William Giarè

We investigate whether early- and late-time dark energy could arise from a single scalar field. Adopting a bottom-up perspective, we first identify the sequence of dynamical regimes that any unified scenario must traverse to account for both an early dark energy phase relevant for pre-recombination solutions of the Hubble tension and the late-time acceleration of the Universe. We derive the corresponding requirements on the scalar energy density and equation of state. We then adopt a complementary top-down perspective and translate these requirements into constraints on the phase-space structure of minimally coupled scalar fields with tracking-like dynamics. We show that satisfying all requirements necessitates a potential with three distinct slopes, arranged in a steep-steeper-shallow hierarchy. This conclusion remains unchanged in the presence of conformal couplings to dark matter. These results place strong constraints on attempts to construct unified models of early- and late-time dark energy. We discuss implications for model-building.

We revisit the cosmic microwave background (CMB) constraints on the spatial curvature of the Universe, assessing how they change when the curvature parameter and the primordial inflationary scalar spectrum are treated consistently within theoretically motivated frameworks. Instead of relying on the phenomenological parametrization commonly used to capture curvature effects at the largest scales, we present a case study based on closed quadratic inflation, where the primordial spectrum is derived in full generality and in a gauge-invariant manner. Within this framework, we analyze both the public release 3 (PR3) and PR4 Planck CMB likelihoods and find that the constraints on Ω K shift toward spatial flatness. In the preference for Ω K < 0 decreases from ≳ 3.5 σ to ∼ 2.5 σ , while in it reduces further to ∼ 2 σ . At large angular scales ( ℓ < 10 ), our model explains the low- ℓ power suppression anomaly, notably improving the fit to the quadrupole. However, the reduced preference for highly negative values of Ω K only partially accounts for the lensing anomaly at high multipoles, worsening the fit to the spectrum at small scales. By contrast, in the PR4 spectrum, where the lensing anomaly is less pronounced, the model yields an overall improvement. Our analysis highlights a key conceptual point: closed-inflation models tie the curvature parameter to the inflationary dynamics and the primordial spectrum, enforcing consistency conditions that do not necessarily allow for the large deviations from flatness seen in phenomenological parametrizations. In the case of quadratic inflation, these restrictions reduce the apparent evidence for negative curvature reported by earlier analyses, while allowing for a mildly closed geometry.

We introduce a novel cosmographic framework to trace the late-time kinematics of the Universe without assuming any underlying dynamics. The method relies on generalized Padé (2, 1) expansions around arbitrary pivot redshifts, which, compared to state-of-the-art calculations, reduce truncation errors by up to two orders of magnitude at high redshift and yield more precise constraints by defining cosmographic parameters exactly where the data lie. This avoids extrapolations, mitigates degeneracies, and enables a clean disentangling of their effects. Using the latest low-redshift datasets, we center the generalized expansion in multiple bins across z ∈ [0, 1] and obtain precise constraints on the redshift evolution of cosmographic parameters. We find that all key parameters deviate from their ΛCDM predictions in a redshift-dependent way that can be naturally explained within dynamical dark energy scenarios. The deceleration parameter q ( z ) follows a redshift evolution consistent with the Chevallier–Polarski–Linder (CPL) parameterization, while the generalized Om ( z ) diagnostic shows deviations of up to ∼4 σ from the constant ΛCDM expectation, closely matching the CPL predictions. Taken together, these results point to footprints of dynamical dark energy in the kinematics of the Universe at z ≲ 1.

Assuming a minimal Λ cold dark matter ( Λ CDM ) cosmology with three massive neutrinos, the joint analysis of Planck cosmic microwave background data, DESI baryon acoustic oscillations, and distance moduli measurements of type Ia supernovae from the Pantheon + sample sets an upper bound on the total neutrino mass, ∑ m ν ≲ 0.06 – 0.07 eV , that lies barely above the lower limit from oscillation experiments. These constraints are mainly driven by mild differences in the inferred values of the matter density parameter across different probes that can be alleviated by introducing additional background-level degrees of freedom (e.g., by dynamical dark energy models). However, in this work, we explore an alternative possibility. Since both Ω m and massive neutrinos critically influence the growth of cosmic structures, we test whether the neutrino mass tension may originate from the way matter clusters, rather than from a breakdown of the Λ CDM expansion history. To this end, we introduce the growth index γ , which characterizes the rate at which matter perturbations grow. Deviations from the standard Λ CDM value ( γ ≃ 0.55 ) can capture a broad class of models, including nonminimal dark sector physics and modified gravity. We show that allowing γ to vary significantly relaxes the neutrino mass bounds to ∑ m ν ≲ 0.13 – 0.2 eV , removing any tension with terrestrial constraints without altering the inferred value of Ω m . However, this comes at the cost of departing from standard growth predictions: to have ∑ m ν ≳ 0.06 eV , one needs γ > 0.55 , and we find a consistent preference for γ > 0.55 at the level of ∼ 2 σ . This preference increases to ∼ 2.5 – 3 σ when a physically motivated prior ∑ m ν ≥ 0.06 eV from oscillation experiments is imposed.

In a broad class of cosmological models where spacetime is described by a pseudo-Riemannian manifold, photons propagate along null geodesics, and their number is conserved, upcoming gravitational wave (GW) observations can be combined with measurements of the baryon acoustic oscillation (BAO) angular scale to provide model-independent estimates of the sound horizon at the baryon drag epoch. By focusing on the accuracy expected from forthcoming surveys such as the Laser Interferometer Space Antenna GW standard sirens and dark energy spectroscopic instrument (DESI) or Euclid angular BAO measurements, we forecast a relative precision of σ r d / r d ∼ 1.5 % within the redshift range z ≲ 1 . This approach will offer a unique model-independent measure of a fundamental scale characterizing the early universe, which is competitive with model-dependent values inferred within specific theoretical frameworks. These measurements can serve as a consistency test for Λ CDM , potentially clarifying the nature of the Hubble tension and confirming or ruling out new physics prior to recombination with a statistical significance of ∼ 4 σ .