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The difference from 4 to 6 σ in the Hubble constant (H0) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as f(z)=H0/(1+z)η, where H0 is H0(z=0) and η is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations. We assume H0=70kms−1Mpc−1 as the local value and divide the Pantheon into three bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously (H0, Ω0m in the ΛCDM model and H0, wa in the w0waCDM model), for each bin we implement a Markov-Chain Monte Carlo analysis (MCMC) obtaining the value of H0 assuming Gaussian priors to restrict the parameters spaces to values we expect from our prior knowledge of the current cosmological models and to avoid phantom Dark Energy models with w<−1. Subsequently, the values of H0 are fitted with the model f(z). Our results show that a decreasing trend with η∼10−2 is still visible in this sample. The η coefficient reaches zero in 2.0 σ for the ΛCDM model up to 5.8 σ for w0waCDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, f(R). This analysis is meant to further cast light on the evolution of H0 and it does not specifically focus on constraining the other parameters. This work is also a preparatory to understand how the combined probes still show an evolution of the H0 by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the Ω0m comparable with the ones achieved through SNe Ia.

To elucidate the robustness of the baryon acoustic oscillation (BAO) data measured by the dark energy spectroscopic instrument (DESI) in capturing the dynamical behavior of dark energy, we assess the model dependence of the evidence for dynamical dark energy inferred from the DESI BAO data. While the DESI BAO data slightly tightens the constraints on model parameters and increases the tension between the Chevallier–Polarski–Linder (CPL) model and the ΛCDM model, we find that the influence of DESI BAO data on the constraint of w0 is small in the SSLCPL model. In comparison to the CPL model, the tension with the ΛCDM model is reduced for the SSLCPL model, suggesting that the evidence for dynamical dark energy from DESI BAO data is dependent on cosmological models. The inclusion of spatial curvature has little impact on the results in the SSLCPL model.

The ΛCDM model, or concordance cosmology, as it is often called, is a paradigm at its maturity. It is clearly able to describe the universe at large scale, even if some issues remain open, such as the cosmological constant problem, the small-scale problems in galaxy formation, or the unexplained anomalies in the CMB. ΛCDM clearly shows difficulty at small scales, which could be related to our scant understanding, from the nature of dark matter to that of gravity; or to the role of baryon physics, which is not well understood and implemented in simulation codes or in semi-analytic models. At this stage, it is of fundamental importance to understand whether the problems encountered by the ΛDCM model are a sign of its limits or a sign of our failures in getting the finer details right. In the present paper, we will review the small-scale problems of the ΛCDM model, and we will discuss the proposed solutions and to what extent they are able to give us a theory accurately describing the phenomena in the complete range of scale of the observed universe.

This review aims at proposing to the field an overview of the Cusp-core problem, including a discussion of its advocated solutions, assessing how each can satisfactorily provide a description of central densities. Whether the Cusp-core problem reflects our insufficient grasp on the nature of dark matter, of gravity, on the impact of baryonic interactions with dark matter at those scales, as included in semi-analytical models or fully numerical codes, the solutions to it can point either to the need for a paradigm change in cosmology, or to to our lack of success in ironing out the finer details of the ΛCDM paradigm.

Alternative dark energy models were proposed to address the limitation of the standard concordance model. Though different phenomenological considerations of such models are widely studied, scenarios where they interact with each other remain unexplored. In this context, we study interacting dark energy scenarios (IDEs), incorporating alternative dark energy models. The three models that are considered in this study are time-varying Λ , Generalized Chaplygin Gas (GCG), and K-essence. Each model includes an interaction rate Γ to quantify energy density transfer between dark energy and matter. Among them, GCG coupled with an interaction term shows promising agreement with the observed TT power spectrum, particularly for ℓ < 70 , when Γ falls within a specific range. The K-essence model ( Γ ≤ 0.1 ) is more sensitive to Γ due to its non-canonical kinetic term, while GCG ( Γ ≥ 1.02 ) and the time-varying Λ ( Γ ≤ 0.01 ) models are less sensitive, as they involve different parameterizations. We then derive a general condition when the non-canonical scalar field ϕ (with a kinetic term X n ) interacts with GCG. This has not been investigated in general form before. We find that current observational constraints on IDEs suggest a unified scalar field with a balanced regime, where it mimics quintessence behavior at n < 1 and phantom behavior at n > 1 . We outline a strong need to consider alternative explanations and fewer parameter dependencies while addressing potential interactions in the dark sector.

Through the analysis of the linearly varying deceleration parameter (LVDP) (q) in the framework of general relativity (GR) and spatially anisotropic Bianchi type (BT) II, VIII and IX Universes, the Tsallis holographic dark energy (THDE) has been examined (Tavayef et al. in Phys. Lett. B 781:195, 2018). As a result of the phase change from the slow expansion of the cosmos to the accelerated expansion of the cosmos, the deceleration parameter(DP) must flip its signatures at the transition redshift, where the DP’s values are constrained as q0=−0.7388 (Cunha in Phys. Rev. D 79:047301, 2009) and transition redshift zt≈0.5 (i.e., 0.5≤zt≤1). The proposed THDE model predicts that the Universe is an expanding one based on the equation of state parameter (EoS) (ωde) and DP (q), along with the ωde−ωde′ plane (the ′ shows the differentiation based on lna) and also supports the recent observational data. The analysis confirms that the quintessence, phantom dark energy regions, and Λ cold dark matter (ΛCDM) limit, exist in our model. We have observed the evolution of (r,s) and (r,q) trajectories in order to study different phases of the Universe and also cosmological quantities such as jerk (j), snap(s), lerk(l) parameters, Om diagnostic, luminosity distance (dl), angular diameter (da) and distance modulus (dm) have been discussed. In addition, we compare the behavior of scale factor (a), Hubble (H), deceleration (q), jerk (j), and snap (s) parameters of ΛCDM and LVDP models and discover that their behavior has been almost identical over the observed Universe’s history.

Modern cosmology continues to struggle with unresolved questions concerning the origins of dark matter and dark energy. To explore these challenges, this study presents the Source Energy Field Theory (SEFT)—a new theoretical framework that offers an alternative view of how cosmic structures may form and evolve. SEFT envisions the universe as filled with a fundamental energy field, where the observed cosmological redshift does not result from accelerated expansion but rather emerges from the distance-dependent modulation of the energy field and the curvature produced by this field. To evaluate this idea, a nonlinear wave equation was developed to connect redshift with right ascension, declination, and distance. The model was optimized using 1701 observational data points from the Pantheon+ and SH0ES samples, which include Type Ia supernovae and Cepheid variables spanning distances from 6.3 to 17,241 Mpc. Its performance was compared with that of the standard ΛCDM model. SEFT achieved a slightly lower root-mean-square error (145.521 vs. 147.665 Mpc), a marginally higher determination coefficient (R2 = 0.9910 vs. 0.9908), and significantly improved information criteria values (ΔAIC = −41.753, ΔBIC = −19.997). These results provide robust statistical support for SEFT and suggest that it can complement—and potentially extend—the ΛCDM paradigm in describing the structure and evolution of the universe.

Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as β, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de Sitterian deformation of the relativistic Maxwell–Jüttner distribution. In this context, the curvature of the de Sitter space-time is characterized by Λ/3, where Λ represents the cosmological constant within the ΛCDM standard model for cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by q=1+ℓcΛ/n, where ℓc=ℏ/mc is the Compton length of the particle and n is a positive numerical factor, the determination of which awaits observational confirmation. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters.

The standard models of particle physics and of cosmology have been enormously successful in correlating a large amount of data. However, there are missing pieces and we are still far from what the ultimate model may look like. We give a broad perspective of both the achievements and of the missing pieces and discuss what may lie beyond.

Although the Λ Cold Dark Matter model is the most accredited cosmological model, information at high redshifts (z) between type Ia supernovae (z=2.26) and the Cosmic Microwave Background (z=1100) is crucial to validate this model further. To this end, we have discovered a sample of 1132 quasars up to z=7.54 exhibiting a reduced intrinsic dispersion of the relation between ultraviolet and X-ray fluxes, δF=0.22 vs. δF=0.29 (24% less), than the original sample. This gold sample, once we correct the luminosities for selection biases and redshift evolution, enables us to determine the matter density parameter ΩM with a precision of 0.09. Unprecedentedly, this quasar sample is the only one that, as a standalone cosmological probe, yields such tight constraints on ΩM while being drawn from the same parent population of the initial sample.