signal physics beyond the standard cosmological model. Here I describe two early modified gravity mechanisms that reconcile the value of $H_0$ by increasing the expansion rate in the
Recently, the formation of primordial black holes (PBHs) from the collapse of primordial fluctuations has received much attention. The abundance of PBHs formed during radiation domination is sensitive to the tail of the probability distribution of pr