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Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$, is constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition, flow properties for generic $1$-dim systems can be analytically obtained in terms of Wigner functions and Wigner currents. For gaussian statistical ensembles, the exact phase-space profile of the quantum fluctuations over the classical trajectories are found, so to interpret them as a suitable Hilbert space state configuration for confronting quantum and classical regimes. In particular, a sort of {\em quantum camouflage} where the stationarity of classical statistical ensembles can be camouflaged by the stationarity of gaussian quantum ensembles is identified. Besides the broadness of the framework worked out in some previous examples, our results provide an encompassing picture of quantum effects on non-linear dynamical systems which can be interpreted as a first step for finding the complete spectrum of non-standard Hamiltonians., Comment: 9 pages. Based on the work presente by by A.E.B. at DICE 2024 Spacetime - Matter - Quantum Mechanics ..., 16th - 20th September 20124, Castiglioncello, Italy

The properties of metric perturbations are determined in the context of an expanding Universe governed by a modified theory of gravity with a non-minimal coupling between curvature and matter. We analyse the dynamics of the 6 components of a general helicity decomposition of the metric and stress-energy perturbations, consisting of scalar, vector and tensor sectors. The tensor polarisations are shown to still propagate luminally, in agreement with recent data from gravitational interferometry experiments, while their magnitude decays with an additional factor sourced by the nonminimal coupling. We show that the production of these modes is associated with a modified quadrupole formula at leading order. The vector perturbations still exhibit no radiative behaviour, although their temporal evolution is found to be modified, with spatial dependence remaining unaffected. We establish that the scalar perturbations can no longer be treated as identical. We investigate the scalar sector by writing the modified model as an equivalent two-field scalar-tensor theory and find the same scalar degrees of freedom as in previous literature. The different sectors are paired with the corresponding polarisation modes, which can be observationally measured by their effects on the relative motion of test particles, thus providing the possibility of testing the modified theory and constraining its parameters., Comment: 34 pages, 3 figures

The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,\,p) = {K}(p) + {V}(q)$ (with $K(p)$ replacing single $p^2$ contributions) is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing non-linear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints., Comment: 28 pages, 4 figures

The study of interactions between dark matter and the Higgs field opens an exciting connection between cosmology and particle physics, since such scenarios can impact the features of dark matter as well as interfering with the spontaneous breaking of the electroweak symmetry. Furthermore, such Higgs-portal models of dark matter should be suitably harmonised with the various epochs of the universe and the phenomenological constraints imposed by collider experiments. At the same time, the prospect of a stochastic gravitational wave background offers a promising new window into the primordial universe, which can complement the insights gained from accelerators. In this study, we examined whether gravitational waves can be generated from a curvature-induced phase transition of a non-minimally coupled dark scalar field with a portal coupling to the Higgs field. The main requirement is that the phase transition is of first order, which can be achieved through the introduction of a cubic term on the scalar potential and the sign change of the curvature scalar. This mechanism was investigated in the context of a dynamical spacetime during the transition from inflation to kination, while also considering the possibility for inducing electroweak symmetry breaking in this manner for a sufficiently low reheating temperature when the Higgs-portal coupling is extremely weak. We considered a large range of inflationary scales and both cases of positive and negative values for the non-minimal coupling, while taking into account the bound imposed by Big Bang Nucleosythesis. The resulting gravitational wave amplitudes are boosted by kination and thus constrain the parameter space of the couplings significantly. Even though the spectra lie at high frequencies for the standard high inflationary scales, there are combinations of parameter space where they could be probed with future experiments., Comment: 28 pages, 6 figures

The presently open problem of the Hubble tension is shown to be removed in the context of a modified theory of gravity with a non-minimal coupling between curvature and matter. By evolving the cosmological parameters that match the cosmic microwave background data until their values from direct late-time measurements, we obtain an agreement between different experimental methods without disrupting their individual validity. These modified gravity models are shown to provide adequate fits for other observational data from recent astrophysical surveys and to reproduce the late-time accelerated expansion of the Universe without the inclusion of a cosmological constant. This compatibility with observations presents further evidence of the versatility of these models in mimicking diverse cosmological phenomena in a unified manner., Comment: 12 pages, 6 figures

In this work, we discuss the de Sitter swampland conjectures in the context of the generalized Chaplygin-inspired inflationary model. We demonstrate that these conjectures can be satisfied, but only in the region of the parameter space far away from the General Relativity limit. The cosmic microwave background data had already been found to restrict the allowed inflationary potentials of this model. Our results impose a further limitation on the possible potentials., Comment: 4 pages, matches published version

We argue that time crystal properties naturally arise from phase-space noncommutative quantum mechanics. In order to exemplify our point we consider the 2-dimensional noncommutative quantum harmonic oscillator and show that it exibihits periodic oscillations that can be identified as time crystals., Comment: 11 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2207.00346