One matter density discrepancy to alleviate them all or further trouble for Λ\LambdaCDM model

We investigate whether the two cosmological discrepancies on the Hubble constant ($H_0$) and the matter fluctuation parameter ($\sigma_8$) could be traded by only one on the present value of the matter density ($\Omega_{\rm{M}}$). We combined different probes in an agnostic approach by, either relaxing the calibration parameters in each probe in order to be set by the data, or by only including priors with the condition that they are obtained independently from the discrepant parameters. We also compiled and used a dataset from previous direct measurements of $\Omega_{\rm{M}}$. We found when combining, as our baseline, galaxy clusters counts + cluster baryon fraction probe + cosmic chronometers + direct $\Omega_{\rm{M}}$ + priors from BBN and CMB, that both parameters, $H_0$ and $\sigma_8$, are consistent with those inferred with local probes, with $\sigma_8 = 0.745 \pm 0.05$ while $H_0 = 73.8 \pm 3.01$, and that for a value of $\Omega_{\rm{M}} = 0.22 \pm 0.01$ at more than 3$\sigma$ from that usually determined by CMB. We also found similar preferences when replacing cosmic chronometers (CC) by the Supernovae (SN) data while allowing its calibration parameter to vary. However discrepancies appeared when we combined SN in addition to CC suggesting either inconsistencies between the SN sample and the other probes used or a serious challenge to our hypothesis. We conclude that, either reconciling both tensions requires local inferred values of matter density at odd with those obtained by CMB, reviving by then an overlooked discrepancy, or simply that further evidences are indicating that $\Lambda$CDM model is facing more difficulties to accommodate simultaneously all the current available observations.(abridged)Comment: Match the submitted version after proof reading and comments and reference requests were taken into accoun

A trium test on beyond Λ\LambdaCDM triggering parameters

We performed a Bayesian study on three beyond LCDM phenomenological triggering parameters, the growth index $\gamma$, the dark energy equation of state parameter $w$ and the lensing deviation from the GR prediction parameter $\Sigma$, using the latest cosmological geometric, growth and lensing probes, all in a consistent implementation within the modified gravity cosmological solver code MGCLASS. We find, when we combined all our probes, i.e. the cosmic microwave background (CMB), the baryonic acoustic oscilation (BAO), the growth measurements $f\sigma_8$ and the 3$\times$2 points galaxy clustering and lensing cross-correlations, assuming flat space, constraints compatible with general relativity and $\Lambda$CDM for $\omega = -1.025\pm0.045$, and $\Sigma = 0.992\pm0.022$ at the 68\% level, while $\gamma = 0.633\pm0.044$ is still within $\sim 2 \sigma$ from the $\Lambda$CDM value of $\gamma \sim 0.55$, and that when $\Sigma$ is considered as constant; while $\gamma_\ell = -0.025 \pm0.045$ when the lensing parameter is parameterised as function of a lensing index, introduced for the first time in this work, as $\Sigma(z)=\Omega_m(z)^{\gamma_\ell}$.Comment: Match the submitted version after proof reading and comments and reference requests were taken into accoun

Untying the growth index to relief the σ8\sigma_8 discomfort

The fluctuation of matter parameter $\sigma_8$ is by model construction degenerate with the growth index $\gamma$. Here we try to study the effect on the cosmological parameters constraints from treating each independently by considering $\sigma_8$ as a free and not derived parameter along with $\gamma$, to then try to constrain all by three probes, namely the CMB spectrum, the growth measurements from redshift space distortions $f\sigma_8$ and the galaxy cluster counts. We also want to asses the impact of this relaxation on the $\sigma_8$ tension. We also propose a more sophisticated correction, along with the classical one that takes into account the impact of cosmology on the growth measurements, which is to adjust the growth to keep the observed power spectrum invariant with the background evolution. We found that untying the two parameters does not shift the maximum likelihood on either $\sigma_8$ or $\gamma$ but rather allow for larger bounds with respect to when $\sigma_8$ is a derived parameter. More precisely, we obtain $\sigma_8 = 0.809\pm 0.043$ and $\gamma = 0.613\pm 0.046$ in agreement with Planck constraints for the former and compatible with $\Lambda$CDM for the latter but with bounds enough wide to accommodate both values subject of tensions for $\sigma_8$. On the other hand, considering a tier correction yields $\sigma_8 = 0.734\pm 0.013$ close to the local values albeit with a growth index $\gamma = 0.636\pm 0.022$ while allowing a massive neutrinos yielded $\sigma_8 = 0.756\pm 0.024$, still preferring low values but with looser constraints, with $\gamma = 0.549\pm 0.048$ and a slight preference for $\Sigma m_\nu \sim 0.19$ value. We conclude that untying $\sigma_8$ and $\gamma$ helps in relieving the discomfort on the former between CMB and local probes and that careful analyze should be followed when using data obtained in a model dependent way.(abridged)Comment: Match the submitted version after proof reading and comments and reference requests were taken into accoun

La cosmologie au delà du modèle LCDM à la lumière de la tension dans l’abondance des amas de galaxies

Le modèle ΛCDM permet de décrire avec une grande précision la plupart des présentes observations cosmologiques. Cependant, l'un de ses paramètres, σ 8, mesurant l'amplitude de fluctuations de la matière, présente une discordance entre sa valeur contrainte par le spectre de puissance angulaire du CMB de la mission Planck, les Cls, et celle déterminée à partir des amas SZ dans l'univers proche. Dans le présent travail on explore divers extensions du modèle ΛCDM comme origines possibles de cette anomalie. Pour tester les effets de ces extensions, nous avons effectué une analyse Monte Carlo on l'on compare les contraintes sur σ 8 à partir de ΛCDM avec celles résultantes de ces extensions, et ceci en utilisant principalement le spectre de puissance CMB seul ou combiné avec des comptages d'amas. Ces derniers sont basés sur différentes relations masse observables et couvrent différents redshift : des amas de rayons X dans l'univers local, des amas de la mission SZ Planck dans l'univers proche ou une estimation des amas détectés par leur richesse photométrique à partir du la future mission Euclid. Du fait qu'une mauvaise détermination de l'étalonnage de la masse des amas pourrait également être la raison de cette divergence, notre approche consistait, lorsqu'on combinait les deux sondes issues des amas et du CMB, à laisser le facteur d'étalonnage libre afin qu'il soit contraint comme les autres paramètres cosmologiques par les deux données. Dans le cas d'introduction de trois neutrinos massifs dégénérés, nous avons trouvé qu'ils n'ont aucun effet significatif sur la correction de l'écart entre les contraintes issues de comptage CMB et ceux issues des Xray ou SZ cluster. Nous avons ensuite permis à l'indice de croissance ƴ de varier. Nous trouvons une corrélation entre ƴ et le paramètre de calibration masse-observable des amas détectés par rayons X qui n'est pas affecté par la présence ou non des neutrinos massifs. [...]The ΛCDM model has proved successful in describing to a high precision most of nowadays cosmological observations. However, one of its parameters, σ 8, measuring the present matter amplitude fluctuations, constrained from CMB angular power spectrum, the Cls, was found by the Planck mission, in significant tension with value constrained by SZ galaxy cluster counts in the near universe. In the present work we investigate extensions to ΛCDM model as possible origins behind this discrepancy. To test these extensions, we performed a Monte Carlo analysis to compare constraints on σ 8 in ΛCDM with constraints under these extensions, using mainly CMB Cls combined with cluster counts sample. The later were based on different mass observables relations and covered different redshift ranges: X-ray cluster in the local universe, SZ Planck mission clusters from the near universe or photometric richness estimated detected clusters from future high redshift upcoming Euclid alike mission. Because an improper determination of the calibration of cluster mass function could also be behind this discrepancy, our approach was, when combined with CMB, to leave the calibration factor free to vary and be constrained by data. Introducing three degenerate massive neutrinos, we found that they have no significant effect on fixing the discrepancy between CMB and Xray or SZ cluster counts. We then allowed the growth index ƴ to vary. We find a correlation in the confidence space between ƴ and the X-ray mass observable factor not affected by the presence of massive neutrinos, indicating that a modifying gravity is favored over massive neutrinos as a way to alleviate the tension. However, when a SZ cluster sample covering a larger redshift range was used, we found that the correlation between ƴ and the calibration factor, is constrained by the evolution of the growth through redshift and limited to a region where it cannot fix the discrepancy. [...

Untying the Growth Index to Relieve the <i>σ</i>₈ Discomfort

The matter fluctuation parameter σ8 is, by model construction, degenerate with the growth index γ. Here, we study the effect on the cosmological parameter constraints by treating each independently from one another, considering σ8 as a free and non-derived parameter along with a free γ. We then try to constrain all parameters using three probes that span from deep to local redshifts, namely the CMB spectrum, the growth measurements from redshift space distortions fσ8, and the galaxy cluster counts. We also aim to assess the impact of this relaxation on the σ8 tension between its inferred CMB value in comparison to that obtained from local cluster counts. We also propose a more sophisticated correction, along with the classical one, that takes into account the impact of cosmology on the growth measurements when the parameters are varied in the Monte Carlo process, which consist in adjusting the growth to keep the observed power spectrum, integrated over all angles and scales, as invariant with the background evolution. We found by using the classical correction that untying the two parameters does not shift the maximum likelihood of either σ8 or γ, but it rather enables larger bounds with respect to when σ8 is a derived parameter, and that when considering CMB + fσ8, or when further combining with cluster counts albeit with tighter bounds. Precisely, we obtain σ8=0.809±0.043 and γ=0.613±0.046 in agreement with Planck’s constraint for the former and compatible with ΛCDM for the latter but with bounds wide enough to accommodate both values subject to the tensions. Allowing for massive neutrinos does not change the situation much. On the other hand, considering a tiered correction yields σ8=0.734±0.013 close to ∼1 σ for the inferred local values albeit with a growth index of γ=0.636±0.022 at ∼2 σ from its ΛCDM value. Allowing for massive neutrinos in this case yielded σ8=0.756±0.024, still preferring low values but with much looser constraints on γ=0.549±0.048 and a slight preference for Σmν∼0.19. We conclude that untying σ8 and γ helps in relieving the discomfort on the former between the CMB and local probes, and that careful analysis should be followed when using data products treated in a model-dependent way

Cosmology beyond ΛCDM model in the light of cluster abundance tension

Le modèle ΛCDM permet de décrire avec une grande précision la plupart des présentes observations cosmologiques. Cependant, l'un de ses paramètres, σ 8, mesurant l'amplitude de fluctuations de la matière, présente une discordance entre sa valeur contrainte par le spectre de puissance angulaire du CMB de la mission Planck, les Cls, et celle déterminée à partir des amas SZ dans l'univers proche. Dans le présent travail on explore divers extensions du modèle ΛCDM comme origines possibles de cette anomalie. Pour tester les effets de ces extensions, nous avons effectué une analyse Monte Carlo on l'on compare les contraintes sur σ 8 à partir de ΛCDM avec celles résultantes de ces extensions, et ceci en utilisant principalement le spectre de puissance CMB seul ou combiné avec des comptages d'amas. Ces derniers sont basés sur différentes relations masse observables et couvrent différents redshift : des amas de rayons X dans l'univers local, des amas de la mission SZ Planck dans l'univers proche ou une estimation des amas détectés par leur richesse photométrique à partir du la future mission Euclid. Du fait qu'une mauvaise détermination de l'étalonnage de la masse des amas pourrait également être la raison de cette divergence, notre approche consistait, lorsqu'on combinait les deux sondes issues des amas et du CMB, à laisser le facteur d'étalonnage libre afin qu'il soit contraint comme les autres paramètres cosmologiques par les deux données. Dans le cas d'introduction de trois neutrinos massifs dégénérés, nous avons trouvé qu'ils n'ont aucun effet significatif sur la correction de l'écart entre les contraintes issues de comptage CMB et ceux issues des Xray ou SZ cluster. Nous avons ensuite permis à l'indice de croissance ƴ de varier. Nous trouvons une corrélation entre ƴ et le paramètre de calibration masse-observable des amas détectés par rayons X qui n'est pas affecté par la présence ou non des neutrinos massifs. Cette corrélation indique que les données favorisent une gravité modifiée sur les neutrinos massifs comme un moyen d'enlever la tension. Cependant, lorsque nous avons effectué l'analyse en utilisant l'échantillon d'amas SZ, couvrant une plus large gamme de redshift, nous avons constaté que la corrélation entre ƴ et le paramètre de calibration, contraint par l'histoire de l'évolution de la croissance fonction du redshift, limite le paramètre de calibration hors de la région ou il peut résoudre la discordance. Nous avons donc essayé de considérer une équation d'énergie sombre avec un paramètre de l'équation d'état constant mais différent de ΛCDM ou une énergie sombre variant avec le redshift pour voir si elle peut atténuer la tension seule ou en combinaison avec les neutrinos. Nous avons constaté que les extensions de l'énergie sombre de ΛCDM ne pouvaient pas résoudre la discordance avec l'échantillon de cluster SZ tandis que pour l'échantillon de rayons X ils pourraient le faire pour des valeurs loin des celles correspondantes au ΛCDM. Cependant, lorsque nous avons combiné avec des sondes capables de mettre des contraintes plus fortes sur w comme BAO et Supernovae, les valeurs qui pourraient corriger l'écart n'étaient plus permises. Pour finir on considère le cas ou on introduit une énergie sombre différente du modèle fiduciel et un ƴ variant en même temps. Nous avons trouvé que ces données favorisent le facteur ƴ plutôt qu'un w différent de -1 comme moyen de corriger l'écart, un signe qu'une théorie de gravité modifiée est plus apte à résoudre l'anomalie qu'une forme d'énergie noire différente de celle du modèle LCDM, mais aussi que l'ajout de w comme un autre degré de liberté à ƴ ne lui permet pas de régler la discordance. Pour voir ce qu'une plus grande précision dans les mesures peut signifier, nous avons effectué des prévisions basées sur des futurs sondages d'amas planifiés permettant de détecter un très grand nombre d'amas que ce qu'on observe aujourd'hui et l'exploration de plages de redshift assez élevées pour contraindre et exclure les modèles au-delà de ΛCDM. Nous avons trouvé que si on fixe les facteurs d'étalonnage dans chaque sonde, le spectre CMB et le comptage d'amas de la mission d'Euclid, considéré séparément, à leurs valeurs fiducielles ou si nous laissons le facteur de calibration masse observable ainsi que l'indice de croissance ƴ libres de varier, lorsque nous combinons les deux sondes, l'étalonnage de masse observable est contraint à 10%, signe que seule une meilleure calibration permettra de résoudre la tension ou une nouvelle théorie différente des extensions au modèle ΛCDM utilisées dans notre étude.The ΛCDM model has proved successful in describing to a high precision most of nowadays cosmological observations. However, one of its parameters, σ 8, measuring the present matter amplitude fluctuations, constrained from CMB angular power spectrum, the Cls, was found by the Planck mission, in significant tension with value constrained by SZ galaxy cluster counts in the near universe. In the present work we investigate extensions to ΛCDM model as possible origins behind this discrepancy. To test these extensions, we performed a Monte Carlo analysis to compare constraints on σ 8 in ΛCDM with constraints under these extensions, using mainly CMB Cls combined with cluster counts sample. The later were based on different mass observables relations and covered different redshift ranges: X-ray cluster in the local universe, SZ Planck mission clusters from the near universe or photometric richness estimated detected clusters from future high redshift upcoming Euclid alike mission. Because an improper determination of the calibration of cluster mass function could also be behind this discrepancy, our approach was, when combined with CMB, to leave the calibration factor free to vary and be constrained by data. Introducing three degenerate massive neutrinos, we found that they have no significant effect on fixing the discrepancy between CMB and Xray or SZ cluster counts. We then allowed the growth index ƴ to vary. We find a correlation in the confidence space between ƴ and the X-ray mass observable factor not affected by the presence of massive neutrinos, indicating that a modifying gravity is favored over massive neutrinos as a way to alleviate the tension. However, when a SZ cluster sample covering a larger redshift range was used, we found that the correlation between ƴ and the calibration factor, is constrained by the evolution of the growth through redshift and limited to a region where it cannot fix the discrepancy. We thus tried to consider a dark energy equation of state parameter w constant but different from ΛCDM value of -1 or a dynamical dark energy to see if it can alleviate the tension alone or when mixed with ƴ or neutrinos. We found that extensions to dark energy from ΛCDM could not fix the discrepancy when constrained by CMB Cls and SZ clusters sample while if the less constrainig local X-ray clusters sample is used, the tension is alleviated only for w at values far from fiducial ones that were ruled out when we added BAO and SN geometrical probes. We found also that when we mixed DE and ƴ, the data favors ƴ correlation with the calibration factor and not with w, a sign that a modified gravity has more ability than a DE different from ΛCDM to fix the discrepancy. To investigate what further precision could imply, we tried to perform forecast from future planned surveys allowing to construct larger cluster samples than the available ones and attending redshift ranges high enough to constrain and rule out models beyond ΛCDM. We found as preliminary results, that if we fixed the calibration factors in each probe to their fiducial values when considered separately, or if we let the mass observable factor in addition to the growth index free to vary when we combine CMB Cls and Euclid like cluster counts, the mass observable factor is constrained to the 10% with respect to the fiducial value, sign that only a better calibration could solve the discrepancy or new physics even beyond the extentions we considered in this work

A Short Review on the Latest Neutrinos Mass and Number Constraints from Cosmological Observables

We review the neutrino science, focusing on its impact on cosmology along with the latest constraints on its mass and number of species. We also discuss its status as a possible solution to some of the recent cosmological tensions, such as the Hubble constant or the matter fluctuation parameter. We end by showing forecasts from next-generation planned or candidate surveys, highlighting their constraining power, alone or in combination, but also the limitations in determining neutrino mass distribution among its species