A Roadmap for Vector Dark Energy Models through Gravitational Waves

• Gabriel Gomez (Universidad Mayor)

The stochastic gravitational-wave background (SGWB) provides a powerful probe of fundamental physics across a broad frequency range, accessible to ground-based interferometers such as the LIGO–Virgo Collaboration and pulsar timing arrays like NANOGrav. In this talk, I explore how SGWB observations can test extensions of the standard cosmological model involving dark vector fields. After a brief overview of current multi-frequency gravitational-wave observations, I introduce a class of vector field models that modify gravitational-wave propagation, producing characteristic signatures in the SGWB such as frequency-dependent distortions and amplitude modulations. Then, I focus on multi-Proca dark energy models, where distinctive imprints—including oscillatory features, scale-dependent suppression or enhancement, and possible chiral signatures—arise in the gravitational-wave spectrum. Finally, I discuss prospects for constraining these scenarios with pulsar timing array data, highlighting the potential of SGWB measurements to reveal new physics in the dark sector and shed light on the cosmological origin of SGWB.

Enhancing cosmological constraints with joint galaxy clustering and weak lensing analysis

• Lina Castiblanco (Newcastle University)

Next-generation galaxy surveys will provide vast datasets that can significantly improve our understanding of the Universe, provided that we fully exploit their cosmological information content. However, the late-time matter distribution is intrinsically non-Gaussian, limiting the information captured by standard two-point statistics. To recover this information, it is essential to incorporate beyond two-point observables, such as one-point probability density functions (PDF). One-point statistics capture key non-Gaussian features of galaxy clustering, while their combination with weak lensing provides a powerful framework to jointly constrain galaxy bias and cosmology. In particular, the weak lensing convergence PDF is sensitive to the physics of the dark Universe, including dark matter and dark energy. At the same time, robust cosmological inference requires an accurate treatment of systematic effects, such as shape noise, intrinsic alignments, photometric redshift uncertainties, and mass-mapping reconstruction. I will present our efforts to model the joint PDF while incorporating these systematic effects, and to improve cosmological constraints by combining the joint PDF with the standard 3x2-point correlation functions.

Cosmological Effects of Fluids with Microstructure (Hyperfluids)

• Damianos Iosifidis (Scuola Superiore Meridionale (SSM), Napoli)

I will discuss how the inclusion of a fluid's microstructure, namely the spin, dilation and shear parts of hypermomentum influence the Cosmological dynamics. In particular, imposing isotropy and homogeneity, I will introduce the concept of a Cosmological Hyperfluid; a generalization of the perfect fluid notion in Metric-Affine (Non-Riemannian) Geometries. Finally, I will discuss some applications of this construction and its relevance for the current challenges in cosmology.

From Cosmological Tensions to Machine Learning: Extracting Information Beyond ΛCDM

• Elena Giusarma (Michigan Technological University)

The current era of precision cosmology has established the ΛCDM model as a remarkably successful framework for describing observations ranging from the Cosmic Microwave Background to the large-scale structure of the Universe. At the same time, persistent tensions among cosmological probes and unresolved questions, including the nature of dark energy, modified gravity scenarios, and the absolute neutrino mass scale, motivate the development of new approaches capable of extracting additional information from cosmological data. Upcoming surveys such as DESI, Euclid, Rubin, and Roman will dramatically increase both the precision and volume of cosmological observations, shifting the challenge from data acquisition toward accurate theoretical modeling and inference. A significant fraction of cosmological information is encoded in nonlinear structure formation, where effects from massive neutrinos, galaxy bias, baryonic physics, and possible extensions beyond ΛCDM become increasingly important and highly degenerate. In this talk, I will discuss recent developments in modeling and extracting cosmological information from nonlinear large-scale structure, with emphasis on galaxy bias and its interplay with cosmological parameters such as neutrino masses. I will then present recent work using machine learning and generative approaches, including diffusion models, to model nonlinear structure formation in cosmologies with massive neutrinos and modified gravity. Particular attention will be given to the question of whether these methods are learning genuine cosmological information beyond traditional summary statistics, opening new opportunities for field-level inference in the era of next-generation surveys.

Dark Energy in Light of Current Observations and Modified Gravity.

• Antonio De Felice (Yukawa Institute for Theoretical Physics, Kyoto University)

Current cosmological observations have established the accelerated expansion of the Universe, yet the physical nature of dark energy remains elusive. We summarize the current status of cosmology as inferred from observational data and discuss the implications for the nature of dark energy. We review the main observational probes, highlight existing tensions between datasets within the standard ΛCDM framework, and present theoretical and experimental efforts aimed at addressing these challenges.

How do superhorizon perturbations look like locally

• Jorge Noreña (Pontificia Universidad Catolica de Valparaiso)

We study the effect of superhorizon scalar and tensor perturbations on local observers. We will show that constant perturbations and constant gradients don't have physical effects if they were sourced by single-field inflation (they are so-called adiabatic modes). The leading physical effect of superhorizon perturbations comes at second order in derivatives. At this order, they induce a small curvature and anisotropy. We will show that the universe is expected to be described by a Bianchi metric with tiny anisotropy and curvature parameters. These would be perceived as cosmic variance, and thus set the observational floor for these parameters.

Field-Level Generative Modeling for Cosmology

• Mauricio Reyes (Michigan Technological University)

Next-generation surveys like DESI, Euclid, and LSST demand fast emulation of nonlinear structure across extended cosmological scenarios, but N-body simulations of modified gravity and massive neutrinos remain computationally prohibitive. I present a solution using denoising diffusion probabilistic models (DDPMs) trained directly on matter density fields from f(R) gravity simulations. Conditional DDPMs reproduce both cosmic web morphology and power spectrum clustering with ±5% accuracy from linear through mildly nonlinear scales (0.01 ≲ k ≲ 0.5 h Mpc⁻¹), achieving orders-of-magnitude speedup over traditional N-body codes. Technical innovations include spectral loss regularization to enforce scale-dependent clustering, physics-motivated multi-channel representations for redshift correlations, and systematic conditioning strategies across f(R) parameter space. Building on earlier work with CNNs (MG-NECOLA) and GANs (νGAN for massive neutrinos), this demonstrates that diffusion models provide a flexible framework for field-level cosmological inference. I discuss remaining challenges in the deeply nonlinear regime (k > 0.5 h Mpc⁻¹), ongoing work toward 3D high-resolution modeling, and integration with likelihood-free inference pipelines for precision beyond-ΛCDM science.

Exploring new physics in the late Universe's expansion\\ through non-parametric inference

• Alexander Bonilla Rivera (Instituto de Física, Universidade Federal Fluminense)

In this study, we investigate deviations from the Planck-$\Lambda$CDM model in the late universe ($z \lesssim 2.5$) using the Gaussian Processes method, with minimal assumptions. Our goal is to understand where exploring new physics in the late universe is most relevant. We analyze recent Cosmic Chronometers (CC), Type Ia Supernovae (SN), and Baryon Acoustic Oscillations (BAO) data. By examining reconstructions of the dimensionless parameter $\delta(z)$, which measures deviations of the Hubble parameter from the Planck-$\Lambda$CDM predictions, we identify intriguing features at low ($z \lesssim 0.5$) and high ($z \gtrsim 2$) redshifts. Deviations from the Planck-$\Lambda$CDM model were not significant between $0.5\lesssim z \lesssim2$. Using the combined CC+SN+BAO dataset, we gain insights into dark energy (DE) dynamics, resembling characteristics of omnipotent DE, extending beyond quintessence and phantom models. DE exhibits n-quintessence traits for $z\gtrsim2$, transitioning with a singularity around $z\sim2$ to usual phantom traits in $1\lesssim z\lesssim2$. DE characteristics differ between scenarios ($H_0$-SH0ES and $H_0$-$\Lambda$\&CMB), with $H_0$-SH0ES leaning towards phantom traits and $H_0$-$\Lambda$\&CMB towards quintessence. We suggest exploring new physics at $z\lesssim0.5$ and $1.5\lesssim z\lesssim2.5$, particularly around $z = 2$, to understand cosmological tensions such as $H_0$ and $S_8$.

A Dynamical No-Go Theorem for Viscous Dark Matter Cosmologies

• David Ricardo Moreno Diaz (Universidad Industrial de Santander)

Dark matter bulk viscosity is frequently proposed as a unified phenomenological mechanism to drive the late-time accelerated expansion of the Universe without a cosmological constant. In this work, we employ a general, parameter-independent dynamical systems approach to rigorously assess the macroscopic viability of such dissipative models across the entire cosmic history. We establish a topological No-Go theorem demonstrating that the inclusion of any thermodynamically consistent bulk viscosity—strictly constrained by the Second Law of Thermodynamics—fundamentally forbids the existence of a stable, physically viable radiation-dominated early universe. To explicitly verify this theoretical breakdown, we analyze a standard power-law parametrization for the bulk viscosity ($\xi \propto H \, \Omega_m^s$), which reveals an inescapable parametric dichotomy. For exponents $s \geq 1$, preserving the linear growth of large-scale structures demands a deeply suppressed viscosity, which completely expels the late-time viscous attractor from the physical phase space and renders the model indistinguishable from standard $\Lambda$CDM. Conversely, for fractional exponents ($s < 1$), the late-time viscous attractor is physically accessible, but the backward integration inevitably triggers a fatal past-time mathematical singularity that severs the cosmic history and prevents the existence of a primordial radiation epoch. We conclude that dark matter bulk viscosity is topologically and dynamically incapable of serving as a viable alternative to dark energy.

Jacobson's thermodynamic approach to classical gravity applied to non-Riemmanian geometries: remarks on the simplicity of Nature

• Jhan Nicolás Martínez Lobo (Universidad Industrial de Santander)

Our purpose is to give a step forward in the search of nature's options to describe classical gravity. Two reasonable hypotheses are invoked: the spacetime is described by a smooth manifold, which might or might not be Riemannian, and the classical gravitational dynamics is intimately related to the laws of thermodynamics (Jacobson's programme). We have found that the Einstein-Hilbert's action is the only one that may describe gravity in the Riemannian case whereas, in presence of torsion, an extra quadratic torsional term is needed (when the Lanczos-Lovelock requirements are also held). We have also found that the same strategy cannot be followed in the full non-Riemannian case as the two approaches are mutually inconsistent since the presence of non metricity forbids a thermodynamic equilibrium description.

Inconsistencies of Tsallis Cosmology within Horizon Thermodynamics and Holographic Scenarios

• PEDRO MARTIN IBARBO PERLAZA (Universidad del Valle)

We investigate the cosmological implications of Tsallis entropy in two widely discussed frameworks: the Cai–Kim thermodynamic derivation of the Friedmann equations and the Tsallis holographic dark energy (HDE) scenario, considering both the Hubble scale and the Granda–Oliveros (GO) cutoff as infrared regulators. In both cases, the dynamics introduce a nonextensivity parameter $\delta$, with the standard Bekenstein–Hawking entropy–area relation recovered for $\delta = 1$. While previous studies have suggested that only small deviations from extensivity are observationally allowed, typically requiring $|1 - \delta| \lesssim 10^{-3}$, here we go further and perform a systematic consistency analysis across the entire expansion history. We show that even mild departures from $\delta = 1$ lead to pathological behavior in the effective dark energy sector: its density can become negative or complex, its equation of state may diverge, or it can contribute an unacceptably large early-time fraction that spoils radiation domination and violates big bang nucelosunthesis and CMB constraints. Our results sharpen and unify earlier hints of tension, providing a clear physical interpretation in terms of corrections that grow uncontrollably with the expansion rate toward the past. We conclude that within both the Cai–Kim and HDE formulations, a viable cosmology emerges only in the extensive limit, effectively reducing the models to $\Lambda$CDM. More broadly, our findings emphasize the importance of dynamical consistency and cosmological viability tests, when assessing nonextensive entropy formalisms as potential frameworks for describing the Universe’s dynamics.