Marek Biesiada

We introduce a density-level pivot construction for the Chevallier–Polarski–Linder parametrization by defining the normalized dark energy density f p ≡ f ( a p ) and the equation of state ω p ≡ ω ( a p ) at an optimized pivot scale factor a p . This reparametrization leaves the underlying cosmology unchanged and allows the two models to be compared using parameters with a direct physical interpretation at the epoch where the data are most sensitive. Accordingly, following the DESI DR2 results, we compare a newly proposed f a f b CDM parametrization, based on a second-order Taylor expansion of the normalized dark energy density, with the standard ω 0 ω a CDM model. In particular, we constrain the original and pivoted parametrizations using the compressed cosmic microwave background, DESI DR2 baryon acoustic oscillations, cosmic chronometers, and Pantheon + Type Ia supernovae data, with the SH0ES prior imposed on H 0 . We find that applying the same density-level pivot prescription to the ω 0 ω a CDM model substantially reduces the correlation between its dark energy parameters and provides less correlated constraints in the pivot variables. The statistical comparison shows that this model remains favored over the Taylor expansion of the dark energy density, even when both models are analyzed in the optimized parameter basis. Moreover, the pivoted Chevallier–Polarski–Linder parametrization accurately reproduces the background evolution of quintessence models, providing a reliable phenomenological approximation to the underlying dark energy dynamics, better than the f a f b CDM model. We conclude that changing the parameter basis improves the performance of the ω 0 ω a CDM model, which emerges as the most suitable framework to describe the dark energy sector within the class of models considered here.

Context. Measuring the expansion rate of the Universe is a central challenge in cosmology, particularly due to the persistent statistically significant discrepancy between the measurements of the Hubble constant, H ₀ , obtained using early- and late-time probes, commonly known as the Hubble tension. Independent and robust methods are therefore essential to validate existing measurements and assess potential systematic effects. Aims. We employed the cosmic chronometer (CC) approach, which uses the differential age evolution of quiescent galaxies to measure the Hubble parameter H ( z ) without assuming an underlying cosmological model. In contrast to previous CC studies, we restricted our analysis to relics – ultra-compact massive galaxies (UCMGs) hosting the oldest stellar populations – thereby minimising uncertainties related to star formation history and merger history. Methods. We selected a sample of 189 relic galaxies in the redshift range 0.07 ≤ z ≤ 0.22 from the E-INSPIRE UCMG catalogue. Using the D _n 4000 spectral index of relic galaxies and its redshift evolution, combined with MILES stellar population synthesis models, we derived the differential age relation required to infer H ( z ). We accounted not only for metallicity effects but also for the impact of α -element enhancement, which has not been explicitly propagated into the systematic uncertainty budget of the D _n 4000 CC method. Results. We obtain an independent measurement of H ( z = 0.15) = 85 ± 53 km s ⁻¹ Mpc ⁻¹ . Although the total uncertainty remains large and dominated by statistical limitations, the systematic component is 13% (8.7% when α enrichment is not propagated), among the tightest estimates in current CC studies. We find that α enrichment plays a major role in the systematic error budget, particularly in the high-metallicity regime, and must be properly accounted for in future analyses. Conclusions. We demonstrate the proof of concept that relic galaxies provide a promising pathway to reduce systematic uncertainties in the CC method. The statistical uncertainties, which dominate the error budget, can be significantly reduced by the increase of data volume expected during the next years with Euclid , the Vera C. Rubin Observatory, DESI, and 4MOST.

Primordial black holes (PBHs) formed in the early Universe represent a well-motivated dark matter candidate. However, their abundance in the intermediate-to-high mass range (10 ⁶ –10 ⁹ M _⊙ ) remains relatively less constrained. In this mass regime, the corresponding Einstein radii on the milliarcsecond scale make very long baseline interferometry (VLBI) the most direct observational probe via milli-lensing of compact radio sources. In this paper, we present predictions for the abundance of PBH dark matter ( f _PBH ) using the large Search for MIlli-LEnses (SMILE) sample of ∼5000 flat-spectrum compact radio sources. Under the optimistic observational conditions (with an angular resolution of 1.5 mas, a maximum image separation of 100 mas, and a maximum detectable flux ratio of 40), assuming that no milli-lensing events are confirmed, we obtain the projected 95% upper limit of f _PBH ≲ 0.12% in the intermediate-to-high mass range, which would be approximately an order of magnitude tighter than previous VLBI milli-lensing limits. Broader lognormal mass functions yield correspondingly weaker projected limits. Generalizing the optical depth to account for magnification bias and finite-core resolvability changes these projected limits by only about 5%. Moreover, we show that the predicted limits are highly sensitive to a small number of confirmed events, i.e., even one confirmed milli-lensing event would relax the projected upper limit to 0.20%, highlighting the critical importance of robust candidate confirmation in the SMILE sample. Finally, under the optimistic baryonic accretion scenario, the PBH mass growth changes the projected limits by ≲1% within the VLBI-sensitive mass range, confirming the robustness of our results.

One of the key unresolved questions in modern cosmology is the Hubble tension, which arises from the inconsistency between determinations of the Hubble constant ( H ₀ ) based on nearby observations and those predicted by early-Universe data under the standard ΛCDM paradigm. Recent advances have identified the new Dark Energy Spectroscopic Instrument (DESI) survey as a promising observational tool for probing late-time cosmology. In this paper, we use the latest DESI DR2 baryon acoustic oscillation (BAO) measurements, combined with nonparametrically reconstructed Type Ia supernovae and cosmic chronometer data, to constrain the Hubble constant using three complementary machine learning methodologies: Gaussian process regression (GPR), artificial neural networks (ANNs), and long short-term memory (LSTM) networks. We perform individual and joint constraints on H ₀ at the effective redshifts of DESI DR2 tracers, yielding H ₀ = 61.8 ± 5.3 km s ⁻¹ Mpc ⁻¹ (GPR), 66.3 ± 5.2 km s ⁻¹ Mpc ⁻¹ (ANN), and 68.7 ± 6.0 km s ⁻¹ Mpc ⁻¹ (LSTM). Our results exhibit excellent agreement with the recent Planck measurements within 1 σ , which highlight the potential of data-driven, model-independent methods to address the Hubble tension. Finally, we further test the sensitivity of our results to potential systematics in the DESI data, emphasizing the importance of understanding systematic uncertainties in BAO surveys.

Strong gravitational lensing provides an independent and powerful probe of cosmic expansion by directly linking observables to cosmological distances. Upcoming surveys such as the Legacy Survey of Space and Time (LSST) will discover a large number of galaxy–galaxy strong-lensing systems, offering a new route to precise cosmological constraints. In this paper, we propose a Fisher-like sensitivity factor to map how the cosmological information of strong-lensing distances changes across the lens-source redshift plane. Applying such a factor to the distance ratio D _ls / D _s , the time-delay distance D _{Δ t} , and the double source plane ratio, we determine the “sensitivity valleys,” where an observable becomes insensitive to a given parameter. The realistically simulated LSST lens population, which largely lies outside the distance ratio valleys, covers the most sensitive region for ( w ₀ , w _a ) parameter space. We then develop a new hierarchical framework, which could calibrate the redshift evolution of lens mass density slopes and constrain cosmological parameters simultaneously. Applying this method to a well-selected sample of 161 galaxy–galaxy strong lenses, we obtain Ω m = 0.3 2 − 0.11 + 0.10 and w = − 1.0 0 − 0.97 + 0.57 in the w CDM model. Focusing on the LSST mock data, we demonstrate that ignoring mass profile evolution can bias Ω _m by up to ∼10 σ , while modeling the lens evolution could perfectly recover the fiducial cosmology and yield stringent cosmological constraints (e.g., ΔΩ _m ≃ 0.01 and Δ w ≃ 0.1 for ∼10 ⁴ lenses).

As plans for the construction of third-generation gravitational-wave (GW) detectors advance, research into strongly lensed GWs has become increasingly critical. It is anticipated that hundreds of multi-image lensed GWs will be detected annually. We present a comprehensive suite of lensed GW mock catalogs derived from a composite lens mass model incorporating dark matter halos, galaxies, and subhalos. We analyze three source populations with four detector network configurations considering Earth’s rotation. Our simulations encompass not only conventional doublets and quadruplets but also subhalo-lensed events, highly magnified systems, and complete three- or five-image systems with a detectable central image, a feature distinct from optical lensing. For the joint Einstein Telescope (ET) + Cosmic Explorer (CE) network, we forecast an annual detection rate of approximately 400 doublets and 36 quadruplets. Notably, this population includes roughly 107 events lensed by subhalos and 20 complete systems with detectable central images. Furthermore, we analyze high-magnification events ( μ > 3), predicting approximately 360 such cases. Under a more relaxed selection criterion that requires only at least one lensed signal to exceed the detection threshold, we estimate a total of approximately 617 lensed events. We also investigate the impact of variations in lens mass models and stellar evolution models on the event rates, as well as the distribution of signal-to-noise ratio and time-delay pairs. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The GW lensing mock catalog has been made publicly available.

In view of the new Dark Energy Spectroscopic Instrument 2025 results, we analyze three types of , based on rational series making use of Padé approximants over the equations of state, namely Padé ω (0, 1) and Padé (1, 1), plus a Padé q (0, 1), i.e., a rational expansion on the dark energy deceleration parameter, in which the numerator and denominator orders are incorporated into the above brackets. These scenarios appear as alternative dark energy parametrizations with respect to the well-known ω 0 ω a CDM model. Accordingly, we perform Monte Carlo Markov chain analyses with the publicly available Boltzmann code, including the three Padé parametrizations, along with the ω 0 ω a CDM and Λ CDM standard pictures. To this end, we combine independent probes from high to low redshifts to obtain reliable constraints on the cosmological parameters of these models and compare them using statistical selection criteria. Our results show that ω 0 ω a CDM parametrization is not significantly preferred over the Padé cosmology. On the contrary, the deviance information criterion identifies Padé (1, 1) as along with the ω 0 ω a CDM parametrization. Based on our bounds, we further investigate the evolution of the squared sound speed, revealing that the Padé q (0, 1) and Padé ω (0, 1) parametrizations exhibit enhanced stability compared with the other cases here considered and, therefore, describe robust alternatives for the cosmological background.

We propose the metastable emergent dark energy (MEDE) model, a novel phenomenological extension of the phenomenological and generalized emergent dark energy frameworks, in which dark energy exhibits a transitionary behavior, appearing at late times and vanishing toward the future. This model naturally enables a smooth crossing of the phantom dividing line in the dark energy equation of state, as hinted at by recent observations. The MEDE model is defined by a hyperbolic tangent dark energy equation of state w ( z ) = − 1 − Δ tanh [ log 10 ( ( 1 + z ) / ( 1 + z t ) ) ] , introducing only two free parameters—the transition redshift z _t and the variation amplitude Δ—allowing both the emergent and transitionary behavior of dark energy. We constrain the MEDE model using a combined dataset of Planck cosmic microwave background (CMB) data, Dark Energy Spectroscopic Instrument (DESI) DR2 baryon acoustic oscillation measurements, and different compilations of Type Ia supernovae, obtaining z t = 0.42 5 − 0.120 + 0.084 and Δ = 0.8 7 − 0.35 + 0.29 (for CMB+DESI+PantheonPlus), indicating a statistically significant deviation from the cosmological constant. Statistical comparisons show that the MEDE model is preferred over ΛCDM by the combined dataset, with ΔDIC _MEDE−ΛCDM = −9.29. The MEDE model performs comparably to the Chevallier–Polarski–Linder (CPL) dynamical dark energy parameterization (ΔDIC _{MEDE −CPL} = 0.74), with no strong statistical distinction from CPL using current data. Notably, MEDE preserves the success of ΛCDM in describing early-universe physics and naturally accommodates the phantom-crossing signature indicated by the latest low-redshift observations. The MEDE scenario provides a compelling dark energy phenomenology that may guide us toward interesting theoretical implications.

Einstein’s weak equivalence principle (WEP), the universality of free fall, is a fundamental component of general relativity and other metric theories of gravity. Its validity can be tested through the post-Newtonian parameter γ , which quantifies the amount of spacetime curvature due to the presence of unit rest mass. In this Letter, we use high-energy neutrino events detected by IceCube and associated with the gamma-ray blazars TXS 0506+056 and PKS 0735+178 to test the WEP via the Shapiro delay induced by the gravitational potential of Laniakea. We find that violation of the equivalence principle for neutrinos and photons is limited to an accuracy of 10 ⁻⁶ , 10 ⁻⁷ , and 10 ⁻⁸ , representing improvements of 1, 2, and 3 orders of magnitude, respectively, over previous constraints obtained from other high-energy neutrino-blazar associations and up to 6 orders of magnitude tighter compared to the constraints obtained with MeV neutrinos from SN 1987A.