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Galaxy evolution emerges from the balance between cosmic gas accretion, fueling star formation, and supernova (SN) feedback, regulating the metal enrichment. Hence, the stellar mass ($M_*$) - gas metallicity relation (MZR) is key to understand the physics of galaxies. High-quality JWST data enable accurate measurements of the MZR up to redshift z=10. Our aims are to understand the observed MZR, its connection with the star formation rate (SFR), the role played by SFR stochasticity, and how it is regulated by SN feedback. We compare the MZR from the JADES, CEERS, and UNCOVER surveys, which comprise about 180 galaxies at $z=3-10$ with $10^6

PDS 456 is the most luminous RQQ at z<0.3 and can be regarded as a local counterpart of the powerful QSOs shining at Cosmic Noon. It hosts a strong nuclear X-ray ultra-fast outflow, and a massive and clumpy CO(3-2) molecular outflow extending up to 5 kpc from the nucleus. We analyzed the first MUSE WFM and AO-NFM optical integral field spectroscopic observations of PDS456. The AO-NFM observations provide an unprecedented spatial resolution, reaching up to 280 pc. Our findings reveal a complex circumgalactic medium around PDS 456, extending up to a maximum projected size of ~46 kpc. This includes a reservoir of gas with a mass of ~1e7-1e8 Modot, along with eight companion galaxies, and a multi-phase outflow. WFM and NFM MUSE data reveal an outflow on a large scale (~12 kpc from the quasar) in [OIII], and on smaller scales (within 3 kpc) with higher resolution (about 280 pc) in Halpha, respectively. The [OIII] outflow mass rate is 2.3 +/- 0.2 Modot/yr which is significantly lower than those typically found in other luminous quasars. Remarkably, the Ha outflow shows a similar scale, morphology, and kinematics to the CO(3-2) molecular outflow, with the latter dominating in terms of kinetic energy and mass outflow rate by two and one orders of magnitude, respectively. Our results therefore indicate that mergers, powerful AGN activity, and feedback through AGN-driven winds will collectively contribute to shaping the host galaxy evolution of PDS 456, and likely, that of similar objects at the brightest end of the AGN luminosity function across all redshifts. Moreover, the finding that the momentum boost of the total outflow deviates from the expected energy-conserving expansion for large-scale outflows highlights the need of novel AGN-driven outflow models to comprehensively interpret these phenomena., Comment: 15 pages, 13 figures accepted for publication in Astronomy & Astrophysics

The study of gas-phase metallicity and its spatial distribution at high redshift is crucial to understand the processes that shaped the growth and evolution of galaxies in the early Universe. Here we study the spatially resolved metallicity in three systems at $z\sim6-8$, namely A2744-YD4, BDF-3299, and COSMOS24108, with JWST NIRSpec IFU low-resolution ($R\sim100$) spectroscopic observations. These are among the highest-$z$ sources in which metallicity gradients have been probed so far. Each of these systems hosts several spatial components in the process of merging within a few kpc, identified from the rest-frame UV and optical stellar continuum and ionised gas emission line maps. The sources have heterogeneous properties, with stellar masses log($M_*/M_\odot) \sim 7.6-9.3$, star formation rates (SFRs) $\sim1-15$ $M_\odot$ yr$^{-1}$, and gas-phase metallicities 12+log(O/H) $\sim 7.7-8.3$, which exhibit a large scatter within each system. Their properties are generally consistent with those of the highest-$z$ samples to date ($z\sim3-10$), though the sources in A2744-YD4 and COSMOS24108 are at the high end of the mass-metallicity relation (MZR) defined by the $z\sim3-10$ sources. Moreover, the targets in this work follow the predicted slope of the MZR at $z\sim 6-8$ from most cosmological simulations. The gas-phase metallicity gradients are consistent with being flat in the main sources of each system. Flat metallicity gradients are thought to arise from gas mixing processes on galaxy scales, such as mergers or galactic outflows and SN winds driven by intense stellar feedback, which wash out any gradient formed in the galaxy. The existence of flat gradients at $z\sim6-8$ sets also important constraints on cosmological simulations and chemical evolution models, whose predictions on the cosmic evolution of metallicity gradients differ significantly, but are mostly limited to $z<3$ so far., Comment: 15 pages (+5 appendix); 7 figures (+8 in appendix); in production on A&A

An increasing number of observations and simulations suggests that low-power (<10$^{44}$ erg s$^{-1}$) jets may be a significant channel of feedback produced by active galactic nuclei (AGN), but little is known about their actual effect on their host galaxies from the observational point of view. We targeted four luminous type 2 AGN hosting moderately powerful radio emission ($\sim$10$^{44}$ erg s$^{-1}$), two of which and possibly a third are associated with jets, with optical integral field spectroscopy observations from the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) to analyze the properties of their ionized gas as well as the properties and effects of ionized outflows. We combined these observations with Very Large Array (VLA) and e-MERLIN data to investigate the relations and interactions between the radio jets and host galaxies. We detected ionized outflows as traced by the fast bulk motion of the gas. The outflows extended over kiloparsec scales in the direction of the jet, when present. In the two sources with resolved radio jets, we detected a strong enhancement in the emission-line velocity dispersion (up to 1000 km s$^{-1}$) perpendicular to the direction of the radio jets. We also found a correlation between the mass and the energetics of this high-velocity dispersion gas and the radio power, which supports the idea that the radio emission may cause the enhanced turbulence. This phenomenon, which is now being observed in an increasing number of objects, might represent an important channel for AGN feedback on galaxies., Comment: 18 pages, 17 figures

We present HOMERUN (Highly Optimized Multi-cloud Emission-line Ratios Using photo-ionizatioN), a new approach to modelling emission lines from photoionized gas that can simultaneously reproduce all observed line intensities from a wide range of ionization levels and with high accuracy. Our approach is based on the weighted combination of multiple single-cloud photoionization models and, contrary to previous works, the novelty of our approach consists in using the weights as free parameters of the fit and constraining them with the observed data. One of the main applications of HOMERUN is the accurate determination of gas-phase metallicities and we show that a critical point is to allow for a variation of the N/O and S/O abundance ratios which can significantly improve the quality of the fit and the accuracy of the results. Moreover, our approach provides a major improvement compared to the single-cloud, constant-pressure models commonly used in the literature. By using high-quality literature spectra of H ii regions where 10 to 20 emission lines (including several auroral lines) are detected with high signal-to-noise ratio, we show that all lines are reproduced by the model with an accuracy better than 10%. In particular, the model is able to simultaneously reproduce [O i]6300, 6363, [O ii]3726, 3729, [O iii]4959, 5007, [S ii]6717, 6731, and [S iii]9069, 9532 emission lines which, to our knowledge, is an unprecedented result. Finally, we show that the gas metallicities estimated with our models for HII regions in the Milky Way are in agreement with the stellar metallicities than the estimates based on the Te-method. Overall, our method provides a new accurate tool to estimate the metallicity and the physical conditions of the ionized gas. It can be applied to many different science cases from HII regions to AGN and wherever there are emission lines from photoionized gas., Comment: A&A in press, new version following referee report

We present a study of molecular gas, traced via CO (3-2) from ALMA data, of four z< 0.2, `radio quiet', type 2 quasars (log [L(bol)/(erg/s)] = 45.3 - 46.2; log [L(1.4 GHz)/(W/Hz)] = 23.7 - 24.3). Targets were selected to have extended radio lobes (>= 10 kpc), and compact, moderate-power jets (1 - 10 kpc; log [Pjet/(erg/s)]= 43.2 - 43.7). All targets show evidence of central molecular outflows, or injected turbulence, within the gas disks (traced via high-velocity wing components in CO emission-line profiles). The inferred velocities (Vout = 250 - 440 km/s) and spatial scales (0.6 - 1.6 kpc), are consistent with those of other samples of luminous low-redshift AGN. In two targets, we observe extended molecular gas structures beyond the central disks, containing 9 - 53 % of the total molecular gas mass. These structures tend to be elongated, extending from the core, and wrap-around (or along) the radio lobes. Their properties are similar to the molecular gas filaments observed around radio lobes of, mostly `radio loud', Brightest Cluster Galaxies. They have: projected distances of 5 - 13 kpc; bulk velocities of 100 - 340 km/s; velocity dispersion of 30 - 130 km/s; inferred mass outflow rates of 4 - 20 Msolar/yr; and estimated kinetic powers of log [Ekin/(erg/s)]= 40.3 - 41.7. Our observations are consistent with simulations that suggest moderate-power jets can have a direct (but modest) impact on molecular gas on small scales, through direct jet-cloud interactions. Then, on larger scales, jet-cocoons can push gas aside. Both processes could contribute to the long-term regulation of star formation., Comment: Accepted for publication in MNRAS; references updated; typos corrected

We present NIRSpec IFS observations of a galaxy group around the massive GS_4891 galaxy at z=3.7 in GOODS-South that includes two other two systems, GS_4891_n to the north and GS_28356 to the east. These observations, obtained as part of the GTO GA-NIFS program, allow for the first time to study the spatially resolved properties of the interstellar medium (ISM) and ionized gas kinematics of a galaxy at this redshift. Leveraging the wide wavelength range spanned with the high-dispersion grating (with resolving power R=2700) observations, covering from [OII]$\lambda$$\lambda$3726,29 to [SII]$\lambda$$\lambda$6716,31, we explore the spatial distribution of star-formation rate, nebular attenuation and gas metallicity, together with the mechanisms responsible for the excitation of the ionized gas. GS_4891 presents a clear gradient of gas metallicity (as traced by 12 + log(O/H)) by more than 0.2dex from the south-east (where a star-forming clump is identified) to the north-west. The gas metallicity in the less-massive northern system, GS_4891_n, is also higher by 0.2 dex than at the center of GS_4891, suggesting that inflows of lower-metallicity gas might be favoured in higher-mass systems. The kinematic analysis shows that GS_4891 presents velocity gradients in the ionized gas consistent with rotation. The region between GS_4891 and GS_4891_n does not present high gas turbulence which, together with the difference in gas metallicities, suggests that these two systems might be in a pre-merger stage. Finally, GS_4891 hosts an ionized outflow that extends out to r_out=1.2 kpc from the nucleus and reaches maximum velocities v_out of approximately 400 km/s. Despite entraining an outflowing mass rate of M_out$\sim$2Msun/yr, the low associated mass-loading factor, $\eta$=0.05, implies that the outflow does not have a significant impact on the star-formation activity of the galaxy., Comment: Submitted to Astronomy & Astrophysics on September 25th, 2023

The $z$~0.1 type-2 QSO J1430+1339 (the 'Teacup') is a complex galaxy showing a loop of ionised gas ~10 kpc in diameter, co-spatial radio bubbles, a compact (~1 kpc) jet, and outflow activity. We used VLT/MUSE optical integral field spectroscopic observations to characterise the properties and effects of the galactic ionised outflow from kpc up to tens of kpc scales and compare them with those of the radio jet. We detect a velocity dispersion enhancement (>300 km/s) elongated over several kpc perpendicular to the radio jet, the AGN ionisation lobes, and the fast outflow, similar to what is found in other galaxies hosting compact, low-power jets, indicating that the jet strongly perturbs the host ISM. The mass outflow rate decreases with distance from the nucleus, from around 100 $M_\odot$/yr in the inner 1-2 kpc to <0.1 $M_\odot$/yr at 30 kpc. The ionised mass outflow rate is ~1-8 times higher than the molecular one, in contrast with what is often quoted in AGN. The driver of the multi-phase outflow is likely a combination of AGN radiation and the jet. The outflow mass-loading factor (~5-10) and the molecular gas depletion time (<10$^8$ yr) indicate that the outflow can significantly affect the star formation and the gas reservoir in the galaxy. However, the fraction of the ionised outflow that is able to escape the dark matter halo potential is likely negligible. We detect blue-coloured continuum emission co-spatial with the ionised gas loop. Here, stellar populations are younger (<100-150 Myr) than in the rest of the galaxy (~0.5-1 Gyr). This constitutes possible evidence for star formation triggered at the edge of the bubble due to the compressing action of the jet and outflow ('positive feedback'), as predicted by theory. All in all, the Teacup constitutes a rich system in which AGN feedback from outflows and jets, in both its negative and positive flavours, co-exist., Comment: 26 pages, 16 figures; Astronomy & Astrophysics, in press

Massive, starbursting galaxies in the early Universe represent some of the most extreme objects in the study of galaxy evolution. One such source is HFLS3 (z~6.34), which was originally identified as an extreme starburst galaxy with mild gravitational magnification ($\mu$~2.2). Here, we present new observations of HFLS3 with the JWST/NIRSpec IFU in both low (PRISM/CLEAR; R~100) and high spectral resolution (G395H/290LP; R~2700), with high spatial resolution (~0.1") and sensitivity. Thanks to the combination of the NIRSpec data and a new lensing model with accurate spectroscopic redshifts, we find that the 3"x3" field is crowded, with a lensed arc (C, $z=6.3425\pm0.0002$), two galaxies to the south (S1 and S2, $z=6.3592\pm0.0001$), two galaxies to the west (W1, $z=6.3550\pm0.0001$; W2, $z=6.3628\pm0.0001$), and two low-redshift interlopers (G1, $z=3.4806\pm0.0001$; G2, $z=2.00\pm0.01$). We present spectral fits and morpho-kinematic maps for each bright emission line from the R2700 data for all sources except G2. From a line ratio analysis, the galaxies in component C are likely powered by star formation, while we cannot rule out or confirm the presence of AGN in the other high-redshift sources. We perform gravitational lens modelling, finding evidence for a two-source composition of the lensed central object and a comparable magnification factor ($\mu$=2.1-2.4) to previous work. The projected distances and velocity offsets of each galaxy suggest that they will merge within the next ~1Gyr. Finally, we examine the dust extinction-corrected SFR(Ha) of each z>6 source, finding that the total star formation ($510\pm140$Msol/yr, magnification-corrected) is distributed across the six z~6.34-6.36 objects over a region of diameter ~11kpc. Altogether, this suggests that HFLS3 is not a single starburst galaxy, but instead is a merging system of star-forming galaxies in the Epoch of Reionisation., Comment: 27 pages, 17 figures, accepted for publication in A&A

Studying the feedback process of Active Galactic Nuclei (AGN) requires characterising multiple kinematical components, such as rotating gas and stellar disks, outflows, inflows, and jets. To compare the observed properties with theoretical predictions of galaxy evolution and feedback models and to assess the mutual interaction and energy injection rate into the interstellar medium (ISM), one usually relies on simplified kinematic models. These models have several limitations, as they often do not take into account projection effects, beam smearing and the surface brightness distribution of the emitting medium. Here, we present MOKA3D, an innovative approach to model the 3D gas kinematics from integral field spectroscopy observations. In this first paper, we discuss its application to the case of AGN ionised outflows, whose observed clumpy emission and apparently irregular kinematics are only marginally accounted for by existing kinematical models. Unlike previous works, our model does not assume the surface brightness distribution of the gas, but exploits a novel procedure to derive it from the observations by reconstructing the 3D distribution of emitting clouds and providing accurate estimates of the spatially resolved outflow physical properties (e.g. mass rate, kinetic energy). As an example, we demonstrate the capabilities of our method by applying it to three nearby Seyfert-II galaxies observed with MUSE at the VLT and selected from the MAGNUM survey, showing that the complex kinematic features observed can be described by a conical outflow with a constant radial velocity field and a clumpy distribution of clouds., Comment: 17 pages, 14 figures

The novel Gaia Multi Peak (GMP) technique has proven to be able to successfully select dual and lensed AGN candidates at sub-arcsec separations. Both populations are important because dual AGN represent one of the central, still largely untested, predictions of lamdaCDM cosmology, and compact lensed quasars allow to probe the central regions of the lensing galaxies. In this work, we present high spatial resolution spectroscopy of twelve GMP-selected systems. We use the the adaptive-optics assisted integral-field spectrograph MUSE at VLT to resolve each system and study the nature of each component. All the targets reveal the presence of two components confirming the GMP selection. We classify five targets as dual AGN, two as lensed systems, and five as a chance alignment of a star and and AGN. Having separations between 0.30" and 0.86", these dual and lensed systems are, to date, among the most compact ever discovered at z >0.3. This is the largest sample of distant dual AGN with sub-arcsec separations ever presented in a single paper., Comment: 16 pages, 11 figures

The Gaia-Multi-Peak (GMP) technique can be used to identify large numbers of dual or lensed AGN candidates at sub-arcsec separation, allowing us to study both multiple SMBHs in the same galaxy and rare, compact lensed systems. The observed samples can be used to test the predictions of the models of SMBH merging once 1) the selection function of the GMP technique is known, and 2) each system has been classified as dual AGN, lensed AGN, or AGN/star alignment. Here we show that the GMP selection is very efficient for separations above 0.15'' when the secondary (fainter) object has magnitude G<20.5. We present the spectroscopic classification of five GMP candidates using VLT/ERIS and Keck/OSIRIS, and compare them with the classifications obtained from: a) the near-IR colors of 7 systems obtained with LBT/LUCI, and b) the analysis of the total, spatially-unresolved spectra. We conclude that colors and integrated spectra can already provide reliable classifications of many systems. Finally, we summarize the confirmed dual AGNs at z>0.5 selected by the GMP technique, and compare this sample with other such systems from the literature, concluding that GMP can provide a large number of confirmed dual AGNs at separations below 7 kpc., Comment: 14 pages,A&A, in press

The factor relating CO emission to molecular hydrogen column density, XCO, is still subject to uncertainty, in particular at low metallicity. Here, to quantify XCO at two different spatial resolutions, we exploit a dust-based method together with ALMA 12-m and ACA data and HI maps of three nearby metal-poor starbursts, NGC625, NGC1705, and NGC5253. Dust opacity at 250pc resolution is derived based on dust temperatures estimated by fitting two-temperature modified blackbodies to Herschel PACS data. By using the HI maps, we are then able to estimate dust-to-gas ratios in the atomic-gas dominated regions, and infer total gas column densities and H2 column densities as the difference with HI. Finally, from the ACA CO(1-0) maps, we derive XCO. We use a similar technique with 40 pc ALMA 12-m data for the three galaxies, but instead derive dust attenuation at 40 pc resolution from reddening maps based on VLT/MUSE data. At 250 pc resolution, XCO $\sim$ 10^22 - 10^23 cm^-2 / K.km/s, 5-1000 times the Milky Way value, with much larger values than would be expected from a simple metallicity dependence. Instead at 40 pc resolution, XCO again shows large variation, but is roughly consistent with a power-law metallicity dependence, given the Z $\sim$ 1/3 Zsun metal abundances of our targets. The large scatter in both estimations could imply additional parameter dependence, that we have investigated by comparing XCO with the observed velocity-integrated brightness temperatures, ICO, as predicted by recent simulations. Indeed, larger XCO is significantly correlated with smaller ICO, but with slightly different slopes and normalizations than predicted by theory. Such behavior can be attributed to the increasing fraction of CO-faint H2 gas with lower spatial resolution. This confirms the idea the XCO is multi-variate, depending not only on metallicity but also on CO brightness temperature and beam size., Comment: A&A, in press (16 figures, 1 appendix)

The existence of multiple active galactic nuclei (AGN) at small projected distances on the sky is due to either the presence of multiple, in-spiraling SMBHs, or to gravitational lensing of a single AGN. Both phenomena allow us to address important astrophysical and cosmological questions. However, few kpc-separation multiple AGN are currently known. Recently, the newly-developed Gaia Multi peak (GMP) method provided numerous new candidate members of these populations. We present spatially resolved, integral-field spectroscopy of a sample of four GMP-selected multiple AGNs candidates. In all of these systems, we detect two or more components with sub-arcsec separations. We find that two of the systems are dual AGNs, one is either an intrinsic triple or a lensed dual AGN, while the last system is a chance AGN/star alignment. Our observations double the number of confirmed multiple AGNs at projected separations below 7 kpc at z > 0.5, present the first detection of a possible triple AGN in a single galaxy at z > 0.5, and successfully test the GMP method as a novel technique to discover previously unknown multiple AGNs., Comment: 6 pages, 2 figures

We present a multifrequency analysis of the radio galaxy 3CR 196.1 ($z = 0.198$), associated with the brightest galaxy of the cool core cluster CIZAJ0815.4-0303. This nearby radio galaxy shows a hybrid radio morphology and an X-ray cavity, all signatures of a turbulent past activity, potentially due to merger events and AGN outbursts. We present results of the comparison between $Chandra$ and VLT/MUSE data for the inner region of the galaxy cluster, on a scale of tens of kpc. We discovered H$\alpha$ + [N II]$\lambda6584$ emission spatially associated with the X-ray cavity (at $\sim$10 kpc from the galaxy nucleus) instead of with its rim. This result differs from previous discoveries of ionized gas surrounding X-ray cavities in other radio galaxies harbored in galaxy clusters and could represent the first reported case of ionized gas filling an X-ray cavity, either due to different AGN outbursts or to the cooling of warm ($10^4

This seventh paper of the MUse RAdio Loud Emission lines Snapshot (MURALES) project presents the results of the observations obtained with the VLT/MUSE integral field spectrograph of 3C radio sources and discusses the optical spectral properties of the nuclei of 26 objects with 0.3

Baryonic feedback is expected to play a key role in regulating the star formation of low-mass galaxies by producing galaxy-scale winds associated with mass-loading factors $\beta\!\sim\!1\!-\!50$. We have tested this prediction using a sample of 19 nearby systems with stellar masses $10^7\!<\!M_\star/{\rm M}_{\odot}\!<\!10^{10}$, mostly lying above the main sequence of star-forming galaxies. We used MUSE@VLT optical integral field spectroscopy to study the warm ionised gas kinematics of these galaxies via a detailed modelling of their H$\alpha$ emission line. The ionised gas is characterised by irregular velocity fields, indicating the presence of non-circular motions of a few tens of km/s within galaxy discs, but with intrinsic velocity dispersion of $40$-$60$ km/s that are only marginally larger than those measured in main-sequence galaxies. Galactic winds, defined as gas at velocities larger than the galaxy escape speed, encompass only a few percent of the observed fluxes. Mass outflow rates and loading factors are strongly dependent on $M_\star$, star formation rate (SFR), SFR surface density and specific SFR. For $M_\star$ of $10^8$ M$_\odot$ we find $\beta\simeq0.02$, which is more than two orders of magnitude smaller than the values predicted by theoretical models of galaxy evolution. In our galaxy sample, baryonic feedback stimulates a gentle gas cycle rather than causing a large-scale blow out., Comment: 26 pages, 12 figures, accepted by A&A

We present integral field spectroscopic observations of NGC 5972 obtained with the Multi Unit Spectroscopic Explorer (MUSE) at VLT. NGC 5972 is a nearby galaxy containing both an active galactic nucleus (AGN), and an extended emission line region (EELR) reaching out to $\sim 17$ kpc from the nucleus. We analyze the physical conditions of the EELR using spatially-resolved spectra, focusing on the radial dependence of ionization state together with the light travel time distance to probe the variability of the AGN on $\gtrsim 10^{4}$ yr timescales. The kinematic analysis suggests multiple components: (a) a faint component following the rotation of the large scale disk; (b) a component associated with the EELR suggestive of extraplanar gas connected to tidal tails; (c) a kinematically decoupled nuclear disk. Both the kinematics and the observed tidal tails suggest a major past interaction event. Emission line diagnostics along the EELR arms typically evidence Seyfert-like emission, implying that the EELR was primarily ionized by the AGN. We generate a set of photoionization models and fit these to different regions along the EELR. This allows us to estimate the bolometric luminosity required at different radii to excite the gas to the observed state. Our results suggests that NGC 5972 is a fading quasar, showing a steady gradual decrease in intrinsic AGN luminosity, and hence the accretion rate onto the SMBH, by a factor $\sim 100$ over the past $5 \times 10^{4}$ yr., Comment: To be published in The Astrophysical Journal

We present observations obtained with the VLT/MUSE optical integral field spectrograph of the radio source 3C277.3, located at a redshift of 0.085 and associated with the galaxy Coma A. An emission line region fully enshrouds the double-lobed radio source, which is ~60 kpc x 90 kpc in size. Based on the emission line ratios, we identified five compact knots in which the gas ionization is powered by young stars located as far as ~60 kpc from the host. The emission line filaments surrounding the radio emission are compatible with ionization from fast shocks (with a velocity of 350-500 km/s), but a contribution from star formation occurring at the edges of the radio source is likely. Coma A might be a unique example in the local Universe in which the expanding outflow triggers star formation throughout the whole radio source., Comment: Pre-proofs version - Accepted for publication in A&A

Starting from a Born-Oppenheimer decomposition of the Wheeler-DeWitt equation for the quantum cosmology of the matter-gravity system, we have performed a Wigner-Weyl transformation and obtained equations involving a Wigner function for the scale factor and its conjugate momentum. This has allowed us to study in more detail than previously the approach to the classical limit of gravitation and the way time emerges in such a limit. To lowest order we reproduce the Friedmann equation and the previously obtained equation for the evolution of matter. We also obtain expressions for higher order corrections to the semi-classical limit., Comment: 15 pages, no figures

We present the analysis of X-ray and optical observations of gas filaments observed in the radio source 3CR 318.1, associated with NGC 5920, the Brightest Cluster Galaxy (BCG) of MKW 3s, a nearby cool core galaxy cluster. This work is one of the first X-ray and optical analyses of filaments in cool core clusters carried out using MUSE observations. We aim at identifying the main excitation processes responsible for the emission arising from these filaments. We complemented the optical VLT/MUSE observations, tracing the colder gas phase, with X-ray $\textit{Chandra}$ observations of the hotter highly ionized gas phase. Using the MUSE observations, we studied the emission line intensity ratios along the filaments to constrain the physical processes driving the excitation, and, using the $\textit{Chandra}$ observations, we carried out a spectral analysis of the gas along these filaments. We found a spatial association between the X-ray and optical morphology of these filaments, which are colder and have lower metal abundance than the surrounding intra-cluster medium (ICM), as already seen in other BCGs. Comparing with previous results from the literature for other BCGs, we propose that the excitation process that is most likely responsible for these filaments emission is a combination of star formation and shocks, with a likely contribution from self-ionizing, cooling ICM. Additionally, we conclude that the filaments most likely originated from AGN-driven outflows in the direction of the radio jet., Comment: 9 pages, 5 figures, ApJL accepted, pre-proof version

Outflows driven by active galactic nuclei (AGN) are expected to have a significant impact on the host galaxy evolution, but it is still debated how they are accelerated and propagate on galaxy-wide scales. This work addresses these questions by studying the link between X-ray, nuclear ultra-fast outflows (UFOs) and extended ionised outflows, for the first time in two quasars close to the peak of AGN activity ($z\sim2$), where AGN feedback is expected to be more effective. As targets, we selected two multiple-lensed quasars at $z\sim1.5$, HS 0810+2554 and SDSS J1353+1138, known to host UFOs and observed with the near-IR integral field spectrometer SINFONI at the VLT. We performed a kinematical analysis of the [O III]$\lambda$5007 optical emission line, in order to trace the presence of ionised outflows. We detected spatially resolved ionised outflows in both galaxies, extended more than 8 kpc and moving up to $v>2000$ km/s. We derived mass outflow rates of $\sim$12 M$_{sun}$/yr and $\sim$2 M$_{sun}$/yr for HS 0810+2554 and SDSS J1353+1138. Comparing with the co-hosted UFO energetics, the ionised outflow energetics in HS 0810+2554 is broadly consistent with a momentum-driven regime of wind propagation, while in SDSS J1353+1138 it differs by a factor of $\sim$100 from theoretical predictions, requiring either a massive molecular outflow or a high variability of the AGN activity to account for such a discrepancy. By additionally considering our results with those from the small sample of well-studied objects (all local but one), with both UFO and extended (ionised/atomic/molecular) outflow detections, we found that in 10 out of 12 galaxies the large-scale outflow energetics is consistent with the theoretical predictions of either a momentum- or an energy-driven scenario. This suggests that such models explain relatively well the acceleration mechanism of AGN-driven winds on large scales., Comment: 19 pages, 9 figures. Accepted for publication in A&A

Outflows accelerated by AGN are commonly observed in the form of coherent, mildly collimated high-velocity gas directed along the AGN ionisation cones and kinetically powerful (>$10^{44-45}$ erg/s) jets. Recent works found that outflows can also be accelerated by low-power (<$10^{44}$ erg/s) jets, and the most recent cosmological simulations indicate that these are the dominant source of feedback on sub-kpc scales. We study the relation between radio jets and the distribution and kinematics of the ionised gas in IC 5063, NGC 5643, NGC 1068, and NGC 1386 as part of our MAGNUM survey of nearby Seyfert galaxies. All these objects host a small-scale (<1 kpc) low-power (<$10^{44}$ erg/s) radio jet that has small inclinations (<45\deg) with respect to the galaxy disc. We employed seeing-limited optical integral field spectroscopic observations from MUSE at VLT to obtain flux, kinematic, and excitation maps of the extended ionised gas, that we compared with archival radio images and Chandra X-ray observations. We detect a strong (up to >800-1000 km/s), extended (>1 kpc) and shock-excited emission-line velocity spread perpendicular to the AGN ionisation cones and jets in all four targets. These broad and symmetric line profiles are not associated with a single coherent velocity of the gas, differently from the 'classical' asymmetric-line outflow observed along the ionisation cones and jets. We interpret the observed phenomenon as due to the action of the jets perturbing the gas in the galaxy disc. These intense and extended velocity spreads perpendicular to AGN jets and cones are indeed currently only observed in galaxies hosting a low-power jet whose inclination is sufficiently low with respect to the galaxy disc to impact on and strongly affect its material. In line with cosmological simulations, our results demonstrate that low-power jets are indeed capable of affecting the host galaxy., Comment: 19 pages, 13 figures. Astronomy & Astrophysics, in press

The scope of this paper is to compare two different approaches for solving the Wheeler-DeWitt (WDW) equation in the presence of homogeneous matter (inflaton) and perturbations around it. The standard Born-Oppenheimer (BO) decomposition, which consists of factorizing out the gravitational wave function and then defining the flow of the time through it, and a more general BO decomposition where the whole minisuperspace wave function is factorized out. The two approaches are compared, for simplicity, in the case of a minimally coupled inflaton with a flat potential. The consistency of the latter decomposition is checked against the former by comparing the resulting perturbation (Mukhanov-Sasaki) equations. Finally a few solutions to the homogeneous WDW not suitable for the traditional BO treatment are presented and the corresponding Mukhanov-Sasaki equations are evaluated., Comment: 21 pages, no figures

We use MUSE adaptive optics (AO) data in Narrow Field Mode to study the properties of the ionised gas in MR 2251-178 and PG 1126-041, two nearby (z~0.06) bright quasars hosting sub-pc scale Ultra Fast Outflows (UFOs) detected in the X-ray band. We decompose the optical emission from diffuse gas into a low- and a high-velocity components. The former is characterised by a clean, regular velocity field and a low (~80 km/s) velocity dispersion. It traces regularly rotating gas in PG 1126-041, while in MR 2251-178 it is possibly associated to tidal debris from a recent merger or flyby. The other component is found to be extended up to a few kpc from the nuclei, and shows a high (~800 km/s) velocity dispersion and a blue-shifted mean velocity, as expected from AGN-driven outflows. We estimate mass outflow rates up to a few Mo/yr and kinetic efficiencies between 0.1-0.4 per cent, in line with those of galaxies hosting AGNs of similar luminosity. The momentum rates of these ionised outflows are comparable to those measured for the UFOs at sub-pc scales, consistent with a momentum-driven wind propagation. Pure energy-driven winds are excluded unless about 100x additional momentum is locked in massive molecular winds. By comparing the outflow properties of our sources with those of a small sample of well-studied QSOs hosting UFOs from the literature, we find that winds seem to systematically lie either in a momentum-driven or in an energy-driven regime, indicating that these two theoretical models bracket very well the physics of AGN-driven winds., Comment: 18 pages, 10 figures. Key figures are 4 and 9. Accepted for publication in A&A

Sources at the brightest end of QSO luminosity function during the peak epoch of star formation and black hole accretion (z~2-4, i.e. Cosmic noon) are privileged sites to study the feeding & feedback cycle of massive galaxies. We perform the first systematic study of cold gas properties in the most luminous QSOs, by characterising their host-galaxies and environment. We analyse ALMA, NOEMA and JVLA observations of FIR continuum, CO and [CII] emission lines in eight QSOs ($L_{\rm Bol}>3\times10^{47}$ erg/s) from the WISSH sample at z~2.4-4.7. We report a 100% emission line detection rate and a 80% detection rate in continuum emission, and we find CO emission to be consistent with the steepest CO ladders observed so far. Sub-mm data reveal presence of (one or more) bright companion galaxies around 80% of WISSH QSOs, at projected distances of 6-130 kpc. We observe a variety of sizes for the molecular gas reservoirs (1.7-10 kpc), associated with rotating disks with disturbed kinematics. WISSH QSOs typically show lower CO luminosity and higher star formation efficiency than FIR matched, z~0-3 main-sequence galaxies, implying that, given the observed SFR ~170-1100 $M_\odot$/yr, molecular gas is converted into stars on <50 Myr. Most targets show extreme dynamical to black-hole mass ratios $M_{\rm dyn}/M_{\rm BH}\sim3-10$, two orders of magnitude smaller than local relations. The molecular gas fraction in WISSH hosts is lower by a factor of ~10-100 than in star forming galaxies with similar $M_*$. WISSH QSOs undergo an intense growth phase of both the central SMBH and host-galaxy. They pinpoint high-density sites where giant galaxies assemble and mergers play a major role in the build-up of the final host-galaxy mass. The observed low molecular gas fraction and short depletion timescale are likely due to AGN feedback, as traced by fast AGN-driven ionised outflows in all our targets., Comment: Accepted for publication in A&A

Galactic outflows are known to consist of several gas phases, however, so far the connection between these multiple phases has been investigated little and only in a few objects. In this paper, we analyse MUSE/VLT data of 26 local (U)LIRGs and study their ionised and neutral atomic phases. We also include objects from the literature to obtain a total sample of 31 galaxies with spatially resolved multi-phase outflow information. We find that the ionized phase of the outflows has on average an electron density three times higher than the disc ($n_{\rm e, disc}$ $\sim$ 145 cm$^{-3}$ vs $n_{\rm e, outflow}$ $\sim$ 500 cm$^{-3}$), suggesting that cloud compression in the outflow is more important that cloud dissipation. We find that the difference in extinction between outflow and disc correlates with the outflow gas mass. Together with the analysis of the outflow velocities, this suggests that at least some of the outflows are associated with the ejection of dusty clouds from the disc. This may support models where radiation pressure on dust contributes to driving galactic outflows. The presence of dust in outflows is relevant for potential formation of molecules inside them. We combine our data with millimetre data to investigate the molecular phase. We find that the molecular phase accounts for more than 60 $\%$ of the total mass outflow rate in most objects and this fraction is higher in AGN-dominated systems. The neutral atomic phase contributes of the order of 10 $\%$, while the ionized phase is negligible. The ionized-to-molecular mass outflow rate declines slightly with AGN luminosity, although with a large scatter., Comment: 33 pages, 26 figures, accepted

We investigated the interstellar medium (ISM) properties in the central regions of nearby Seyfert galaxies characterised by prominent conical or bi-conical outflows belonging to the MAGNUM survey by exploiting the unprecedented sensitivity, spatial and spectral coverage of the integral field spectrograph MUSE at the Very Large Telescope. We developed a novel approach based on the gas and stars kinematics to disentangle high-velocity gas in the outflow from gas in the disc to spatially track the differences in their ISM properties. This allowed us to reveal the presence of an ionisation structure within the extended outflows that can be interpreted with different photoionisation and shock conditions, and to trace tentative evidence of outflow-induced star formation (''positive'' feedback) in a galaxy of the sample, Centaurus A., Comment: 5 pages, 3 figures. To appear in Proceedings of IAU Symposium 359 (T. Storchi-Bergmann, R. Overzier, W. Forman & R. Riffel, eds.)

We illustrate the recently proposed generalized unimodular gravity using simple examples of the Friedmann, Kantowski-Sachs and Schwarzschild geometries and show that it can be further generalized and reveal some unexpected and interesting effects., Comment: 6 pages, to be published in Journal of Experimental and Theoretical Physics Letters

We present the highest resolution --- 15 pc (0.03'') --- ALMA $^{12}$CO(2-1) line emission and 1.3mm continuum maps, tracers of the molecular gas and dust, respectively, in the nearby merging galaxy system NGC 6240, that hosts two supermassive black holes growing simultaneously. These observations provide an excellent spatial match to existing Hubble optical and near-infrared observations of this system. A significant molecular gas mass, $\sim$9$\times$10$^9$M$_\odot$, is located in between the two nuclei, forming a clumpy stream kinematically dominated by turbulence, rather than a smooth rotating disk as previously assumed from lower resolution data. Evidence for rotation is seen in the gas surrounding the southern nucleus, but not in the northern one. Dynamical shells can be seen, likely associated with nuclear supernovae remnants. We further detect the presence of significant high velocity outflows, some of them reaching velocities $>$500 km/s, affecting a significant fraction, $\sim$11\% of the molecular gas in the nuclear region. Inside the spheres of influence of the northern and southern supermassive black holes we find molecular masses of 7.4$\times$10$^8$M$_\odot$ and 3.3$\times$10$^9$M$_\odot$, respectively. We are thus directly imaging the reservoir of gas that can accrete onto each supermassive black hole. These new ALMA maps highlight the critical need for high resolution observations of molecular gas in order to understand the feeding of supermassive black holes and its connection to galaxy evolution in the context of a major galaxy merger., Comment: 27 pages, 13 figures, accepted for publication by The Astrophysical Journal

We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the problem of the introduction of time is addressed and a generalized method, with respect to that used for the minimal coupling case, is illustrated. Such a generalized method can be applied to the universe wave function when, through the Born-Oppenheimer factorization, we decompose it into a part which contains the minisuperspace degrees of freedom and another which describes the perturbations., Comment: 24 pages, no figures

We study the Wheeler-DeWitt equation for a class of induced gravity models in the minisuperspace approximation. In such models a scalar field nonminimally coupled to gravity determines the effective Newton's constant. For simplicity our analysis is limited to power-law potentials for the scalar field which have exact classical solutions. We show that these models have exact solutions also when quantised. Finally the Einstein Frame form of these solutions is obtained and a classical-quantum correspondence is found. Realistic induced gravity models also must include a symmetry breaking term which is needed in order to obtain a gravitational constant, successful inflation and a subsequent standard cosmological evolution. Nonetheless the potentials considered are important as they may describe the inflationary phase when the symmetry breaking part of the potential is negligible., Comment: 8 pages, no figures

We present observations of a complete sub-sample of 20 radio galaxies from the Third Cambridge Catalog (3C) with redshift <0.3 obtained from VLT/MUSE optical integral field spectrograph. These data have been obtained as part of the survey MURALES (a MUse RAdio Loud Emission line Snapshot survey) with the main goal of exploring the Active Galactic Nuclei (AGN) feedback process in a sizeable sample of the most powerful radio sources at low redshift. We present the data analysis and, for each source, the resulting emission line images and the 2D gas velocity field. Thanks to their unprecedented depth (the median 3 sigma surface brightness limit in the emission line maps is 6X10^-18 erg s-1 cm-2 arcsec-2, these observations reveal emission line structures extending to several tens of kiloparsec in most objects. In nine sources the gas velocity shows ordered rotation, but in the other cases it is highly complex. 3C sources show a connection between radio morphology and emission line properties. Whereas, in three of the four Fanaroff and Riley Class I radio galaxies (FRIs), the line emission regions are compact, ~1 kpc in size; in all but one of the Class II radiogalaxies FRIIs, we detected large scale structures of ionized gas with a median extent of 17 kpc. Among the FRIIs, those of high and low excitation show extended gas structures with similar morphological properties, suggesting that they both inhabit regions characterized by a rich gaseous environment on kpc scale., Comment: Accepted for publication in A&A

We investigated the interstellar medium properties of the disc and outflowing gas in the central regions of nine nearby Seyfert galaxies, all characterised by prominent outflows. These objects are part of the Measuring Active Galactic Nuclei Under MUSE Microscope survey, which aims to probe their physical conditions and ionisation mechanism by exploiting MUSE unprecedented sensitivity. We studied the different properties of the gas in the disc and outflow with spatially and kinematically resolved maps by dividing the strongest emission lines in velocity bins. We associated the core of the lines with the disc, consistent with the stellar velocity, and the redshifted and the blueshifted wings with the outflow. We find that the outflowing gas is characterised by higher values of density and ionisation parameter than the disc, which presents a higher dust extinction. Moreover, we distinguish high- and low-ionisation regions across the portion of spatially resolved narrow-line region traced by the outflowing gas. The high-ionisation regions characterised by the lowest [NII]/H{\alpha} and [SII]/H{\alpha} line ratios generally trace the innermost parts along the axis of the emitting cones where the [SIII]/[SII] line ratio is enhanced, while the low-ionisation regions follow the cone edges and/or the regions perpendicular to the axis of the outflows, also characterised by a higher [OIII] velocity dispersion. A possible scenario to explain these features relies on the presence of two distinct populations of line emitting clouds: one is optically thin to the radiation and is characterised by the highest excitation, while the other is optically thick and is impinged by a filtered, and thus harder, radiation field which generates strong low-excitation lines. The highest values of [NII]/H{\alpha} and [SII]/H{\alpha} line ratios may be due to shocks and/or a hard filtered radiation field from the AGN., Comment: 28 pages, 19 figures. Forthcoming article in A&A

We observed the FRII radio galaxy 3C459 (z=0.22) with the MUSE spectrograph at the Very Large Telescope (VLT) as part of the MURALES project (a MUse RAdio Loud Emission line Snapshot survey). We detected diffuse nuclear emission and a filamentary ionized gas structure forming a one-sided, triangular-shaped region extending out to $\sim$80 kpc. The central emission line region is dominated by two compact knots of similar flux: the first (N1) cospatial with the radio core and the (N2) second located 1.2" (5.3 kpc) to the SE. The two regions differ dramatically from the point of view of velocity (with an offset of ~400 km/s), line widths, and line ratios. This suggests that we are observing a dual AGN system formed by a radio loud AGN and type 2 QSO companion, which is the result of the recent merger that also produced its disturbed host morphology. The alternative possibility that N2 is just a bright emission line knot resulting from, for example, a jet-cloud interaction, is disfavored because of 1) the presence of a high ionization bicone whose apex is located at N2; 2) the observed narrow line widths; 3) its line luminosity (~10^42 erg s-1) typical of luminous QSOs; and 4) its location, which is offset from the jet path. The putative secondary AGN must be highly obscured, since we do not detect any emission in the Chandra and infrared Hubble Space Telescope images., Comment: 6 pages, 6 figures, A&A in press

Ionized outflows, revealed by broad asymmetric wings of the [OIII] line, are commonly observed in AGN but the low intrinsic spatial resolution of observations has generally prevented a detailed characterization of their properties. The MAGNUM survey aims at overcoming these limitations by focusing on the nearest AGN, including NGC 1365, a nearby Seyfert galaxy (D~17 Mpc), hosting a low-luminosity AGN (Lbol ~ 2x10^43 erg/s). We want to obtain a detailed picture of the ionized gas in the central ~5 kpc of NGC 1365 in terms of physical properties, kinematics, and ionization mechanisms. We also aim to characterize the warm ionized outflow as a function of distance from the nucleus and its relation with the nuclear X-ray wind. We employed VLT/MUSE optical integral field spectroscopic observations to investigate the warm ionized gas and Chandra ACIS-S X-ray data for the hot highly-ionized phase. We obtained flux, kinematic, and diagnostic maps of the optical emission lines, which we used to disentangle outflows from disk motions and measure the gas properties down to a spatial resolution of ~70 pc. [OIII] emission mostly traces an AGN-ionized kpc-scale biconical outflow with velocities up to ~200 km/s. H{\alpha} emission traces instead star formation in a circumnuclear ring and along the bar, where we detect non-circular motions. Soft X-rays are mostly due to thermal emission from the star-forming regions, but we could isolate the AGN photoionized component which matches the [OIII] emission. The mass outflow rate of the extended ionized outflow matches that of the nuclear X-ray wind and then decreases with radius. However, the hard X-ray emission from the circumnuclear ring suggests that star formation might contribute to the outflow. The integrated mass outflow rate, kinetic energy rate, and outflow velocity are broadly consistent with the typical relations observed in more luminous AGN., Comment: Accepted for publication on Astronomy and Astrophysics. 22 pages, 14 figures

We study molecular outflows in a sample of 45 local galaxies, both star forming and AGN, primarily by using CO data from the ALMA archive and from the literature. For a subsample we also compare the molecular outflow with the ionized and neutral atomic phases. We infer an empirical analytical function relating the outflow rate simultaneously to the SFR, $L_{\rm AGN}$, and galaxy stellar mass; this relation is much tighter than the relations with the individual quantities. The outflow kinetic power shows a larger scatter than in previous, more biased studies, spanning from 0.1 to 5 per cent of $L_{\rm AGN}$, while the momentum rate ranges from 1 to 30 times $L_{\rm AGN}/c$, indicating that these outflows can be both energy-driven, but with a broad range of coupling efficiencies with the ISM, and radiation pressure-driven. For about 10 per cent of the objects the outflow energetics significantly exceed the maximum theoretical values; we interpret these as 'fossil outflows' resulting from activity of a past strong AGN, which has now faded. We estimate that, in the stellar mass range probed here ($>$ 10$^{10}~\rm M_{\odot}$), less than 5 per cent of the outflowing gas escapes the galaxy. The molecular gas depletion time associated with the outflow can be as short as a few million years in powerful AGN, however, the total gas (H$_2$+HI) depletion times are much longer. Altogether, our findings suggest that even AGN-driven outflows might be relatively ineffective in clearing galaxies of their entire gas content, although they are likely capable of clearing and quenching the central region., Comment: 33 pages, 29 figures, accepted by MNRAS

In the context of Quantum Cosmology and the Wheeler-DeWitt equation we investigate the possible effects of a non semiclassical wave-function of the universe on the evolution of the inflationary perturbations. These are associated with the quantum behaviour of the homogenous degrees of freedom (in particular the radius of the universe) in the early stages of the inflationary expansion, which in turn can affect the dynamics of the trans-Planckian modes of the fields present. The existence of a bounce for the homogeneous gravitational wave-function is studied. This can lead to an interference between a contracting and an expanding universe and, as a consequence, to the above quantum gravitational effects on the primordial spectra. In the traditional study of the inflationary fluctuations such effects are neglected and a quasi-classical behaviour for the homogeneous inflaton-gravity system is taken., Comment: 14 pages, 1 figure

We have considered the Pauli-Zeldovich mechanism for the cancellation of the ultraviolet divergences in vacuum energy. This mechanism arises because bosons and fermions give contributions of the opposite signs. In contrast with the preceding papers devoted to this topic wherein mainly free fields were studied, here we have taken their interactions into account to the lowest order of perturbation theory. We have constructed some simple toy models having particles with spin 0 and spin 1/2, where masses of the particles are equal while the interactions can be quite non-trivial., Comment: 12 pages

We report observations of the radio galaxy 3C317 (at z=0.0345) located at the center of the Abell cluster A2052, obtained with the VLT/MUSE integral field spectrograph. The Chandra images of this cluster show cavities in the X-ray emitting gas, which were produced by the expansion of the radio lobes inflated by the active galactic nucleus (AGN). Our exquisite MUSE data show with unprecedented detail the complex network of line emitting filaments enshrouding the northern X-ray cavity. We do not detect any emission lines from the southern cavity, with a luminosity asymmetry between the two regions higher than about 75. The emission lines produced by the warm phase of the interstellar medium (WIM) enable us to obtain unique information on the properties of the emitting gas. We find dense gas (up to 270 cm-3) that makes up part of a global quasi spherical outflow that is driven by the radio source, and obtain a direct estimate of the expansion velocity of the cavities (265 km s-1). The emission lines diagnostic rules out ionization from the AGN or from star-forming regions, suggesting instead ionization from slow shocks or from cosmic rays. The striking asymmetric line emission observed between the two cavities contrasts with the less pronounced differences between the north and south sides in the hot gas; this represents a significant new ingredient for our understanding of the process of the exchange of energy between the relativistic plasma and the external medium. We conclude that the expanding radio lobes displace the hot tenuous phase of the interstellar medium (ISM), but also impact the colder and denser ISM phases. These results show the effects of the AGN on its host and the importance of radio mode feedback., Comment: 7 pages, 9 figures, A&A in press

We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We also write down the solution for the Bianchi-I Universe in the induced gravity cosmology., Comment: 11 pages, 3 figures, final version, to appear in Physical Review D

We study integrable models in the Bianchi I metric case with scalar fields minimally and non-minimally coupled with gravity and the correspondence between their general solutions. Using the model with a minimally coupled scalar field and a constant potential as an example, we demonstrate how to obtain the general solutions of the corresponding models in the Jordan frame., Comment: 6 pages, v2: minor corrections, references added

We study the integrable model with minimally and non-minimally coupled scalar fields and the correspondence of their general solutions. Using the model with a minimally coupled scalar field and a the constant potential as an example we demonstrate the difference between the general solutions of the corresponding models in the Jordan and the Einstein frames., Comment: 6 pages