arXiv subjects

Marek Biesiada

Publications and source records attributed to Marek Biesiada.

At least 19 recordsLinked to original sources

arXiv2026

Predictions on the abundance of primordial black holes: results from the SMILE VLBI milli-lensing sample

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 ($10^6$-$10^9\,M_\odot$) 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 ($f_{\rm PBH}$) using the large SMILE sample of $\sim 5000$ flat-spectrum compact radio sources. Under the optimistic observational conditions (with an angular resolution of $1.5\,\mathrm{mas}$, a maximum image separation of $100\,\mathrm{mas}$, and a maximum detectable flux ratio of $40$), assuming that no milli-lensing events are confirmed, we obtain the projected 95% upper limit of $f_{\rm PBH}\lesssim0.12%$ 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. Generalising 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 $\lesssim 1$% within the VLBI-sensitive mass range, confirming the robustness of our results.

astro-ph.CO↗

arXiv2026

Gravitational-Wave Image Multiplicity as a Topological Probe of Dark-Matter Core Collapse

Dark-matter self-interactions can drive subhalos through gravothermal core collapse, but conventional lensing observables vary continuously with uncertain inner profiles. We show that gravitational-wave image multiplicity provides a discrete alternative. Near a macro-critical minimum, increasing subhalo central convergence opens two caustics in sequence, converting one detectable waveform into three and then five stationary images. Using weighted SASHIMI subhalos and an ET+CE selection model, we forecast almost 2 systems with at least three copies detectable in five years if dense remnants survive, compared with the prediction of 0.36 in 5yrs for standard CDM. The much more diagnostic second case is rare: the corresponding 5yrs yield with at least four detectable copies is 0.149, versus $1.55\times10^{-6}$ for CDM. According to the Poisson statistics, this gives only a 13.8\% probability of at least one event detected in 5 years. Thus this is a rare-event, exposure-limited test rather than a guaranteed detection: a resolved second pair would be difficult to reconcile with the fiducial single-halo CDM population, whereas a five-year null result would not by itself constrain remnant survival strongly.

astro-ph.CO↗

arXiv2026

Probing Dark Matter Substructure with Wave-Optics Distortions of Strongly Lensed LISA Gravitational Waves

Strong lensing changes the phase of a gravitational-wave signal as well as its amplitude and arrival time. We study whether this phase information can distinguish between three dark-matter structures in the lens: a Navarro--Frenk--White halo (NFW), a self-interacting dark matter (SIDM) halo, and a fuzzy-dark-matter field (FDM). We generate waveforms for the detectable lensed massive-black-hole-binary population of a four-year LISA mission and fit every signal with the same smooth singular-isothermal-ellipsoid lens with external shear. In 132 lens systems, 311 images are resolved as separate signals in time. NFW and SIDM produce real waveform changes, but their slowly varying part is largely degenerate with the constant, gradient, and Hessian of the smooth Fermat potential at the image. The coherent density fluctuations of FDM leave a larger frequency-dependent residual after this fit. The NFW--FDM and SIDM--FDM populations become distinguishable with about 60 and 110 resolved image waveforms, respectively. These results show that repeated lensed LISA signals can probe the spatial form of dark matter in lens galaxies, rather than only the total lensing mass.

astro-ph.CO↗

arXiv2026

CORN -- Chronometers of Relic Nature I: The first estimate of the expansion rate of the Universe using compact relic galaxies

Measuring the expansion rate of the Universe is a central challenge in cosmology. Independent and robust methods are essential to validate existing measurements and assess potential systematic effects. We employ 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 restrict 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. We select a sample of 189 relic galaxies in the redshift range 0.07< z <0.22 from the E-INSPIRE UCMGs catalogue. Using the D_n4000 spectral index of relic galaxies and its redshift evolution, combined with MILES stellar population synthesis models, we derive the differential age relation required to infer H(z). We account not only for metallicity effects but also for the impact of alpha-element enhancement, which has not been explicitly propagated into the systematic uncertainty budget of the D_n4000 cosmic chronometer method. We obtain an independent measurement of H(z=0.15) = 85\pm53 km/s/Mpc. The total uncertainty is dominated by statistical limitations. The systematic component is 13% (8.7% when alpha-enrichment is not propagated), among the tightest estimates in current CC studies. We find that alpha-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. 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.

astro-ph.CO↗

arXiv2026

Do we really need alternatives to the $ω_0ω_a$CDM parameterization after the DESI DR2?

We introduce a density-level pivot construction for the Chevallier-Polarski-Linder (CPL) parameterization by defining the normalized dark energy density $f_p\equiv f_{\rm DE}(a_p)$ and the equation of state $ω_p\equiv ω(a_p)$ at an optimized pivot scale factor $a_p$. This reparameterization leaves the underlying CPL 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 parameterization, based on a second-order Taylor expansion of the normalized dark energy density, with the standard $w_0w_a$CDM model. In particular, we constrain the original and pivoted parameterizations using compressed cosmic microwave background (CMB), DESI DR2 baryon acoustic oscillations (BAO), cosmic chronometers (CC), 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 $w_0w_a$CDM model substantially reduces the correlation between its dark energy parameters and provides tighter and more stable constraints. 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 CPL parameterization accurately reproduces the background evolution of quintessence models, providing a reliable phenomenological approximation to the underlying dark energy dynamics, better than the $f_af_b$CDM model. We conclude that changing the parameter basis improves the performance of the $w_0w_a$CDM model, which emerges as the most suitable framework to describe the dark energy sector within the class of models considered here.

astro-ph.CO↗

arXiv2026

Probing globular clusters parameters through gravitational wave lensing with stellar-mass black hole binaries

Globular clusters (GCs) can act as gravitational lenses for gravitational waves(GWs) in the wave-optics regime, imprinting frequency-dependent signatures on the observed signal. We investigate whether such lensing effects can be used to probe intrinsic properties of GCs, in particular their central velocity dispersion. Modeling GCs as singular isothermal spheres, we simulate lensed GW150914-like signals and perform Bayesian parameter estimation using waveform templates that include both source and lens parameters. We show that the effective lensing mass can be recovered and, when combined with GW sky localization information and GC catalogs, allows for an estimate of the cluster velocity dispersion. For favorable source-lens alignments, the injected values are well recovered within credible intervals. Our results demonstrate that lensed GWs can provide a complementary probe of GC dynamics and motivate searches for such signatures in current and future observations.

gr-qc↗

arXiv2026

Extragalactic test of General Relativity with time-delay gravitational lenses

Strong gravitational lensing, a key prediction of General Relativity (GR), offers a unique environment for examining alternative modified gravity theories. In this Letter, we employ a model-independent approach to estimate the parameterized post-Newtonian parameter $γ_{\rm PPN}$ using the time-delay measurements from H0LiCOW strong lensing systems. To minimize potential biases from cosmological models in testing GR, we use Gaussian Process regression (GPR) to reconstruct angular diameter distances ($D_{\rm A}$) from the newest baryon acoustic oscillation (BAO) measurements, provided by the Dark Energy Spectroscopic Instrument (DESI) DR2 data. Based on the reconstructed angular diameter distances and four H0LiCOW lenses, we directly estimate the post-Newtonian parameter $γ_{\rm PPN}=0.93^{+0.16}_{-0.17}$ and the sound horizon scale $r_{\rm d}=136.36^{+5.14}_{-3.20}~{\rm Mpc}$. This is the first simultaneous measurement of $γ_{\rm PPN}$ and $r_{\rm d}$ without any assumptions about the contents of the universe or the theory of gravity. In the new framework of distance ratio $D_{Δt}/D_{\rm l}$ which avoids the bias introduced by $r_{\rm d}$, the $γ_{\rm PPN}$ constraint can be further improved to $γ_{\rm PPN}=0.89^{+0.19}_{-0.15}$. Our results provide a direct test of GR at the extragalactic scale, which is well consistent with the prediction of GR within $1σ$.

astro-ph.CO↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Space-borne Detectors

Future space-borne gravitational-wave (GW) detectors, such as LISA and DECIGO, are expected to detect a large number of GW events, a fraction of which may be strongly lensed by intervening galaxies or galaxy clusters. In this work, we develop a comprehensive framework to simulate strongly lensed GWs in the context of space-borne detectors. Based on realistic astrophysical models for both the source population and the lens distribution, we construct mock catalogs of lensed GW events, referred to as \textbf{GW-LMC-Space}. Our results show that, for a four-year LISA observation, the expected number of lensed events ranges from $0$ to $131$, depending on the adopted formation model of massive black hole binaries (MBHBs). The corresponding lensing probability for MBHBs can reach up to $\sim 0.3\%$. For DECIGO, we find that the number of lensed events in a one-year observation is expected to lie in the range of $0$--$44$, with a lensing probability of $\sim 0.15\%$ for stellar-mass binary black holes (BBHs), binary neutron stars (BNSs), and neutron star--black hole binaries (NSBHs). We further show that the overlap of lensed signals is a common feature in space-borne detectors, which can significantly affect both the signal-to-noise ratio (SNR) estimation and event identification. These results highlight the importance of accounting for signal overlap in the analysis of strongly lensed GW events in future space-borne GW observations.

astro-ph.CO↗

arXiv2026

Metastability in Emergent Dark Energy: A New Framework Confronting Cosmological Observations

We propose the Metastable Emergent Dark Energy (MEDE) model, a novel phenomenological extension of the Phenomenological (PEDE) and Generalized (GEDE) 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 divide 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 CMB, DESI DR2 BAO, and different compilations of Type Ia supernovae, obtaining $z_t=0.425^{+0.084}_{-0.120}$ and $Δ=0.87^{+0.29}_{-0.35}$ (for CMB+DESI+PantheonPlus), indicating a statistically significant deviation from the cosmological constant. Statistical comparisons show that the MEDE model is preferred over $Λ$CDM by the combined dataset, with $Δ\rm DIC_{ MEDE-ΛCDM}= -9.29$. The MEDE model performs comparably to the CPL dynamical dark energy parametrization ($Δ\rm DIC_{MEDE-CPL} = 0.74$), with no strong statistical distinction from CPL using current data. Notably, MEDE preserves the success of $Λ$CDM 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.

astro-ph.CO↗

arXiv2026

Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors

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 catalog 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 the earth 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 ET+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 event rates, as well as the distributions of SNR pairs and time delays. These results establish a more physically grounded statistical prior for the future identification and authentication of lensed GW signals. The Gravitational Waves-Lensing Mock Catalog (GW-LMC) have been made publicly available.

astro-ph.CO↗

arXiv2026

Testing Weak Equivalence Principle with IceCube Event and Blazar

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 gamma, which quantifies the amount of spacetime curvature due to the presence of unit rest mass. In this paper, 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 one, two, and three orders of magnitude, respectively, over previous constraints obtained from other high-energy neutrino-blazar associations and up to six orders of magnitude tighter compared to the constraints obtained with MeV neutrinos from SN1987A.

astro-ph.HE↗

arXiv2026

Hierarchical cosmological constraints through strong lensing distance ratio

Strong gravitational lensing provides an independent and powerful probe of cosmic expansion by directly linking observables to cosmological distances. Upcoming surveys such as LSST will discover 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 factor to the distance ratio $D_{ls}/D_s$, the time-delay distance $D_{Δt}$, 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. Focusing on the LSST mock data, we demonstrate that ignoring mass-profile evolution can bias $Ω_m$ by up to $\sim 10σ$, while modeling the lens evolution could perfectly recovers the fiducial cosmology and yield stringent cosmological constraints (e.g., $ΔΩ_m \simeq 0.01$ and $Δw \simeq 0.1$ for $\sim 10^4$ lenses).

astro-ph.CO↗

arXiv2026

Probing Cosmic Expansion and Early Universe with Einstein Telescope

Over the next two decades, gravitational-wave (GW) observations are expected to evolve from a discovery-driven endeavour into a precision tool for astrophysics, cosmology, and fundamental physics. Current second-generation ground-based detectors have established the existence of compact-binary mergers and enabled GW multi-messenger astronomy, but they remain limited in sensitivity, redshift reach, frequency coverage, and duty cycle. These limitations prevent them from addressing many fundamental open questions in cosmology. By the 2040s, wide-field electromagnetic surveys will have mapped the luminous Universe with unprecedented depth and accuracy. Nevertheless, key problems including the nature of dark matter, the physical origin of cosmic acceleration, the properties of gravity on cosmological scales, and the physical conditions of the earliest moments after the Big Bang will remain only partially constrained by electromagnetic observations alone. Progress on these fronts requires access to physical processes and epochs that do not emit light. Gravitational waves provide a unique and complementary observational channel: they propagate over cosmological distances largely unaffected by intervening matter, probe extreme astrophysical environments, and respond directly to the geometry of spacetime. In this context, next-generation GW observatories such as the Einstein Telescope (ET) will be transformative for European astronomy. Operating at sensitivities and frequencies beyond existing detectors, ET will observe binary black holes and neutron stars out to previously inaccessible redshifts, enable continuous high signal-to-noise monitoring of compact sources, and detect gravitational-wave backgrounds of astrophysical and cosmological origin. Together with space-based detectors, ET will play a central role in advancing our understanding of cosmic evolution and fundamental physics.

astro-ph.CO↗

arXiv2025

Challenging the $ω_0ω_a$CDM parametrization through rational expansions in view of DESI data release

In view of the new Dark Energy Spectroscopic Instrument (DESI) 2025 results, we analyze three types of \emph{Padé cosmology}, based on rational series making use of Padé approximants over the equations of state, namely Padé$^ω$ (0,1) and Padé$^ω$ (1,1), plus a Padé$^{q}$ (0,1), i.e., a rational expansion on the dark energy deceleration parameter, in which where the numerator and denominator orders are incorporated into the above brackets. These scenarios appear alternative dark energy parameterizations with respect to the well-known $ω_0ω_a$CDM model, claimed as the most viable model by DESI. Accordingly, we perform Monte Carlo Markov chain (MCMC) analyses with the publicly available \texttt{CLASS} Boltzmann code, including the three Padé cosmology, along with the $ω_0ω_a$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. \emph{Our results show that Padé cosmology is neither statistically excluded nor worse than the $ω_0ω_a$CDM parametrization}. On the contrary, the Akaike Information Criterion (AIC) identifies Padé$^{q}$ (0,1) as \emph{the best-fit model}, with weak evidence against the $ω_0ω_a$CDM parameterization, while the Deviance Information Criterion (DIC) provides \emph{strong evidence against the $ω_0ω_a$CDM model, favoring Padé (1,1)}. 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) parameterizations exhibit enhanced stability compared with the other cases here considered and, therefore, describe robust alternatives for the cosmological background.

astro-ph.CO↗

arXiv2025

Microlensing of long-duration gravitational wave signals originating from Galactic sources

Detection of quasi-monochromatic, long-duration (continuous) gravitational wave radiation emitted by, e.g., asymmetric rotating neutron stars in our Galaxy requires a long observation time to distinguish it from the detector's noise. If this signal is additionally microlensed by a lensing object located in the Galaxy, its magnitude would be temporarily magnified, which may lead to its discovery and allow probing of the physical nature of the lensing object and the source. We study the observational effect of microlensing of continuous gravitational wave signals for Galactic sources and lenses in the point mass lens approximation. In particular, we examine the regions of the parameter space that are promising for lensed CW searches, and perform example simulations to demonstrate how the lensing effect affects the continuous-wave signal. We show that an analytical lensing pattern can be identified from the lensed continuous wave signal using the Time-Domain F-statistic search, as the estimated signal-to-noise ratio in each time-domain segment scales directly with the amplification factor.

gr-qc↗

arXiv2025

Torsion cosmology in the light of DESI, supernovae and CMB observational constraints

In this work, we investigate a torsion-based cosmological model within the Einstei-Cartan framework, constrained by the latest combined datasets including DESI DR2 BAO, PantheonPlus and DESY5 supernovae, and the full Planck 2018 CMB measurements (temperature, polarization, and joint NPIPE PR4 + ACT DR6 lensing). The torsion parameter is constrained to $α= -0.00066 \pm 0.00098$ with the full dataset combination, consistent with zero at less than $1σ$, while yielding a Hubble constant $H_0 = 68.41 \pm 0.32$ km/s/Mpc and matter clustering amplitude $S_8 = 0.812 \pm 0.006$. The model shows notable potential in alleviating cosmological tensions, reducing the $S_8$ discrepancy with KiDS-1000 from $\sim 2.3σ$ in $Λ$CDM to only $0.1σ$. Model comparisons based on the Akaike information criterion show consistent improvements across all datasets, with $Δ{\rm AIC}$ values ranging from $-5.68$ to $-6.62$, indicating a statistically preferred fit for the torsion model. These results suggest that the torsion framework provides a physically well-motivated extension to $Λ$CDM, capable of simultaneously addressing key cosmological tensions while maintaining excellent agreement with diverse observational probes.

astro-ph.CO↗

arXiv2025

Advancing Cosmological Parameter Estimation and Hubble Parameter Reconstruction with Long Short-Term Memory and Efficient-Kolmogorov-Arnold Networks

In this work, we propose a novel approach for cosmological parameter estimation and Hubble parameter reconstruction using Long Short-Term Memory (LSTM) networks and Efficient-Kolmogorov-Arnold Networks (Ef-KAN). LSTM networks are employed to extract features from observational data, enabling accurate parameter inference and posterior distribution estimation without relying on solvable likelihood functions. This method achieves performance comparable to traditional Markov Chain Monte Carlo (MCMC) techniques, offering a computationally efficient alternative for high-dimensional parameter spaces. By sampling from the reconstructed data and comparing it with mock data, our designed LSTM constraint procedure demonstrates the superior performance of this method in terms of constraint accuracy, and effectively captures the degeneracies and correlations between the cosmological parameters. Additionally, the Ef-KAN model is introduced to reconstruct the Hubble parameter H(z) from both observational and mock data. Ef-KAN is entirely data-driven approach, free from prior assumptions, and demonstrates superior capability in modeling complex, non-linear data distributions. We validate the Ef-KAN method by reconstructing the Hubble parameter, demonstrating that H(z) can be reconstructed with high accuracy. By combining LSTM and Ef-KAN, we provide a robust framework for cosmological parameter inference and Hubble parameter reconstruction, paving the way for future research in cosmology, especially when dealing with complex datasets and high-dimensional parameter spaces.

astro-ph.CO↗

arXiv2025

Investigating the Redshift Evolution of Lensing Galaxy Density Slopes via Model-Independent Distance Ratios

Strong lensing systems, expected to be abundantly discovered by next-generation surveys, offer a powerful tool for studying cosmology and galaxy evolution. The connection between galaxy structure and cosmology through distance ratios highlights the need to examine the evolution of lensing galaxy mass density profiles. We propose a novel, dark energy-model-independent method to investigate the mass density slopes of lensing galaxies and their redshift evolution using an extended power-law (EPL) model. We employ a non-parametric approach based on Artificial Neural Networks (ANNs) trained on Type Ia Supernovae (SNIa) data to reconstruct distance ratios of strong lensing systems. These ratios are compared with theoretical predictions to estimate the evolution of EPL model parameters. Analyses conducted at three levels, including the combined sample, individual lenses, and binned groups, ensure robust and reliable estimates. A negative trend in the mass density slope with redshift is observed, quantified as $\partialγ/\partial z = -0.20 \pm 0.12$ under a triangular prior for anisotropy. This study demonstrates that the redshift evolution of density slopes in lensing galaxies can be determined independently of dark energy models. Simulations based on LSST Rubin Observatory forecasts, which anticipate 100,000 strong lenses, show that spectroscopic follow-up of just 10 percent of these systems can constrain the redshift evolution coefficient with uncertainty ($Δ\partialγ/\partial z$) to 0.021. This precision distinguishes evolving and non-evolving density slopes, providing new insights into galaxy evolution and cosmology.

astro-ph.CO↗