Cosmic Microwave Background Constraints Research Articles

Feedback in the dark: a critical examination of CMB bounds on primordial black holes

If present in the early universe, primordial black holes (PBHs) would have accreted matter and emitted high-energy photons, altering the statistical properties of the Cosmic Microwave Background (CMB). This mechanism has been used to constrain the fraction of dark matter that is in the form of PBHs to be much smaller than unity for PBH masses well above one solar mass. Moreover, the presence of dense dark matter mini-halos around the PBHs has been used to set even more stringent constraints, as these would boost the accretion rates.In this work, we critically revisit CMB constraints on PBHs taking into account the role of the local ionization of the gas around them. We discuss how the local increase in temperature around PBHs can prevent the dark matter mini-halos from strongly enhancing the accretion process, in some cases significantly weakening previously derived CMB constraints. We explore in detail the key ingredients of the CMB bound and derive a conservative limit on the cosmological abundance of massive PBHs.

Cosmic microwave background constraints on extended dark matter objects

Primordially formed extended dark objects would accrete baryonic matter and impact the ionisation history of the Universe. Insisting on consistency with the anisotropies of the cosmic microwave background, we derive constraints on the dark matter fraction for various classes of objects, of different sizes. We introduce a novel scaling technique to speed up numerical calculations and release our calculation framework in the form of a Mathematica notebook. Conservatively, we focus on spherical accretion and collisional ionisation. We find strong constraints limiting the dark matter fraction to subpercent level for objects of up to 104 AU in size.

Limits on non-relativistic matter during Big-bang nucleosynthesis

Big-bang nucleosynthesis (BBN) probes the cosmic mass-energy density at temperatures ∼ 10 MeV to ∼ 100 keV. Here, we consider the effect of a cosmic matter-like species that is non-relativistic and pressureless during BBN. Such a component must decay; doing so during BBN can alter the baryon-to-photon ratio, η, and the effective number of neutrino species. We use light element abundances and the cosmic microwave background (CMB) constraints on η and Nν to place constraints on such a matter component. We find that electromagnetic decays heat the photons relative to neutrinos, and thus dilute the effective number of relativistic species to N eff < 3 for the case of three Standard Model neutrino species. Intriguingly, likelihood results based on Planck CMB data alone find Nν = 2.800 ± 0.294, and when combined with standard BBN and the observations of D and 4He give Nν = 2.898 ± 0.141. While both results are consistent with the Standard Model, we find that a nonzero abundance of electromagnetically decaying matter gives a better fit to these results. Our best-fit results are for a matter species that decays entirely electromagnetically with a lifetime τX = 0.89 sec and pre-decay density that is a fraction ξ = (ρX /ρ rad|10 MeV = 0.0026 of the radiation energy density at 10 MeV; similarly good fits are found over a range where ξτX 1/2 is constant. On the other hand, decaying matter often spoils the BBN+CMB concordance, and we present limits in the (τX ,ξ) plane for both electromagnetic and invisible decays. For dark (invisible) decays, standard BBN (i.e. ξ = 0) supplies the best fit. We end with a brief discussion of the impact of future measurements including CMB-S4.

Large curvature fluctuations from no-scale supergravity with a spectator field

We investigate the large curvature perturbations which can lead to the formation of primordial black holes (PBHs) in the context of no-scale supergravity. Our study does not depend on any exotic scenario, such as scalar potentials with inflection points or bulks, and aims to avoid the fine-tuning of model parameters to achieve the formation of PBHs. This formation relies on the quantum fluctuations of a light spectator stochastic field after the inflationary period. Our analysis is based on the SU(2,1)/SU(2)×U(1) symmetry, considering both the inflaton and the spectator field. Specifically, we examine existing no-scale models with Starobinsky-like scalar potentials that are consistent with observable constraints on inflation from measurements of the cosmic microwave background (CMB). These models involve two chiral fields: the inflaton and the modulus field. We propose a novel role for the modulus field as a spectator field, responsible for generating PBHs. Our hypothesis suggests that while the inflaton field satisfies the CMB constraints of inflation, it is the modulus field acting as the spectator that leads to large curvature perturbations, capable to explain the production of PBHs. Additionally, we prioritize retaining the inflationary constraints from the CMB through the consideration of spectator fluctuations. Therefore, by exploring the relationship between these fields within the framework of the SU(2,1)/SU(2)×U(1) symmetry, our aim is to unveil their implications for the formation of PBHs.

KiDS-1000: Cosmology with improved cosmic shear measurements

We present refined cosmological parameter constraints derived from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000). Our main improvements include enhanced galaxy shape measurements made possible by an updated version of thelensfit code and improved shear calibration achieved with a newly developed suite of multi-band image simulations. Additionally, we incorporated recent advancements in cosmological inference from the joint Dark Energy Survey Year 3 and KiDS-1000 cosmic shear analysis. Assuming a spatially flat standard cosmological model, we constrainS8 ≡ σ8(Ωm/0.3)0.5 = 0.776−0.027−0.003+0.029+0.002, where the second set of uncertainties accounts for the systematic uncertainties within the shear calibration. These systematic uncertainties stem from minor deviations from realism in the image simulations and the sensitivity of the shear measurement algorithm to the morphology of the galaxy sample. Despite these changes, our results align with previous KiDS studies and other weak lensing surveys, and we find a ∼2.3σlevel of tension with thePlanckcosmic microwave background constraints onS​8.

Unimodular Theory of Gravity in Light of the Latest Cosmological Data

The unimodular theory of gravity is an alternative perspective to the traditional general relativity of Einstein and opens new possibilities for exploring its implications in cosmology. In this paper, we investigated Unimodular Gravity (UG) with the cosmological data from the Pantheon sample of Type Ia Supernovae (SNs) (2018), Baryon Acoustic Oscillations (BAOs), and the observational H(z) data from the Differential Age method (DA). We also used the Cosmic Microwave Background (CMB) distance priors from the Planck 2018 results. We considered a model consisting of a generalized cosmological constant, radiation, and a dark matter component along with normal matter. The considered theory respects only unimodular coordinate transformations. We first fit our model with low-redshift data from SNs and DA and determined the value of the model parameters (ξ,H0). We found the best-fit value of parameter ξ=6.03±0.40, which deviates slightly from 6, for which the theory becomes the standard general theory of relativity. We observed a small deviation in the value of the Hubble constant (H0=72.6±3.5 km s−1 Mpc−1) in the UG model compared with the standard ΛCDM model (H0=72.2±1.2 km s−1 Mpc−1). Using the BAO + CMB constraint in the UG model, we obtained H0=68.45±0.66kms−1Mpc−1, and ξ is ∼6.029. For the combined datasets (SN + DA + BAO + CMB), the estimated H0=69.01±0.60kms−1Mpc−1 with ξ∼6.037, and in standard gravity, H0=68.25±0.40kms−1Mpc−1.

Precision CMB constraints on eV-scale bosons coupled to neutrinos

The cosmic microwave background (CMB) has proven to be an invaluable tool for studying the properties and interactions of neutrinos, providing insight not only into the sum of neutrino masses but also the free streaming nature of neutrinos prior to recombination. The CMB is a particularly powerful probe of new eV-scale bosons interacting with neutrinos, as these particles can thermalize with neutrinos via the inverse decay process, nu bar{nu } rightarrow X, and suppress neutrino free streaming near recombination – even for couplings as small as lambda _{nu } sim {mathcal {O}}(10^{-13}). Here, we revisit CMB constraints on such bosons, improving upon a number of approximations previously adopted in the literature and generalizing the constraints to a broader class of models. This includes scenarios in which the boson is either spin-0 or spin-1, the number of interacting neutrinos is either N_{textrm{int}} = 1,2 or 3, and the case in which a primordial abundance of the species is present. We apply these bounds to well-motivated models, such as the singlet majoron model or a light U(1)_{L_{mu }-L_{tau }} gauge boson, and find that they represent the leading constraints for masses m_Xsim 1, {textrm{eV}}. Finally, we revisit the extent to which neutrino-philic bosons can ameliorate the Hubble tension, and find that recent improvements in the understanding of how such bosons damp neutrino free streaming reduces the previously found success of this proposal.

Constraints on the non-minimally coupled Witten-O'Raifeartaigh inflation

We investigate the impact of a non-minimal coupling of the scalar field with gravity in inflationary models, where a small coupling is allowed. As a concrete example, we consider the Witten-O'Raifeartaigh model, where, in line with other models, the presence of a coupling strength ξ can recover concordance of the inflationary parameters with cosmic microwave background (CMB) constraints, provided by the Planck collaboration. We go beyond the slow-roll regime and investigate the impact in the description of CMB anisotropies by performing a statistical analysis of the model with the most recent Planck + Baryon Acoustic Oscillations (BAO) data to seek for any indication of a non-zero coupling by data within the model. We find that not only the presence of a non-minimal coupling is seen, but the model has a slight statistical preference when compared with the standard ΛCDM one. We also discuss the results on the minimally-coupled model, which in general, favours the simple setting where the associated mass scale is equal to the reduced Planck mass Mp while being, in general, disfavored concerning the standard model.

BEYONDPLANCK

We present posterior sample-based cosmic microwave background (CMB) constraints fromPlanckLFI and WMAP observations as derived through global end-to-end Bayesian processing within the BEYONDPLANCKframework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previousPlanckproducts and found a generally good agreement, however, with notably higher noise due to our exclusion ofPlanckHFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previousPlanckresults. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions forPlanckinstrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with bothPlanckand WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up toℓ ≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

Minihalos as probes of the inflationary spectrum:accurate boost factor calculation and new CMB constraints

Although the spectrum of primordial fluctuations has been accurately measured on scales above ∼ 0.1 Mpc, only upper limits exist on smaller scales. In this study, we investigate generic monochromatic enhancements to the ΛCDM spectrum that trigger the collapse of ultracompact minihalos (UCMHs) well before standard structure formation. We refine previous treatments by considering a mixed population of halos with different density profiles, that should realistically arise as a consequence of late-time accretion and mergers. Assuming that dark matter (DM) can self-annihilate, we find, as expected, that UCMHs can greatly enhance the annihilation rate around recombination, significantly imprinting the cosmic microwave background (CMB) anisotropies. However, we provide additional insight on the theoretical uncertainties that currently impact that boost and which may affect late-time probes such as the 21 cm line or γ-ray signals. We derive constraints on the primordial power spectrum on small scales using the ExoCLASS/HYREC codes and the Planck legacy data. We account for the velocity dependence of the DM annihilation cross-section (s- or p-wave), annihilation channel, the DM particle mass and the inclusion of late-time halo mergers. Our s-wave constraints are competitive with previous literature, excluding primordial amplitudes \U0001d49c*≳ 10-6.5 at wavenumbers k ∼ 104 - 107 Mpc-1. For the first time, we highlight that even p-wave processes have constraining power on the primordial spectrum for cross-sections still allowed by currently the strongest astrophysical constraints. Finally, we provide an up-to-date compilation of the most stringent limits on the primordial power spectrum across a wide range of scales.

Direct Detection of Dark Photon Dark Matter Using Radio Telescopes.

Dark photons can be the ultralight dark matter candidate, interacting with Standard Model particles via kinetic mixing. We propose to search for ultralight dark photon dark matter (DPDM) through the local absorption at different radio telescopes. The local DPDM can induce harmonic oscillations of electrons inside the antenna of radio telescopes. It leads to a monochromatic radio signal and can be recorded by telescope receivers. Using the observation data from the FAST telescope, the upper limit on the kinetic mixing can already reach 10^{-12} for DPDM oscillation frequencies at 1-1.5GHz, which is stronger than the cosmic microwave background constraint by about one order of magnitude. Furthermore, large-scale interferometric arrays like LOFAR and SKA1 telescopes can achieve extraordinary sensitivities for direct DPDM search from 10MHz to 10GHz.

Revisiting sterile neutrino dark matter in gauged U(1)B−L model

We reexamine sterile neutrino dark matter in gauged $U(1)_{B-L}$ model. Improvements have been made by tracing and careful evaluation of the evolution of the number densities of sterile neutrinos $N$ and extra neutral gauge bosons $Z'$. As a result, the cosmologically-interesting gauge coupling of $U(1)_{B-L}$ for freeze-in sterile neutrinos turns out to be smaller than the values reported in the literature. This avoids the overproduction of $Z'$ so that it is consistent with the big bang nucleosynthesis and the cosmic microwave background constraints on the effective number of neutrino species. Similarly, the free-streaming length constraints exclude a large parameter space derived in previous studies. In addition to known freeze-in pair production of $N$ from the standard model fermion pairs, we find the case that $N$ is dominantly produced from a pair of $Z'$ at the temperature characterized by the $B-L$ breaking scalar mass. Thus, the naive truncation of the $U(1)_{B-L}$ scalar contribution made in the literature is not valid.

New thermal relic targets for inelastic vector-portal dark matter

We examine the vector-portal inelastic dark matter (DM) model with DM mass $m_\chi$ and dark photon mass $m_{A'}$, in the `forbidden dark matter' regime where $1 \lesssim m_{A'}/m_\chi \lesssim 2$, carefully tracking the dark sector temperature throughout freezeout. The inelastic nature of the dark sector relaxes the stringent cosmic microwave background (CMB) and self-interaction constraints compared to symmetric DM models. We determine the CMB limits on both annihilations involving excited states and annihilation into $e^+e^-$ through initial-state-radiation of an $A'$, as well as limits on the DM self-scattering, which proceeds at the one-loop level. The unconstrained parameter space serves as an ideal target for accelerator $A'$ searches, and provides a DM self-interaction cross section that is large enough to observably impact small-scale structure.

Probing physics beyond the standard model: limits from BBN and the CMB independently and combined

We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number Nν of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates d + d ⟶ 3He + n and d + d ⟶ 3H+ p. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs Nν and η prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives Nν = 2.898 ± 0.141, resulting in Nν < 3.180 at 2σ. We apply these limits to a wide variety of new physics scenarios including right-handed neutrinos, dark radiation, and a stochastic gravitational wave background. The strength of the independent BBN and CMB constraints now opens a new window: we can search for limits on potential changes in Nν and/or the baryon-to-photon ratio η between the two epochs. The present data place strong constraints on the allowed changes in Nν between BBN and CMB decoupling; for example, we find -0.708 < Nν CMB - Nν BBN < 0.328 in the case where η and the primordial helium mass fraction Yp are unchanged between the two epochs; we also give limits on the allowed variations in η or in (η, Nν ) jointly. We discuss scenarios in which such changes could occur, and show that BBN+CMB results combine to place important constraints on some early dark energy models to explain the H0 tension. Looking to the future, we forecast the tightened precision for Nν arising from both CMB Stage 4 measurements as well as improvements in astronomical 4He measurements. We find that CMB-S4 combined with present BBN and light element observation precision can give σ(Nν ) ≃ 0.03. Such future precision would reveal the expected effect of neutrino heating (Neff -3 = 0.044) of the CMB during BBN, and would be near the level to reveal any particle species ever in thermal equilibrium with the standard model. Improved Yp measurements can push this precision even further.

Scalar induced gravitational waves from primordial black hole Poisson fluctuations in f(R) gravity

The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave (GW) background through second-order gravitational effects. This GW background can be abundantly generated in a cosmic era dominated by ultralight primordial black holes, with masses m PBH < 109g. In this work, we consider f(R) gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After a general analysis, we focus on the R 2 gravity model. In particular, by requiring that the scalar induced GWs (SIGWs) are not overproduced, we find an upper bound on the abundance of PBHs at formation time ΩPBH,f as a function of their mass, namely that ΩPBH,f < 5.5 × 10-5 (109g/m PBH)1/4, which is 45% tighter than the respective upper bound in general relativity. Afterwards, by considering R 2 gravity as an illustrative case study of an f(R) gravity model, we also set upper bound constraints on its mass parameter M. These mass parameter constraints, however, should not be regarded as physical given the fact that the Cosmic Microwave Background (CMB) constraints on R 2 gravity are quite tight. Finally, we conclude that the portal of SIGWs associated to PBH Poisson fluctuations can act as a novel complementary probe to constrain alternative gravity theories.

Galaxy number-count dipole and superhorizon fluctuations

In view of the growing tension between the dipole anisotropy of number counts of cosmologically distant sources and of the cosmic microwave background (CMB), we investigate the number count dipole induced by primordial perturbations with wavelength comparable to or exceeding the Hubble radius today. First, we find that neither adiabatic nor isocurvature superhorizon modes can generate an intrinsic number count dipole. However a superhorizon isocurvature mode does induce a relative velocity between the CMB and the (dark) matter rest frames and thereby affects the CMB dipole. We revisit the possibility that it has an intrinsic component due to such a mode, thus enabling consistency with the galaxy number count dipole if the latter is actually kinematic in origin. Although this scenario is not particularly natural, there are possible links with other anomalies and it predicts a concommitant galaxy number count quadrupole which may be measurable in future surveys. We also investigate the number count dipole induced by modes smaller than the Hubble radius, finding that subject to CMB constraints this is too small to reconcile the dipole tension.

Investigation of CMB constraints for dark matter-helium scattering

We study dark matter-helium scattering in the early Universe and its impact on constraints from cosmic microwave background (CMB) anisotropy measurements. We describe possible theoretical frameworks for dark matter-nucleon interactions via a scalar, pseudoscalar, or vector mediator; such interactions give rise to hydrogen and helium scattering, with cross sections that have a power-law dependence on relative velocity. Within these frameworks, we consider three scenarios: dark matter coupling to only neutrons, to only protons, and to neutrons and protons with equal strength. For these various cases, we use Planck 2018 temperature, polarization, and lensing anisotropy data to place constraints on dark matter scattering with hydrogen and/or helium for dark matter masses between 10 keV and 1 TeV. For any model that permits both helium and hydrogen scattering with a non-negative power-law velocity dependence, we find that helium scattering dominates the constraint for dark matter masses well above the proton mass. Furthermore, we place the first CMB constraints on dark matter that scatters dominantly/exclusively with helium in the early Universe.

Joint Cosmic Microwave Background and Big Bang Nucleosynthesis Constraints on Light Dark Sectors with Dark Radiation

Dark sectors provide a compelling theoretical framework for thermally producing sub-GeV dark matter, and motivate an expansive new accelerator and direct-detection experimental program. We demonstrate the power of constraining such dark sectors using the measured effective number of neutrino species, N_{eff}, from the cosmic microwave background (CMB) and primordial elemental abundances from big bang nucleosynthesis. As a concrete example, we consider a dark matter particle of arbitrary spin that interacts with the standard model via a massive dark photon, accounting for an arbitrary number of light degrees of freedom in the dark sector. We exclude dark matter masses below ∼4 MeV at 95%confidence for all dark matter spins and dark photon masses. These bounds hold regardless of additional new light, inert degrees of freedom in the dark sector, and for dark matter-electron scattering cross sections many orders of magnitude below current experimental constraints. The strength of these constraints will only continue to improve with future CMB experiments.

Cosmological Results from the RAISIN Survey: Using Type Ia Supernovae in the Near Infrared as a Novel Path to Measure the Dark Energy Equation of State

Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012 to 2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SNe Ia (0.2 ≲ z ≲ 0.6) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-z HST data with 42 SNe Ia at z < 0.1 observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical photometry) to pursue a unique avenue to constrain the dark energy equation-of-state parameter, w. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size ∼0.06-0.1 mag with 1.5σ−2.5σ significance depending on the method and step location used. Combining our NIR sample with cosmic microwave background constraints, we find 1 + w = −0.17 ± 0.12 (statistical + systematic errors). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measure H 0 = 75.9 ± 2.2 km s−1 Mpc−1 from stars with geometric distance calibration in the hosts of eight SNe Ia observed in the NIR versus H 0 = 71.2 ± 3.8 km s−1 Mpc−1 using an inverse distance ladder approach tied to Planck. Using optical data, we find 1 + w = −0.10 ± 0.09, and with optical and NIR data combined, we find 1 + w = −0.06 ± 0.07; these shifts of up to ∼0.11 in w could point to inconsistency in the optical versus NIR SN models. There will be many opportunities to improve this NIR measurement and better understand systematic uncertainties through larger low-z samples, new light-curve models, calibration improvements, and eventually by building high-z samples from the Roman Space Telescope.

The XXL survey

Context. We present the forward cosmological analysis of an XMM-selected sample of galaxy clusters out to a redshift of unity. We derive mass-observable relations in a self-consistent manner using the sample alone. Special care is given to the modelling of selection effects. Aims. Following our previous 2018 study based on the dn/dz quantity alone, we perform an upgraded cosmological analysis of the same XXL C1 cluster catalogue (178 objects), with a detailed account of the systematic errors. The results are combined with external constraints from baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). Methods. This study follows the ASpiX methodology: we analysed the distribution of the observed X-ray properties of the cluster population in a 3D observable space (count rate, hardness ratio, redshift) and modelled as a function of cosmology along with the scaling relations and the selection function. Compared to more traditional methods, ASpiX allows the inclusion of clusters down to a few tens of photons and is much simpler to use. Two M − T relations are considered: that from the Canada-France-Hawaii Telescope (hereafter CFHT) and another from the more recent Subaru lensing analyses. Results. We obtain an improvement by a factor of two compared to the previous analysis, which dealt with the cluster redshift distribution for the XXL sample alone, letting the normalisation of the M − T relation and the evolution of the L–T relation free. Adding constraints from the XXL cluster two-point correlation function and the BAO from various surveys decreases the uncertainties by 23% and 53%, respectively, and 62% when adding both. The central value is in excellent agreement with the Planck CMB constraints. Switching to the scaling relations from the Subaru analysis and leaving more parameters free to vary provides less stringent constraints, but those obtained are still consistent with the Planck CMB at the 1-sigma level. Our final constraints are $ \sigma_8 = 0.99^{+0.14}_{-0.23} $, $ \Omega_m = 0.296 \pm 0.034\,(S_8 = 0.98^{+0.11}_{-0.21} $) for the XXL sample alone. Combining XXL ASpiX, the XXL cluster two-point correlation function, and the BAO, leaving 11 parameters free to vary, and allowing for the cosmological dependence of the scaling relations in the fit induces a shift of the central values, which is reminiscent of that observed for the Planck S-Z cluster sample. We find $ \sigma_8 = 0.793^{+0.063}_{-0.12} $ and $ \Omega_m = 0.364 \pm 0.015\,(S_8 = 0.872^{+0.068}_{-0.12} $), which are still compatible with Planck CMB at 2.2σ. Conclusions. The results obtained by the ASpiX method are promising; further improvement is expected from the final XXL cosmological analysis involving a cluster sample that is twice as large. Such a study paves the way for the analysis of the eROSITA and future Athena surveys.