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$^{\omega}$ (0,1) and Padé$^{\omega}$ (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 $\omega_0\omega_a$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 $\omega_0\omega_a$CDM and $\Lambda$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 $\omega_0\omega_a$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 $\omega_0\omega_a$CDM parameterization, while the Deviance Information Criterion (DIC) provides \emph{strong evidence against the $\omega_0\omega_a$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$^{\omega}$ (0,1) parameterizations exhibit enhanced stability compared with the other cases here considered and, therefore, describe robust alternatives for the cosmological background.

With the upcoming space- and Moon-based gravitational-wave detectors, LISA and LGWA respectively, a new era of GW astronomy will begin with the possibility of detections of the mergers of intermediate-mass black holes (IMBHs) and supermassive black holes (SMBHs). We generate populations of synthetic black hole (BH) binaries with masses ranging from the intermediate ($10^3-10^5 M_\odot$) to the supermassive regime ($>10^5 M_\odot$), formed from the dynamical processes of merging halos and their residing galaxies, assuming that each galaxy is initially seeded with a single black hole at its centre. The aim is to estimate the rate of these BH mergers which could be detected by LISA and LGWA. Using PINOCCHIO cosmological simulation and a semi-analytical model based on GAEA, we construct a population of merging BHs by implementing a "light" seeding scheme and calculating the merging timescales using the Chandrasekhar prescription. We provide upper and lower limits of dynamical friction timescale by varying the mass of the infalling object to create "pessimistic" and "optimistic" merger rates respectively. We find that for our synthetic population of MBHs, both LGWA and LISA are able to detect more than $15$ binary IMBH mergers per year in the optimistic case, while in the pessimistic case less than $\sim5$ detections would be possible considering the entire lifetime of the detectors. For SMBHs, the rates are slightly lower in both cases. Most mergers below $z\approx4$ are detected in the optimistic case, although mergers beyond $z=8$ are also detectable at a lower rate. We find that LGWA is better suited for high-SNR IMBH detections at higher redshift, while LISA is more sensitive to massive SMBHs. Joint observations will probe the full BH mass spectrum and constrain BH formation and seeding models.

We investigate the properties of the most distant quasars ULASJ134208.10+092838.61 ($z = 7.54$), ULASJ112001.48+064124.3 ($z = 7.08$) and DELSJ003836.10-152723.6 ($z = 7.02$) studying their Optical-UV emission that shows clear evidence of the presence of an accretion disk. We model such emission applying the relativistic disk models KERRBB and SLIMBH for which we have derived some analytical approximations to describe the observed emission as a function of the black hole mass, accretion rate, spin and the viewing angle. We found that: 1] our black hole mass estimates are compatible with the ones found using the virial argument but with a smaller uncertainty; 2] assuming that the virial argument is a reliable method to have a black hole mass measurement (with no systematic uncertainties involved), we found an upper limit for the black hole spin of the three sources: very high spin values are ruled out; 3] our Eddington ratio estimates are smaller than those found in previous studies by a factor $\sim 2$: all sources are found to be sub-Eddington. Using our results, we explore the parameter space (efficiency, accretion rate) to describe the possible evolution of the black hole assuming a $\sim 10^{2-4} M_{\odot}$ seed: if the black hole in these sources formed at redshift $z = 10 - 20$, we found that the accretion has to proceed at the Eddington rate with a radiative efficiency $\eta \sim 0.1$ in order to reach the observed masses in less than $\sim 0.7$ Gyr.

It has been pointed out in arXiv:2211.17057 that our recent (published) paper might be revised, due to an incorrect evaluation of the diffusion coefficients, $D(E)$, employed in the calculations. Unfortunately, there is no indication as to where the incorrectness might be. Here we offer the opportunity to be more specific, by providing the community with the whole description of the equations involved in the calculation of $D(E)$, which is missing in the {\tt arXiv} note. In this context, we mention that no \textit{ad hoc} parameterisation has been used in our paper. Furthermore, any assumption on the injection mechanisms is explicitly described in the paper as an input factor and is obviously part of the modelisation procedure, hence the final outcome is subject to it. Finally, we discuss in a more broad context what, in this calculation of the diffusion coefficient, we believe is the key message.

Twenty-two extragalactic fast X-ray transients (FXTs) have now been discovered from two decades of Chandra data (analyzing ~259 Ms of data), with 17 associated with distant galaxies (>100 Mpc). Different mechanisms and progenitors have been proposed to explain their properties; nevertheless, after analyzing their timing, spectral parameters, host-galaxy properties, luminosity function, and volumetric rates, their nature remains uncertain. We interpret a sub-sample of nine FXTs that show a plateau or a fast-rise light curve within the framework of a binary neutron star (BNS) merger magnetar model. We fit their light curves and derive magnetar (magnetic field and initial rotational period) and ejecta (ejecta mass and opacity) parameters. This model predicts two zones: an orientation-dependent free zone (where the magnetar spin-down X-ray photons escape freely to the observer) and a trapped zone (where the X-ray photons are initially obscured and only escape freely once the ejecta material becomes optically thin). We argue that six FXTs show properties consistent with the free zone and three FXTs with the trapped zone. This sub-sample of FXTs has a similar distribution of magnetic fields and initial rotation periods to those inferred for short gamma-ray bursts (SGRBs), suggesting a possible association. We compare the predicted ejecta emission fed by the magnetar emission (called merger-nova) to the optical and near-infrared upper limits of two FXTs, XRT 141001 and XRT 210423 where contemporaneous optical observations are available. The non-detections place lower limits on the redshifts of XRT 141001 and XRT 210423 of z>1.5 and >0.1, respectively. If the magnetar remnants lose energy via gravitational waves, it should be possible to detect similar objects with the current advanced LIGO detectors out to a redshift z<0.03, while future GW detectors will be able to detect them out to z=0.5.