A bias-free cosmological analysis with quasars alleviating H0_{0} tension

Cosmological models and their parameters are widely debated because of theoretical and observational mismatches of the standard cosmological model, especially the current discrepancy between the value of the Hubble constant, H$_{0}$, obtained by Type Ia supernovae (SNe Ia), and the cosmic microwave background radiation (CMB). Thus, considering high-redshift probes like quasars (QSOs), having intermediate redshifts between SNe Ia and CMB, is a necessary step. In this work, we use SNe Ia and the most updated QSO sample, reaching redshifts up to z ∼ 7.5, applying the Risaliti–Lusso QSO relation based on a nonlinear relation between ultraviolet and X-ray luminosities. We consider this relation both in its original form and corrected for selection biases and evolution in redshift through a reliable statistical method also accounting for the circularity problem. We also explore two approaches: with and without calibration on SNe Ia. We then investigate flat and nonflat standard cosmological models and a flat $_{w}$CDM model, with a constant dark energy equation-of-state parameter w. Remarkably, when correcting for the evolution as a function of cosmology, we obtain closed constraints on Ω$_{M}$ using only noncalibrated QSOs. We find that considering noncalibrated QSOs combined with SNe Ia and accounting for the same correction, our results are compatible with a flat ΛCDM model with Ω$_{M}$ = 0.3 and H$_{0}$ = 70 km s$^{-1}$ Mpc$^{-1}$. Intriguingly, the H$_{0}$ values obtained are placed halfway between the one from SNe Ia and CMB, paving the way for new insights into the H$_{0}$ tension

Reduced uncertainties up to 43\% on the Hubble constant and the matter density with the SNe Ia with a new statistical analysis

Type Ia Supernovae (SNe Ia) are considered the most reliable \textit{standard candles} and they have played an invaluable role in cosmology since the discovery of the Universe's accelerated expansion. During the last decades, the SNe Ia samples have been improved in number, redshift coverage, calibration methodology, and systematics treatment. These efforts led to the most recent \textit{``Pantheon"} (2018) and \textit{``Pantheon +"} (2022) releases, which enable to constrain cosmological parameters more precisely than previous samples. In this era of precision cosmology, the community strives to find new ways to reduce uncertainties on cosmological parameters. To this end, we start our investigation even from the likelihood assumption of Gaussianity, implicitly used in this domain. Indeed, the usual practise involves constraining parameters through a Gaussian distance moduli likelihood. This method relies on the implicit assumption that the difference between the distance moduli measured and the ones expected from the cosmological model is Gaussianly distributed. In this work, we test this hypothesis for both the \textit{Pantheon} and \textit{Pantheon +} releases. We find that in both cases this requirement is not fulfilled and the actual underlying distributions are a logistic and a Student's t distribution for the \textit{Pantheon} and \textit{Pantheon +} data, respectively. When we apply these new likelihoods fitting a flat $\Lambda$CDM model, we significantly reduce the uncertainties on $\Omega_M$ and $H_0$ of $\sim 40 \%$. This boosts the SNe Ia power in constraining cosmological parameters, thus representing a huge step forward to shed light on the current debated tensions in cosmology.Comment: 15 pages with 7 figures (with multiple panels), 1 table. This work includes the suggestions of scientists from the community who reached out. The paper is now under consideration in Ap

Quasars: standard candles up to z=7.5 with the precision of Supernovae Ia

Currently, the $\Lambda$ Cold Dark Matter model, which relies on the existence of cold dark matter and a cosmological constant $\Lambda$, best describes the Universe. However, we lack information in the high-redshift ($z$) region between Type Ia Supernovae (SNe Ia) (up to $z=2.26$) and the Cosmic Microwave Background ($z=1100$), an interval crucial to test cosmological models and their possible evolution. We have defined a sample of 983 Quasars up to $z=7.54$ with reduced intrinsic dispersion $\delta=0.007$ which determines the matter density parameter $\Omega_M$ with the same precision of SNe Ia. Although previous analysis have been used Quasars as cosmological tools (e.g. Risaliti and Lusso 2019), this is the first time that high-redshift sources, in this case Quasars, as standalone cosmological probes yield such tight constraints on $\Omega_M$. Our results show the importance of correcting cosmological relationships for selection biases and redshift evolution and how the choice of a golden sample reduces considerably the intrinsic scatter. This proves the reliability of Quasars as standard cosmological candles.Comment: Accepted for publication in Ap

A bias-free cosmological analysis with quasars alleviating H0H_0 tension

Cosmological models and their parameters are widely debated because of theoretical and observational mismatches of the standard cosmological model, especially the current discrepancy between the value of the Hubble constant, $H_{0}$, obtained by Type Ia supernovae (SNe Ia), and the Cosmic Microwave Background Radiation (CMB). Thus, considering high-redshift probes like quasars (QSOs), having intermediate redshifts between SNe Ia and CMB, is a necessary step. In this work, we use SNe Ia and the most updated QSO sample, reaching redshifts up to $z\sim7.5$, applying the Risaliti-Lusso QSO relation based on a non-linear relation between ultraviolet and X-ray luminosities. We consider this relation both in its original form and corrected for selection biases and evolution in redshift through a reliable statistical method also accounting for the circularity problem. We also explore two approaches: with and without calibration on SNe Ia. We then investigate flat and non-flat standard cosmological models and a flat $w$CDM model, with a constant dark energy equation of state parameter $w$. Remarkably, when correcting for the evolution as a function of cosmology, we obtain closed constraints on $\Omega_M$ using only non-calibrated QSOs. We find that considering non-calibrated QSOs combined with SNe Ia and accounting for the same correction, our results are compatible with a flat $\Lambda$CDM model with $\Omega_M = 0.3$ and $H_0 = 70 \, \mathrm{km\,s^{-1}\,Mpc^{-1}}$. Intriguingly, the $H_0$ values obtained place halfway between the one from SNe Ia and CMB, paving the way for new insights into the $H_0$ tension.Comment: Accepted to be published in ApJS; 24 pages, 12 figure

Quasars as Standard Candles IV. Analysis of the X-ray and UV indicators of the disc-corona relation

Context: A non-linear relation between quasar monochromatic luminosities at 2500A and 2 keV holds at all observed redshifts and luminosities, and it has been used to derive quasar distances and to build a Hubble Diagram of quasars. The choice of the X-ray and UV indicators has so far been somewhat arbitrary, and has typically relied on photometric data. Aims: We want to determine the X-ray and UV proxies that provide the smallest dispersion of the relation, in order to obtain more precise distance estimates, and to confirm the reliability of the X-ray to UV relation as a distance indicator. Methods: We performed a complete UV spectroscopic analysis of a sample of $\sim$1800 quasars with SDSS optical spectra and XMM- Newton X-ray serendipitous observations. In the X-rays, we analysed the spectra of all the sample objects at redshift z $>$1.9, while we relied on photometric measurements at lower redshifts. As done in previous studies, we analysed the relation in small redshift bins, using fluxes instead of luminosities. Results: We show that the monochromatic fluxes at 1 keV and 2500A are, respectively, the best X-ray and UV continuum indicators among those that are typically available. We also find a tight relation between soft X-ray and Mg ii2800A line fluxes, and a marginal dependence of the X-ray to UV relation on the width of the Mg ii line. Conclusions: Our analysis suggests that the physical quantities that are more tightly linked to one another are the soft X-ray flux at $\sim$1 keV and the ionizing UV flux blueward of the Lyman limit. However, the "usual" monochromatic fluxes at 2 keV and 2500A estimated from photometric data provide an almost as-tight X-ray to UV relation, and can be used to derive quasar distances. The Hubble diagram obtained using spectroscopic indicators is fully consistent with the one presented in previous papers, based on photometric data.Comment: accepted for publication in A&

Quasars as standard candles: VI. Spectroscopic validation of the cosmological sample

A sample of quasars has been recently assembled to investigate the non-linear relation between their monochromatic luminosities at 2500 Å and 2 keV and to exploit quasars as a new class of ‘standardized candles’. The use of this technique for cosmological purposes relies on the non-evolution with redshift of the UV-optical spectral properties of quasars, as well as on the absence of possible contaminants such as dust extinction and host galaxy contribution. We address these possible issues by analysing the spectral properties of our cosmological quasar sample. We produced composite spectra in different bins of redshift and accretion parameters (black hole mass, bolometric luminosity), to investigate any possible evolution of the spectral properties of the continuum of the composites with these parameters. We found a remarkable similarity amongst the various stacked spectra. Apart from the well known evolution of the emission lines with luminosity (i.e. the Baldwin effect) and black hole mass (i.e. the virial relation), the overall shape of the continuum, produced by the accretion disc, does not show any statistically significant trend with black-hole mass (MBH), bolometric luminosity (Lbol), or redshift (z). The composite spectrum of our quasar sample is consistent with negligible levels of both intrinsic reddening (with a colour excess E(B − V)≲0.01) and host galaxy emission (less than 10%) in the optical. We tested whether unaccounted dust extinction could explain the discrepancy between our cosmographic fit of the Hubble–Lemaître diagram and the concordance ΛCDM model. The average colour excess required to solve the tension should increase with redshift up to unphysically high values (E(B − V)≃0.1 at z > 3) that would imply that the intrinsic emission of quasars is much bluer and more luminous than ever reported in observed spectra. The similarity of quasar spectra across the parameter space excludes a significant evolution of the average continuum properties with any of the explored parameters, confirming the reliability of our sample for cosmological applications. Lastly, dust reddening cannot account for the observed tension between the Hubble–Lemaître diagram of quasars and the ΛCDM model

Quasar standardization : overcoming selection biases and redshift evolution

Quasars (QSOs) are extremely luminous active galactic nuclei currently observed up to redshift z = 7.642. As such, they have the potential to be the next rung of the cosmic distance ladder beyond Type Ia supernovae, if they can reliably be used as cosmological probes. The main issue in adopting QSOs as standard candles (similarly to gamma-ray bursts) is the large intrinsic scatter in the relations between their observed properties. This could be overcome by finding correlations among their observables that are intrinsic to the physics of QSOs and not artifacts of selection biases and/or redshift evolution. The reliability of these correlations should be verified through well-established statistical tests. The correlation between the ultraviolet and X-ray fluxes developed by Risaliti & Lusso is one of the most promising relations. We apply a statistical method to correct this relation for redshift evolution and selection biases. Remarkably, we recover the the same parameters of the slope and the normalization as Risaliti & Lusso. Our results establish the reliability of this relation, which is intrinsic to the QSO properties and not merely an effect of selection biases or redshift evolution. Hence, the possibility to standardize QSOs as cosmological candles, thereby extending the Hubble diagram up to z = 7.54

Reducing the uncertainty on the Hubble constant up to 35\% with an improved statistical analysis: different best-fit likelihoods for Supernovae Ia, Baryon Acoustic Oscillations, Quasars, and Gamma-Ray Bursts

Cosmological models and their parameters are widely debated, especially about whether the current discrepancy between the values of the Hubble constant, $H_{0}$, obtained by type Ia supernovae (SNe Ia), and the Planck data from the Cosmic Microwave Background Radiation could be alleviated when alternative cosmological models are considered. Thus, combining high-redshift probes, such as Gamma-Ray Bursts (GRBs) and Quasars (QSOs), together with Baryon Acoustic Oscillations (BAO) and SNe Ia is important to assess the viability of these alternative models and if they can cast further light on the Hubble tension. In this work, for GRBs, we use a 3-dimensional relation between the peak prompt luminosity, the rest-frame time at the end of the X-ray plateau, and its corresponding luminosity in X-rays: the 3D Dainotti fundamental plane relation. Regarding QSOs, we use the Risaliti-Lusso relation among the UV and X-ray luminosities for a sample of 2421 sources. We correct both the QSO and GRB relations by accounting for selection and evolutionary effects with a reliable statistical method. We here use both the traditional Gaussian likelihoods ($\cal L_G$) and the new best-fit likelihoods ($\cal L_N$) to infer cosmological parameters of a non-flat $\Lambda$CDM and flat $w$CDM models. We obtain for all the parameters reduced uncertainties, up to $35\%$ for $H_{0}$, when applying the new $\cal L_N$ likelihoods in place of the Gaussian ones. Our results remain consistent with a flat $\Lambda$CDM model, although with a shift of the dark energy parameter $w$ toward $w<-1$ and a curvature density parameter toward $\Omega_k<0$.Comment: Accepted for publication at Ap

Quasars as standard candles. V. Accounting for the dispersion in the LX-LUV relation down to ≤ 0.06 dex

A characteristic feature of quasars is the observed non-linear relationship between their monochromatic luminosities at rest-frame 2500 {\AA} and 2 keV. This relationship is evident across all redshifts and luminosities and, due to its non-linearity, can be implemented to estimate quasar distances and construct a Hubble Diagram for quasars. Historically, a significant challenge in the cosmological application of this relation has been its high observed dispersion. Recent studies have demonstrated that this dispersion can be reduced by excluding biased objects from the sample. Nevertheless, the dispersion remains considerable ($\delta \sim 0.20$ dex), especially when compared to the Phillips relation for supernovae Ia. Given the absence of a comprehensive physical model for the relation, it remains unclear how much of the remaining dispersion is intrinsically tied to the relation itself and how much can be attributed to observational factors not addressed by the sample selection and by the choice of X-ray and UV indicators. Potential contributing factors include (i) the scatter produced by using X-ray photometric results instead of spectroscopic ones, (ii) the intrinsic variability of quasars, and (iii) the inclination of the accretion disc relative to our line of sight. In this study, we thoroughly examine these three factors and quantify their individual contributions to the observed dispersion. Based on our findings, we argue that the intrinsic dispersion of the X-ray/UV luminosity relation is likely below 0.06 dex. We also discuss why high-redshift subsamples can show a significantly lower dispersion than the average one

The most luminous blue quasars at 3.0<z<3.3. II. CIV/X-ray emission and accretion disc physics

We analyse the properties of the CIV broad emission line in connection with the X-ray emission of 30 bright SDSS quasars at z~3.0-3.3 with pointed XMM-Newton observations, which were selected to test the suitability of AGN as cosmological tools. In our previous work, we found that a large fraction (~25%) of the quasars in this sample are X-ray underluminous by factors of >3-10. As absorbing columns of >10$^{23}$ cm$^{-2}$ can be safely ruled out, their weakness is most likely intrinsic. Here we explore possible correlations between the UV and X-ray features of these sources to investigate the origin of X-ray weakness. We fit their UV SDSS spectra and analyse their CIV properties (e.g., equivalent width, EW; line peak velocity, $\upsilon_{\rm peak}$) as a function of the X-ray photon index and 2-10 keV flux. We confirm the trends of CIV $\upsilon_{\rm peak}$ and EW with UV luminosity at 2500 angstrom for both X-ray weak and X-ray normal quasars, as well as the correlation between X-ray weakness and CIV EW. In contrast to some recent work, we do not observe any clear relation between the 2-10 keV luminosity and $\upsilon_{\rm peak}$. We find a correlation between the hard X-ray flux and the integrated CIV flux for X-ray normal quasars, whilst X-ray weak quasars deviate from the main trend by more than 0.5 dex. We argue that X-ray weakness might be interpreted in a starved X-ray corona picture associated with an ongoing disc-wind phase. If the wind is ejected in the vicinity of the black hole, the extreme-UV radiation that reaches the corona will be depleted, depriving the corona of seeds photons and generating an X-ray weak quasar. Yet, at the largest UV luminosities (>10$^{47}$ erg s$^{-1}$), there will still be an ample reservoir of ionising photons that can explain the excess CIV emission observed in the X-ray weak quasars with respect to normal sources of similar X-ray luminosities.Comment: 22 pages, 15 figures (with 3 more figures in the Appendix), abstract abridged. Accepted for publication in A&