The vast majority of close binaries containing a compact object form through common-envelope (CE) evolution. Despite this importance, we struggle to even understand the energy budget of CE evolution. For decades, observed long-period post-CE binaries have been interpreted as evidence for additional energies to contribute during CE evolution. We have recently shown that this argument is based on simplified assumptions for all long-period post-CE binaries containing massive white dwarfs. The only remaining post-CE binary star that has been claimed to require contributions from additional energy sources to understand its formation is KOI 3278. Here we address in detail the potential evolutionary history of KOI 3278. In particular, we investigated whether extra energy sources, such as recombination energy, are indeed required to explain its existence. We used the 1D stellar evolution code MESA to carry out binary evolution simulations and searched for potential formation pathways for KOI 3278 that are able to explain its observed properties. We found that KOI 3278 can be explained if the white dwarf progenitor filled its Roche lobe during a helium shell flash. In this case, the orbital period of KOI 3278 can be reproduced if the CE binding energy is calculated taking into account gravitational energy and thermodynamic internal energy. While the CE evolution that led to the formation of KOI 3278 must have been efficient, that is, most of the available orbital energy must have been used to unbind the CE, recombination energy is not required. We conclude that currently not a single observed post-CE binary requires to assume energy sources other than gravitational and thermodynamic energy to contribute to CE evolution. KOI 3278, however, remains an intriguing post-CE binary as, unlike its siblings, understanding its existence requires highly efficient CE ejection.

We present a model--independent reconstruction of the normalized dark energy density function, $X(z) \equiv \rho_{\mathrm{de}}(z)/\rho_{\mathrm{de}}(0)$, derived directly from the DES-SN5YR Type~Ia supernova sample. The analysis employs an inversion formalism that relates the derivative of the distance modulus, $\mu^{\prime}(z)$, to the expansion history, allowing the data to determine the shape of $X(z)$ without assuming a specific equation--of--state or dark energy density parameterization. A statistically optimized binning of the supernova sample (using 17 intervals following the Freedman--Diaconis criterion and 34 following Scott's rule) ensures a stable estimation of $\mu^{\prime}(z)$ and a controlled propagation of uncertainties throughout the inversion process. The resulting $X(z)$ remains statistically consistent with a constant value within one standard deviation across the entire redshift range, showing no significant evidence for an evolving dark energy component at present. In a direct comparison among $\Lambda$CDM, CPL, and the quadratic $X^2(z)$ parameterization -- where CPL and $X^2(z)$ each introduce two additional free parameters relative to $\Lambda$CDM -- the CPL model attains the best statistical agreement with the data, albeit only marginally and strictly within this restricted model set. These outcomes indicate that current observations are compatible with an almost constant dark energy density ($w \simeq -1$), while the inversion framework remains sensitive to subtle departures that forthcoming high--precision surveys could resolve.

The Gaia Galactic survey mission is designed and optimized to obtain astrometry, photometry, and spectroscopy of nearly two billion stars in our Galaxy. Yet as an all-sky multi-epoch survey, Gaia also observes several million extragalactic objects down to a magnitude of G~21 mag. Due to the nature of the Gaia onboard selection algorithms, these are mostly point-source-like objects. Using data provided by the satellite, we have identified quasar and galaxy candidates via supervised machine learning methods, and estimate their redshifts using the low resolution BP/RP spectra. We further characterise the surface brightness profiles of host galaxies of quasars and of galaxies from pre-defined input lists. Here we give an overview of the processing of extragalactic objects, describe the data products in Gaia DR3, and analyse their properties. Two integrated tables contain the main results for a high completeness, but low purity (50-70%), set of 6.6 million candidate quasars and 4.8 million candidate galaxies. We provide queries that select purer sub-samples of these containing 1.9 million probable quasars and 2.9 million probable galaxies (both 95% purity). We also use high quality BP/RP spectra of 43 thousand high probability quasars over the redshift range 0.05-4.36 to construct a composite quasar spectrum spanning restframe wavelengths from 72-100 nm.

Resolved high-redshift galaxy gas kinematics is a rapidly evolving field driven by increasingly powerful instrumentation. However, the resolution and sensitivity still impose constraints on interpretation. We investigate the uncertainties inherent to high-$z$ galaxy kinematical analysis by modelling a suite of rotating disk galaxies, generating synthetic interferometric ALMA observations, and fitting them with the 3D-kinematical tools 3DBarolo, GalPaK3D, and Qubefit. We present the recovered 3D-fitted kinematical parameters to assess their reliability, quantify the range of values possible for individual source studies, and establish the systematic biases present for observed samples. The $V/\sigma_{\rm V}$ ratio, which indicates how dynamically cold a system is, is of particular importance and depends on the choice of 3D-fitting tool. On average, 3DBarolo and Qubefit slightly overestimates $V/\sigma_{\rm V}$ (<1\sigma) and GalPaK3D underestimates it (<2\sigma). Therefore, all three tools are reliable for kinematical studies of averages of high-redshift galaxy samples. The value range possible for individual sources is significant, however, even more so for samples of not purely rotation dominated sources. To determine whether an observed galaxy is rotation dominated enough to be fitted with a 3D-kinematical tool, $V/\sigma_{\rm V}$ can be extracted directly from the observed data cube, with some caveats. We recommend that the median offsets, value ranges, and tool-dependent biases presented in this paper are taken into account when interpreting 3D-fitted kinematics of observed high-redshift galaxies.

As the statistical precision of cosmological measurements increases, the accuracy of the theoretical description of these measurements needs to increase correspondingly in order to infer the underlying cosmology that governs the Universe. To this end, we have created the Cosmology Likelihood for Observables in Euclid (CLOE), which is a novel cosmological parameter inference pipeline developed within the Euclid Consortium to translate measurements and covariances into cosmological parameter constraints. In this first in a series of six papers, we describe the theoretical recipe of this code for the Euclid primary probes. These probes are composed of the photometric 3x2pt observables of cosmic shear, galaxy-galaxy lensing, and galaxy clustering, along with spectroscopic galaxy clustering. We provide this description in both Fourier and configuration space for standard and extended summary statistics, including the wide range of systematic uncertainties that affect them. This includes systematic uncertainties such as intrinsic galaxy alignments, baryonic feedback, photometric and spectroscopic redshift uncertainties, shear calibration uncertainties, sample impurities, photometric and spectroscopic galaxy biases, as well as magnification bias. The theoretical descriptions are further able to accommodate both Gaussian and non-Gaussian likelihoods and extended cosmologies with non-zero curvature, massive neutrinos, evolving dark energy, and simple forms of modified gravity. These theoretical descriptions that underpin CLOE will form a crucial component in revealing the true nature of the Universe with next-generation cosmological surveys such as Euclid.

Theoretical and observational studies have suggested that ram-pressure stripping by the intracluster medium can be enhanced during cluster interactions, boosting the formation of the "jellyfish" galaxies. In this work, we study the incidence of galaxies undergoing ram-pressure stripping in 52 clusters of different dynamical states. We use optical data from the WINGS/OmegaWINGS surveys and archival X-ray data to characterise the dynamical state of our cluster sample, applying eight different proxies. We then compute the number of ram-pressure stripping candidates relative to the infalling population of blue late-type galaxies within a fixed circular aperture in each cluster. We find no clear correlation between the fractions of ram-pressure stripping candidates and the different cluster dynamical state proxies considered. These fractions also show no apparent correlation with cluster mass. To construct a dynamical state classification closer to a merging "sequence", we perform a visual classification of the dynamical states of the clusters, combining information available in optical, X-ray, and radio wavelengths. We find a mild increase in the RPS fraction in interacting clusters with respect to all other classes (including post-mergers). This mild enhancement could hint at a short-lived enhanced ram-pressure stripping in ongoing cluster mergers. However, our results are not statistically significant due to the low galaxy numbers. We note this is the first homogeneous attempt to quantify the effect of cluster dynamical state on ram-pressure stripping using a large cluster sample, but even larger (especially wider) multi-wavelength surveys are needed to confirm the results.

We present the JWST Emission Line Survey (JELS), a JWST imaging programme exploiting the wavelength coverage and sensitivity of NIRCam to extend narrow-band rest-optical emission line selection into the epoch of reionization (EoR) for the first time, and to enable unique studies of the resolved ionised gas morphology in individual galaxies across cosmic history. The primary JELS observations comprise $\sim4.7\mu$m narrow-band imaging over $\sim63$ arcmin$^{2}$ designed to enable selection of H$\alpha$ emitters at z~6.1 and a host of novel emission-line samples, including [OIII] ($z\sim8.3$) and Paschen $\alpha/\beta$ ($z\sim1.5/2.8$). For the F466N/F470N narrow-band observations, the emission-line sensitivities achieved are up to $\sim2\times$ more sensitive than current slitless spectroscopy surveys (5$\sigma$ limits of 0.8-1.2$\times10^{-18}\,\text{erg s}^{-1}\text{cm}^{-2}$), corresponding to unobscured H$\alpha$ star-formation rates (SFRs) of 0.9-1.3 $\text{M}_{\odot}\text{yr}^{-1}$ at z~6.1, extending emission-line selections in the EoR to fainter populations. Simultaneously, JELS also adds F200W broadband and F212N narrow-band imaging (H$\alpha$ at z~2.23) that probes SFRs $\gtrsim5\times$ fainter than previous ground-based narrow-band studies ($\sim0.2\text{M}_{\odot}\text{yr}^{-1}$), offering an unprecedented resolved view of star formation at cosmic noon. We present the detailed JELS survey design, key data processing steps specific to the survey observations, and demonstrate the exceptional data quality and imaging sensitivity achieved. We then summarise the key scientific goals of JELS, demonstrate the precision and accuracy of the expected redshift and measured emission line recovery through detailed simulations, and present examples of spectroscopically confirmed H$\alpha$ and [OIII] emitters discovered by JELS that illustrate the novel parameter space probed.

We present cosmo_learn, an open-source python-based software package designed to simulate cosmological data and perform data-driven inference using a range of modern statistical and machine learning techniques. Motivated by the growing complexity of cosmological models and the emergence of observational tensions, cosmo_learn provides a standardized and flexible framework for benchmarking cosmological inference methods. The package supports realistic noise modeling for key observables in the late Universe, including cosmic chronometers, supernovae Ia, baryon acoustic oscillations, redshift space distortions, and gravitational wave bright sirens. We demonstrate the internal consistency of the simulated data with the input cosmology via residuals and parameter recovery using a fiducial $w$CDM model. Built-in learning and inference modules include traditional Markov Chain Monte Carlo, as well as more recent approaches such as genetic algorithms, Gaussian processes, Bayesian ridge regression, and artificial neural networks. These methods are implemented in a modular and extensible architecture designed to facilitate comparisons across inference strategies in a common pipeline. By providing a flexible and transparent simulation and learning environment, cosmo_learn supports both educational and research efforts at the intersection of cosmology, statistics, and machine learning.

We present a statistical study of spatially resolved chemical enrichment in 18 main-sequence galaxies at $z=4$--6, observed with \jwst/NIRSpec IFU as part of the ALPINE-CRISTAL-\jwst\ survey. Performing an optimized reduction and calibration procedure, including local background subtraction, light-leakage masking, stripe removal, and astrometry refinement, we achieve robust emission-line mapping on kiloparsec scales. Although line-ratio distributions vary across galaxies in our sample, we generally find mild central enhancements in [O\,\textsc{iii}]/H$\beta$, [O\,\textsc{ii}]/[O\,\textsc{iii}], [S\,\textsc{ii}]$_{6732}$/[S\,\textsc{ii}]$_{6718}$, H$\alpha$/H$\beta$, and $L_{\rm H\alpha}/L_{\rm UV}$, consistent with elevated electron density, dust obscuration, and bursty star formation accompanied by reduced metallicity and ionization parameter. These features point to inside-out growth fueled by recent inflows of pristine gas. Nevertheless, the median metallicity gradient is nearly flat over a few kpc scale, $\Delta \log({\rm O/H}) = 0.02 \pm 0.01$ dex kpc$^{-1}$, implying efficient chemical mixing through inflows, outflows, and mergers. From pixel-by-pixel stellar and emission-line characterizations, we further investigate the resolved Fundamental Metallicity Relation (rFMR). Metallicity is described by a fundamental plane with stellar mass and SFR surface densities, but with a stronger dependence on $\Sigma_{\rm SFR}$ than seen in local galaxies. Our results indicate that the regulatory processes linking star formation, gas flows, and metal enrichment were already vigorous $\sim$1 Gyr after the Big Bang, producing the nearly flat metallicity gradient and a stronger coupling between star formation and metallicity than observed in evolved systems in the local universe.

The galaxy integrated star-formation rate (SFR) surface density ($\Sigma_{\rm SFR}$) has been proposed as a valuable diagnostic of the mass accumulation in galaxies as being more tightly related to the physics of star-formation (SF) and stellar feedback than other SF indicators. In this paper, we assemble a statistical sample of 230 galaxies observed with JWST in the GLASS and CEERS spectroscopic surveys to estimate Balmer line based dust attenuations and SFRs, and UV rest-frame effective radii. We study the evolution of galaxy SFR and $\Sigma_{\rm SFR}$ in the first 1.5 Billion years of our Universe, finding that $\Sigma_{\rm SFR}$ is mildly increasing with redshift with a linear slope of $0.16 \pm 0.06$. We also explore the dependence of SFR and $\Sigma_{\rm SFR}$ on stellar mass, showing that a SF 'Main-Sequence' and a $\Sigma_{\rm SFR}$ `Main-Sequence' are in place out to z=10, with a similar slope compared to the same relations at lower redshifts. We find that the specific SFR (sSFR) and $\Sigma_{\rm SFR}$ are correlated with the [OIII]5007/[OII]3727 ratio and with indirect estimates of the escape fraction of Lyman continuum photons, hence they likely play an important role in the evolution of ionization conditions and in the escape of ionizing radiation. We also search for spectral outflow signatures in a subset of galaxies observed at high resolution, finding an outflow incidence of $2/11$ ($=20\%^{32\%}_{9\%}$) at z<6, but no evidence at z>6 (<26\%). Finally, we find a positive correlation between A$_V$ and $\Sigma_{\rm SFR}$, and a flat trend as a function of sSFR, indicating that there is no evidence of a drop of A$_V$ in extremely star-forming galaxies between z=4 and 10. This might be at odds with a dust-clearing outflow scenario, which might instead take place at redshifts $z\geq 10$, as suggested by some theoretical models.

The Southern Photometric Local Universe Survey (S-PLUS) is a project to map $\sim9300$ sq deg of the sky using twelve bands (seven narrow and five broadbands). Observations are performed with the T80-South telescope, a robotic telescope located at the Cerro Tololo Observatory in Chile. The survey footprint consists of several large contiguous areas, including fields at high and low galactic latitudes, and towards the Magellanic Clouds. S-PLUS uses fixed exposure times to reach point source depths of about $21$ mag in the $griz$ and $20$ mag in the $u$ and the narrow filters. This paper describes the S-PLUS Data Release 4 (DR4), which includes calibrated images and derived catalogues for over 3000 sq deg, covering the aforementioned area. The catalogues provide multi-band photometry performed with the tools \texttt{DoPHOT} and \texttt{SExtractor} -- point spread function (\PSF) and aperture photometry, respectively. In addition to the characterization, we also present the scientific potential of the data. We use statistical tools to present and compare the photometry obtained through different methods. Overall we find good agreement between the different methods, with a slight systematic offset of 0.05\,mag between our \PSF and aperture photometry. We show that the astrometry accuracy is equivalent to that obtained in previous S-PLUS data releases, even in very crowded fields where photometric extraction is challenging. The depths of main survey (MS) photometry for a minimum signal-to-noise ratio $S/N = 3$ reach from $\sim19.5$ for the bluer bands to $\sim21.5$ mag on the red. The range of magnitudes over which accurate \PSF photometry is obtained is shallower, reaching $\sim19$ to $\sim20.5$ mag depending on the filter. Based on these photometric data, we provide star-galaxy-quasar classification and photometric redshift for millions of objects.

The Euclid satellite will provide data on the clustering of galaxies and on the distortion of their measured shapes, which can be used to constrain and test the cosmological model. However, the increase in precision places strong requirements on the accuracy of the theoretical modelling for the observables and of the full analysis pipeline. In this paper, we investigate the accuracy of the calculations performed by the Cosmology Likelihood for Observables in Euclid (CLOE), a software able to handle both the modelling of observables and their fit against observational data for both the photometric and spectroscopic surveys of Euclid, by comparing the output of CLOE with external codes used as benchmark. We perform such a comparison on the quantities entering the calculations of the observables, as well as on the final outputs of these calculations. Our results highlight the high accuracy of CLOE when comparing its calculation against external codes for Euclid observables on an extended range of operative cases. In particular, all the summary statistics of interest always differ less than $0.1\,\sigma$ from the chosen benchmark, and CLOE predictions are statistically compatible with simulated data obtained from benchmark codes. The same holds for the comparison of correlation function in configuration space for spectroscopic and photometric observables.

Quasi-periodic eruptions (QPEs) are recurring X-ray bursts originating from the vicinity of supermassive black holes, but their driving mechanisms remain under debate. This study analyzes new NICER observations of QPEs in Ansky (a transient event in the nucleus of the galaxy SDSS J1335+0728), taken between January and June 2025. By examining flare durations, peak-to-peak recurrence times, and profiles, we compare the 2025 data with those from 2024 to investigate changes in energy, timescales, and flare shapes. The 2025 QPEs are found to be four times more energetic, with recurrence times of approximately 10 days and flare durations ranging from 2.5 to 4 days, making them both about twice as long as in 2024. Additionally, the flare profiles have become more asymmetric, showing longer decays. We explore different theoretical scenarios to explain the observed properties of the QPEs in Ansky, including evolving stream-disk interactions in an extreme mass-ratio inspiral (EMRI) system as a potential mechanism behind the observed changes in recurrence time and energetics, while also considering alternative models based on mass transfer and accretion disk instabilities. Continued observational efforts will be crucial for unveiling the nature of Ansky.

Mass loss from massive stars plays a determining role in their evolution through the upper Hertzsprung-Russell diagram. The hydrodynamic theory that describes their steady-state winds is the line-driven wind theory (m-CAK). From this theory, the mass loss rate and the velocity profile of the wind can be derived, and estimating these properly will have a profound impact on quantitative spectroscopy analyses from the spectra of these objects. Currently, the so-called beta-law, which is an approximation for the fast solution, is widely used instead of m-CAK hydrodynamics, and when the derived value is beta greater than 1.2, there is no hydrodynamic justification for these values. This review focuses on (1) a detailed topological analysis of the equation of motion (EoM), (2) solving the EoM numerically for all three different (fast and two slow) wind solutions, (3) deriving analytical approximations for the velocity profile via the LambertW function and (4) presenting a discussion of the applicability of the slow solutions.

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way.

We present a very deep CO(3-2) observation of a massive, gas-rich, main sequence, barred spiral galaxy at $z\approx1.52$. Our data were taken with the IRAM-NOEMA interferometer for a 12-antenna equivalent on-source integration time of $\sim$ 50 hours. We fit the major axis kinematics using forward modelling of a rotating disk, and then subtract the two-dimensional beam convolved best-fit model revealing signatures of planar non-circular motions in the residuals. The inferred in-plane radial velocities are remarkably large, of the order of $\approx60$ km/s. Direct comparisons with a high-resolution, simulated, gas-rich, barred galaxy, obtained with the moving mesh code AREPO and the TNG sub-grid model, show that the observed non-circular gas flows can be explained as radial flows driven by the central bar, with an inferred net inflow rate of the order of the SFR. Given the recent evidence for a higher-than-expected fraction of barred disk galaxies at cosmic noon, our results suggest that rapid gas inflows due to bars could be important evolutionary drivers for the dominant population of star-forming galaxies at the peak epoch of star and galaxy formation.

We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from JWST MIRI presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming subhalo abundance predicted by the semi-analytic model {\tt{galacticus}} (N-body simulations), we infer (Bayes factor of 10:1) m_{\rm{hm}} < 10^{7.4} \mathrm{M}_{\odot} (m_{\rm{hm}} < 10^{7.2} \mathrm{M}_{\odot}), a 0.4 dex (0.3 dex) improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of $7.4$ and $8.4$ keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos (10^6 < m/M_{\odot}<10^{10.7}) of $1.6_{-1.1}^{+2.4} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. This is consistent with {\tt{galacticus}} predictions ($0.6 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$), but in tension with recent N-body simulations ($0.3 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$). Our results are the strongest limits on WDM, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

WEAVE, the new wide-field, massively multiplexed spectroscopic survey facility for the William Herschel Telescope, will see first light in late 2022. WEAVE comprises a new 2-degree field-of-view prime-focus corrector system, a nearly 1000-multiplex fibre positioner, 20 individually deployable 'mini' integral field units (IFUs), and a single large IFU. These fibre systems feed a dual-beam spectrograph covering the wavelength range 366$-$959\,nm at $R\sim5000$, or two shorter ranges at $R\sim20\,000$. After summarising the design and implementation of WEAVE and its data systems, we present the organisation, science drivers and design of a five- to seven-year programme of eight individual surveys to: (i) study our Galaxy's origins by completing Gaia's phase-space information, providing metallicities to its limiting magnitude for $\sim$3 million stars and detailed abundances for $\sim1.5$ million brighter field and open-cluster stars; (ii) survey $\sim0.4$ million Galactic-plane OBA stars, young stellar objects and nearby gas to understand the evolution of young stars and their environments; (iii) perform an extensive spectral survey of white dwarfs; (iv) survey $\sim400$ neutral-hydrogen-selected galaxies with the IFUs; (v) study properties and kinematics of stellar populations and ionised gas in z<0.5 cluster galaxies; (vi) survey stellar populations and kinematics in $\sim25\,000$ field galaxies at $0.3\lesssim z \lesssim 0.7$; (vii) study the cosmic evolution of accretion and star formation using >1 million spectra of LOFAR-selected radio sources; (viii) trace structures using intergalactic/circumgalactic gas at z>2. Finally, we describe the WEAVE Operational Rehearsals using the WEAVE Simulator.

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability of Persistence Images (PIs) to infer parameters, comparing them to the combined Power Spectrum and Bispectrum (PS/BS). We also compare two classes of models: neural-based and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS for parameters that can be constrained, i.e., for $\{\Omega_{\rm m}, \sigma_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$. PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, highlighting the potential of persistent homology for constraining primordial non-Gaussianity. Our results indicate that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little additional or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\rm NL}^{\rm loc}$ and for $\Omega_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $\Omega_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ is additionally informed by filaments (1-cycles).