Andronikos Paliathanasis

We present a novel physically approach for deriving analytic solutions of the gravitational field equations in cosmological models. Focusing on a class of constrained dynamical systems that naturally arise in gravity, in particular within the minisuperspace formulation of cosmology, we demonstrate that their dynamics can be mapped, via a specific class of canonical transformations, to those of a linear system. This linearization has a clear geometric interpretation, the evolution of the gravitational is reformulated as geodesic motion in an effective extended minisuperspace geometry. For the construction we employ the Jacobi-Maupertius principle and the Eisenhart–Duval lift. This framework offers new information into the integrability of cosmological models and the derivation of analytic solutions.

Gravitational physics now connects precise measurements of cosmic expansion and structure with observations of compact objects, while its foundational questions remain open. General relativity and the standard cosmological model provide exceptionally productive baselines, yet the physical nature of the dark sector, the status of apparent data tensions, the fate of singularities and the relation between gravity and quantum theory remain under investigation. This editorial introduction situates the fourteen research contributions to SAGS2025 within that landscape. It explains the volume’s progression from cosmological inference and competing expansion histories, through mathematical cosmology and modified gravity, to strong-field systems and proposals for quantum spacetime and unification. The chapters share problems and methods rather than a single theoretical conclusion. Throughout, we distinguish well-tested frameworks, observational indications, conditional model results and exploratory hypotheses. We close by identifying the standards by which connections across the volume should be judged: internal consistency, controlled limits, identifiable observables and reproducible comparison with data.

Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In the symmetric teleparallel formulation, and under a Friedmann-Lemaître-Robertson-Walker background, three distinct branches of the connection arise, leading to three different cosmological scenarios. We perform a detailed dynamical analysis of these models by examining the phase space and determining the asymptotic cosmological solutions. The analysis reveals a rich hierarchy of critical points, including matter-dominated epochs, kinetic-dominated stiff-fluid regimes, and steep potential-dominated de Sitter solutions, along with asymptotic trajectories that approach Big Crunch or Big Rip singularities, as well as transient, unstable matter-dominated eras. The stability of the steep potential-dominated de Sitter points is further studied using Center Manifold Theory, showing that, under specific parametric conditions, the model can provide a unified description of both the early and late-time acceleration phases of the universe.

In this work we introduce exact cosmological solutions in General Relativity in (3+1) dimensions which take into account both the usual fluid component as well as a superfluid component describing superfluid Pionic vortices. Such superfluid vortices are source of inhomogeneities which can be treated exactly, no perturbation theory is required. These analytic solutions are relevant to obtain a non-perturbative description of inhomogeneities in cosmology. We discuss the peculiar effects of these hadronic inhomogeneities on the propagation of electromagnetic fields on such cosmological backgrounds analyzing possible observable effects. Finally, the properties that the effective superfluid satisfy for such solutions to exist are discussed, together with possible extensions of this family of solutions.

We investigate a non‐minimally coupled scalar field theory within the framework of scalar–tensor non‐metricity gravity, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with Hubble‐normalized variables, we reformulate the field equations into an autonomous system and analyze the resulting critical points. Four distinct cases, determined by the scalar coupling and potential functions, are studied in detail. For each case, we identify the existence and stability of equilibrium points, classify their cosmological behavior, and compute key observables such as the deceleration parameter and effective equation of state. Our results reveal that the theory admits matter‐dominated eras, parameter‐dependent saddle solutions, and stable de Sitter attractors capable of driving late‐time cosmic acceleration. The additional scalar degree of freedom introduced by the non‐coincident gauge plays a crucial role in determining the system's dynamics and viability. These findings emphasize the potential of scalar–tensor non‐metricity gravity as a robust extension of general relativity and motivate further confrontation of the model with observational data.

The Kasner spacetimes are exact solutions that are self‐similar and of significant interest because they can describe the dynamic evolution of kinematic variables near the singularity of the Mixmaster universe. The chaotic behavior of the Mixmaster universe is related to the Kasner relations. This study investigates Kasner and Kasner‐like solutions in symmetric teleparallel ‐gravity. We consider three families of connections for the spatially flat Friedmann–Lemaître–Robertson–Walker. We found that Kasner‐like solutions are present in the theory when the nonmetricity scalar vanishes. Kasner‐like relations are introduced only for the field equations of the connection defined in the coincident gauge. Finally, we perform a detailed phase‐space analysis to understand the dynamics of ‐gravity in the evolution of anisotropies and the effects of different connections on this evolution.

In light of recent cosmological observations, we examine a generalized Chaplygin gas model with a redshift‐dependent exponent as a framework for describing the dark energy and dark matter content of the Universe. Specifically, we treat this fluid as a single unified component and test it against late‐time background observational data. We employ Type Ia supernova data, cosmic chronometers, and baryon acoustic oscillations from the second data release of the Dark Energy Spectroscopic Instrument. We perform a Bayesian analysis for parameter estimation and compare the model with . We find that the generalized Chaplygin gas provides systematically higher values of the combined likelihood; nevertheless, once the larger number of free parameters is taken into account, both the Bayesian evidence and the Akaike Information Criterion suggest that the model is statistically indistinguishable from .

We investigate the linearization of the 1+1 Poisson equation u ,xx + u ,yy + Ω (x, y) u -3 = 0, through equivalent systems, where u -3 demonstrates the Ermakov-Pinney potential. We introduce a maximally symmetric system of Laplace equations that describes the solutions of our equation for an arbitrary potential Ω (x, y). We investigate the admitted Lie symmetries and Noetherian conservation laws for the two systems. This provides us with important information regarding the nature and origin of the Lie symmetries. Our results can be extended to the case of the 1 + n Poisson equation and on the Schrödinger equation.