Universe

Although the standard cosmological model successfully describes most current observational data, it faces several theoretical and observational challenges that motivate the exploration of alternative frameworks. In this work, we investigate a class of geometric cosmology models (GC) obtained by adding an infinite tower of higher-order curvature invariants to the Einstein–Hilbert action. Focusing on an exponential ansatz for the characteristic function entering the modified Friedmann equations, we derive the late-time background evolution for three families of solutions within this framework, named as (i) GILA, (ii) GR-deformation, and (iii) non-GR contribution. These models are confronted with recent Cosmic Chronometer and Type Ia supernova data, as well as age estimates of the oldest globular clusters—a constraint frequently overlooked in the literature. The stiffness of the equations in certain regions of parameter space, together with technical difficulties arising from the inclusion of the globular cluster bound, motivates the development of a dedicated methodology as an alternative to standard Markov Chain Monte Carlo techniques. Our results show that two entire families of GC models (non-GR contribution and GR-deformation) are ruled out by the data, whereas some families within the GILA model can successfully account for all data sets. For these models, meaningful constraints on their free parameters can be derived from the statistical analysis. Nevertheless, model comparison criteria reveal a preference in the data for $\Lambda$CDM over the GILA models examined here. Although none of the proposed models provides a preferred alternative to $\Lambda$CDM given the specific characteristic function considered here, this work establishes a clear methodology for testing alternative cosmological models, including the globular cluster constraint, and indicates the way for future research of GILA models with alternative choices of the characteristic function.

We explore a phenomenological extension of the Polyakov–Nambu–Jona-Lasinio (PNJL) model by introducing a curvature-sensitive effective contribution to the Polyakov-loop potential, motivated by the hypothesis that the non-perturbative QCD vacuum in the confined phase may retain a residual sensitivity to cosmic expansion. In a spatially flat FLRW background, this modification reduces to a term proportional to $\alpha {(H/H_0)}^{d}f(\Phi ,{\Phi }^{*})$, which naturally vanishes in the deconfined regime and behaves as an effective dynamical vacuum component at late times, without invoking a fundamental cosmological constant. The construction provides an effective thermodynamic description of the QCD sector within an adiabatic framework and introduces a minimal phenomenological extension characterized by the exponent d and the amplitude parameter $\alpha$. We analyze the cosmological implications at the background level and compare the model with low-redshift observations, including cosmic chronometers, Type Ia supernovae, HII galaxies, and quasars. Using Bayesian Monte Carlo techniques, we constrain the model parameters and compare its performance with the ΛCDM. Our results indicate that the modified PNJL cosmology provides a statistically competitive fit to current data while allowing small departures from the ΛCDM within observational uncertainties. We also investigate the impact of the coupling on the QCD phase diagram and the critical end point. The framework offers a tractable effective approach to connect confinement physics with late-time cosmology and suggests directions for further theoretical development in QCD under curved backgrounds.

We investigate the impact of ultrastrong magnetic fields on the structure of neutron stars within a density-dependent relativistic mean-field framework (DDME2). In the first case, we incorporate a magnetic field framework through Landau quantization of charged particles, yielding anisotropic pressure contributions and showing that field-induced stiffening increases stellar radii, maximum masses, and tidal deformabilities. To capture anisotropic stresses and geometric distortions, we employ axisymmetric equilibrium configurations computed with the XNS 4.0 code under the extended conformally flat condition. For magnetic field strengths up to $4.5\times {10}^{17}$ G, we analyze purely poloidal and toroidal geometries across a representative mass range (1.2–2.0 $M_{\odot }$). Axisymmetric models reveal that purely toroidal fields induce prolate deformations reaching $|\overline{e}| \approx 0.67$ for a 1.2 $M_{\odot }$ star, while purely poloidal fields drive oblate deformations with $\overline{e}\approx 0.24$, both diminishing with increasing stellar mass as greater gravitational binding resists magnetic reshaping. These macroscopic effects, combined with microphysical stiffening, have direct implications for gravitational-wave emission and systematic biases in radius measurements. Our study provides a systematic mapping between magnetic field strength, topology, and dense-matter stiffness, offering constraints relevant to multimessenger observations of magnetized neutron stars.