Redshift Space Distortion Data Research Articles

Constraints on Power Law and Exponential models in f(Q) Gravity

In this paper, we observationally test the f(Q) gravity model at both background and perturbation levels using Pantheon+, Hubble measurements, and Redshift Space Distortion Data. We obtain the best-fit parameters by solving numerically the modified Friedmann equations for two distinct cosmological models of f(Q) gravity namely the Power law and Exponential models. This involves performing a Markov Chain Monte Carlo analysis for these specific forms of f(Q). To evaluate the statistical significance of the f(Q) gravity models, we use the Bayesian and corrected Akaike Information Criteria. Our results indicate that the Exponential model in f(Q) gravity is statistically favored over both the Power-law model and the ΛCDM model.

Growth of cosmic perturbations in the modified [formula omitted] gravity

We explore the generalized f(R,T) modified theory of gravity, where the gravitational Lagrangian is a function of Ricci scalar R and the trace of the energy–momentum tensor T. We derive modified field equations to the linear order of perturbations in the context of f(R,T) model. We then investigate the growth of perturbations in the context of f(R,T) modified gravity. Primary numerical investigations based on matter power spectra diagrams indicate a structure growth suppression in f(R,T) gravity, which exhibits consistency with local measurements. Also, we notice that matter-geometry interaction in f(R,T) model would results in the specific feature named as “matter acoustic oscillations” appeared in matter power spectra diagrams. Moreover, we put constraints on the cosmological parameters of f(R,T) model, utilizing current observations, chiefly cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results based on MCMC calculations imply that f(R,T) is a qualified theory of modified gravity in reconciling Planck CMB data with local probes of large scale structures, by reporting lower values for the structure growth parameter σ8 compared to the standard model of cosmology.

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

Scrutinizing coupled vector dark energy in light of data

Since current challenges faced by ΛCDM might be hinting at new unravelled physics, here we investigate a plausible cosmological model where a vector field acts as source of dark energy. In particular, we examine whether an energy-momentum exchange between dark energy and dark matter could provide an explanation for current discrepancies in cosmological parameters. We carefully work out equations governing background and linear order perturbations and implement them in a Boltzmann code. We found that a negative coupling makes the dark energy equation of state less negative and closer to a cosmological constant during the matter dominated epoch than an uncoupled vector dark energy model. While the effect of the coupling is hardly noticeable through its effect on matter density perturbations, matter velocity perturbations and gravitational potentials are enhanced at late-times when dark energy dominates. Therefore, data of redshift space distortions help to narrow down these kinds of couplings in the dark sector. We computed cosmological constraints and found common parameters also present in ΛCDM are in good agreement with the Planck collaboration baseline result. Our best fit for a negatively coupled vector field predicts a higher growth rate of matter perturbations at low redshift, thus exacerbating the disagreement with redshift space distortions data. While a positively coupled vector field can lead to power suppression of P m(k,z = 0) on small scales as well as a lower growth rate of matter perturbations than the standard model, it might compromise the goodness of fit to the CMB angular power spectrum on small scales. We conclude that our negatively coupled vector dark energy model does not solve current tensions (i.e., H 0 and σ 8). Moreover, having three additional parameters with respect to ΛCDM, the negatively coupled vector dark energy model is heavily disfavoured by Bayesian evidence.

Cosmological constraints on f(Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q)$$\\end{document} gravity with redshift space distortion data

In this paper, we explore one of Einstein’s alternative formulations which involves the non-metricity scalar, Q, within the framework of f(Q) theory. Our study focuses on solving the modified Friedmann equations for the case of dust matter, ρ=ρm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho =\\rho _{m}$$\\end{document}, and a form of f(Q)=α+βQn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q) = \\alpha + \\beta Q^n$$\\end{document}. We investigate the behavior of our model in both linear (n=1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n=1)$$\\end{document} and nonlinear (n≠1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n\ e 1)$$\\end{document} scenarios at the background and perturbation levels. By employing the Markov chain Monte Carlo (MCMC) method, we constrain our model using observational datasets including redshift space distortion, cosmic chronometers, and Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document}. Without using any parameterization of the growth rate index which quantifies the deviation from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model, both models exhibit good accuracy in describing the redshift space distortion. We further analyze the dynamics of the Universe using cosmography parameters, where our model exhibits a phase transition between deceleration and acceleration phases at z=0.789\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=0.789$$\\end{document}. Our findings reveal that our model exhibits a phantom-like behavior based on statefinder diagnostic analysis. Interestingly, the model demonstrates a rich variety of behaviors, resembling either a quintessence-like scenario for (n<1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n<1)$$\\end{document} or phantom-like scenario for (n≥1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n\\ge 1)$$\\end{document}. Using the MCMC best fit and parameterizing the growth index, the evolution of the growth index also depends on the parameter n, either remaining constant (in the linear case) or showing a decreasing trend (in the nonlinear case), indicating a weaker growth rate of density perturbations during earlier cosmic times. Finally, we compare our findings of the growth index with the values obtained in the literature.

Growth of structures using redshift space distortion in f(T) cosmology

ABSTRACT Cosmology faces a pressing challenge with the Hubble constant (H0) tension, where the locally measured rate of the Universe’s expansion does not align with predictions from the cosmic microwave background calibrated with lambda-cold dark matter model. Simultaneously, there is a growing tension involving the weighted amplitude of matter fluctuations, known as S8,0 tension. Resolving both tensions within one framework would boost confidence in any one particular model. In this work, we analyse constraints in f(T) gravity, a framework that shows promise in shedding light on cosmic evolution. We thoroughly examine prominent f(T) gravity models using a combination of data sources, including pantheon+ (SN), cosmic chronometers, baryonic acoustic oscillations, and redshift space distortion data. We use these models to derive a spectrum of H0 and S8,0 values, aiming to gauge their ability to provide insights into, and potentially address, the challenges posed by the H0 and S8,0 tensions.

Cosmological Tensions and the Transitional Planck Mass Model

In this follow-up analysis, we update previous constraints on the transitional Planck mass (TPM) modified gravity model using the latest version of EFTCAMB and provide new constraints using South Pole Telescope (SPT) and Planck anisotropy data along with Planck cosmic microwave background lensing, baryon acoustic oscillations, and Type Ia supernovae data and a Hubble constant, H 0, prior from local measurements. We find that large shifts in the Planck mass lead to large suppression of power on small scales that is disfavored by both the SPT and Planck data. Using only the SPT temperature-polarization–polarization-polarization (TE-EE) data, this suppression of power can be compensated for by an upward shift of the scalar index to n s = 1.003 ± 0.016, resulting in km m−1 Mpc−1 and a ∼7% shift in the Planck mass. Including the Planck temperature-temperature (TT) ℓ ≤ 650 and Planck TE-EE data restricts the shift to be <5% at 2σ with H 0 = 70.65 ± 0.66 km m−1 Mpc−1. Excluding the H 0 prior, the SPT and Planck data constrain the shift in the Planck mass to be <3% at 2σ with a best-fit value of 0.04%, consistent with the Λ cold dark matter limit. In this case km s−1 Mpc−1, which is partially elevated by the dynamics of the scalar field in the late Universe. This differs from early dark energy models that prefer higher values of H 0 when the high-ℓ Planck TT data are excluded. We additionally constrain TPM using redshift space distortion data from BOSS DR12 and cosmic shear, galaxy–galaxy lensing, and galaxy clustering data from DES Y1, finding both disfavor transitions close to recombination, but earlier Planck mass transitions are allowed.

Constraining disformal couplings with Redshift Space Distortion

We study a quintessence model for which the scalar field is disformally coupled to dark matter. The background mimics the ΛCDM cosmological evolution and the quintessence potential is not specified. A disformal effect due to the quintessential mass is seen in the growth rate of the cosmological structure on large scales. The disformal parameter renders no appreciable effect on the evolution of the total matter perturbation. An analysis of the conformal parameter and quintessential mass is investigated using the Redshift Space Distortion data to find the best-fit values that might explain the well-known σ 8 tension.

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions: Dark energy beyond Λ

Combining supernovae, baryon acoustic oscillations, and redshift-space distortions data from the next generation of (stage-IV) cosmological surveys, we aim to reconstruct the expansion history up to large redshifts using forward-modeling of ${f}_{\mathrm{DE}}(z)={\ensuremath{\rho}}_{\mathrm{DE}}(z)/{\ensuremath{\rho}}_{\mathrm{DE},0}$ with Gaussian processes (GP). In order to reconstruct cosmological quantities at high redshifts where few or no data are available, we adopt a new approach to GP which enforces the following minimal assumptions: (a) Our cosmology corresponds to a flat Friedman-Lema\^{\i}tre-Robertson-Walker universe; (b) An Einstein de Sitter (EdS) universe is obtained on large redshifts. This allows us to reconstruct the perturbations growth history from the reconstructed background expansion history. Assuming various DE models, we show the ability of our reconstruction method to differentiate them from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at $\ensuremath{\gtrsim}2\ensuremath{\sigma}$.

KiDS and Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography

We present a tomographic weak lensing analysis of the Kilo Degree Survey Data Release 4 (KiDS-1000), using a new pseudo angular power spectrum estimator (pseudo-Cℓ) under development for the ESA Euclid mission. Over 21 million galaxies with shape information are divided into five tomographic redshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measured pseudo-Cℓ using eight bands in the multipole range 76 &lt; ℓ &lt; 1500 for auto- and cross-power spectra between the tomographic bins. A series of tests were carried out to check for systematic contamination from a variety of observational sources including stellar number density, variations in survey depth, and point spread function properties. While some marginal correlations with these systematic tracers were observed, there is no evidence of bias in the cosmological inference. B-mode power spectra are consistent with zero signal, with no significant residual contamination from E/B-mode leakage. We performed a Bayesian analysis of the pseudo-Cℓ estimates by forward modelling the effects of the mask. Assuming a spatially flat ΛCDM cosmology, we constrained the structure growth parameter S8 = σ8(Ωm/0.3)1/2 = 0.754−0.029+0.027. When combining cosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift space distortion data from recent Sloan Digital Sky Survey (SDSS) measurements of luminous red galaxies, as well as the Lyman-α forest and its cross-correlation with quasars, we tightened these constraints to S8 = 0.771−0.032+0.006. These results are in very good agreement with previous KiDS-1000 and SDSS analyses and confirm a ∼3σ tension with early-Universe constraints from cosmic microwave background experiments.

Constraining decaying dark matter with BOSS data and the effective field theory of large-scale structures

We update cosmological constraints on two decaying dark matter models in light of BOSS-DR12 data analyzed under the effective field theory of large-scale structures (EFTofLSS) formalism, together with Planck, Pantheon and other BOSS measurements of the baryonic acoustic oscillation (BAO). In the first model, a fraction ${f}_{\mathrm{dcdm}}$ of cold dark matter (CDM) decays into dark radiation (DR) with a lifetime $\ensuremath{\tau}$. In the second model (recently suggested as a potential resolution to the ${S}_{8}$ tension), all the CDM decays with a lifetime $\ensuremath{\tau}$ into DR and a massive warm dark matter (WDM) particle, with a fraction $ϵ$ of the CDM rest mass energy transferred to the DR. Using numerical codes from the recent literature, we perform the first calculation of the mildly nonlinear (matter and galaxy) power spectra with the EFTofLSS for these two models. In the case of DR products, we obtain the constraints ${f}_{\mathrm{dcdm}}\ensuremath{\lesssim}0.022$ (95% C.L.) for lifetimes shorter than the age of the Universe, and $\ensuremath{\tau}/{f}_{\mathrm{dcdm}}\ensuremath{\gtrsim}250\text{ }\text{ }\mathrm{Gyr}$ in the long-lived regime assuming ${f}_{\mathrm{dcdm}}\ensuremath{\rightarrow}1$. We show that Planck data contributes the most to these constraints, with EFTofBOSS providing a marginal improvement over conventional BAO and redshift space distortions ($f{\ensuremath{\sigma}}_{8}$) data. In the case of DR and WDM decay products, we find that EFTofBOSS data significantly improves the constraints at 68% C.L. on the CDM lifetime with a ${S}_{8}$ prior from KiDS-1000. We show that, in order to fit EFTofBOSS data while lowering ${S}_{8}$ to match KiDS-1000, the best-fit model has a longer lifetime $\ensuremath{\tau}=120\text{ }\text{ }\mathrm{Gyr}$, with a larger kick velocity ${v}_{\mathrm{kick}}/c\ensuremath{\simeq}ϵ\ensuremath{\simeq}1.2%$, than that without EFTofBOSS ($\ensuremath{\tau}=43\text{ }\text{ }\mathrm{Gyr}$, $ϵ=0.6%$). We anticipate that future surveys will provide exquisite constraints on such models.

Constraining the curvature density parameter in cosmology

The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is performed adopting the non-parametric Gaussian Processes (GP). The constraints on $\Omega_{k0}$ are obtained via a Markov Chain Monte Carlo (MCMC) analysis. Late-time cosmological probes viz., the Supernova (SN) distance modulus data, the Cosmic Chronometer (CC) and the radial Baryon Acoustic Oscillations ($r$BAO) measurements of the Hubble data have been utilized for this purpose. The results are further combined with the data from redshift space distortions (RSD) which studies the growth of large scale structure in the universe. The only \textit{a priori} assumption is that the universe is homogeneous and isotropic, described by the FLRW metric. Results indicate that a spatially flat universe is well consistent in 2$\sigma$ within the domain of reconstruction $0<z<2$ for the background data. On combining the RSD data we find that the results obtained are consistent with spatial flatness mostly within 2$\sigma$ and always within 3$\sigma$ in the domain of reconstruction $0<z<2$.

Model-independent constraints on Ωm and H(z) from the link between geometry and growth

ABSTRACT We constrain the expansion history of the Universe and the cosmological matter density fraction in a model-independent way by exclusively making use of the relationship between background and perturbations under a minimal set of assumptions. We do so by employing a Gaussian process to model the expansion history of the Universe from present time to the recombination era. The expansion history and the cosmological matter density are then constrained using recent measurements from cosmic chronometers, Type-Ia supernovae, baryon acoustic oscillations, and redshift-space distortion data. Our results show that the evolution in the reconstructed expansion history is compatible with the Planck 2018 prediction at all redshifts. The current data considered in this study can constrain a Gaussian process on H(z) to an average $9.4 {{\ \rm per\ cent}}$ precision across redshift. We find Ωm = 0.224 ± 0.066, lower but statistically compatible with the Planck 2018 cosmology. Finally, the combination of future DESI measurements with the CMB measurement considered in this work holds the promise of $8 {{\ \rm per\ cent}}$ average constraints on a model-independent expansion history as well as a five-fold tighter Ωm constraint using the methodology developed in this work.

The S8 tension in light of updated redshift-space distortion data and PAge approximation

One of the most prominent challenges to the standard Lambda cold dark matter ($\Lambda$CDM) cosmology is the tension between the structure growth parameter $S_8$ constrained by the cosmic microwave background (CMB) data and the smaller one suggested by the cosmic shear data. Recent studies show that, for $\Lambda$CDM cosmology, redshift-space distortion (RSD) data also prefers a smaller $S_8$ that is $\sim 2$-$3\sigma$ lower than the CMB value, but the result is sensitive to the cosmological model. In the present work we update the RSD constraint on $S_8$ with the most up-to-date RSD data set where the correlation between data points are properly taken into account. To reduce the model dependence, we add in our Monte Carlo Markov Chain calculation the most up-to-date data sets of Type Ia supernovae (SN) and baryon acoustic oscillations (BAO), whose correlation with RSD is also taken into account, to constrain the background geometry. For $\Lambda$CDM cosmology we find $S_8= 0.812 \pm 0.026$, which is $\sim 2\sigma$ larger than previous studies, and hence is consistent with the CMB constraint. By replacing $\Lambda$CDM with the Parameterization based on cosmic Age (PAge), an almost model-independent description of the late universe, we find that the RSD + SN + BAO constraint on $S_8$ is insensitive to the cosmological model.

Observational constraints on Tsallis modified gravity

ABSTRACT The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive Tsallis entropy, S ∼ Aβ here, we first derive the corresponding gravitational field equations by applying the Clausius relation δQ = TδS to the horizon. We then construct the Friedmann equations of Friedmann-Lemaître-Robertson-Walker Universe based on Tsallis modified gravity (TMG). Moreover, in order to constrain the cosmological parameters of TMG model, we use observational data, including Planck cosmic microwave background, weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results indicate that TMG model with a quintessential dark energy is more compatible with the low redshift measurements of large scale structures by predicting a lower value for the structure growth parameter σ8 with respect to ΛCDM model. This implies that TMG model would slightly alleviate the σ8 tension.

First evidence that non-metricity f(Q) gravity could challenge ΛCDM

We propose a novel model in the framework of f(Q) gravity, which is a gravitational modification class arising from the incorporation of non-metricity. The model has General Relativity as a particular limit, it has the same number of free parameters to those of ΛCDM, however at a cosmological framework it gives rise to a scenario that does not have ΛCDM as a limit. Nevertheless, confrontation with observations at both background and perturbation levels, namely with Supernovae type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), cosmic chronometers (CC), and Redshift Space Distortion (RSD) data, reveals that the scenario, according to AIC, BIC and DIC information criteria, is in some datasets slightly preferred comparing to ΛCDM cosmology, although in all cases the two models are statistically indiscriminate. Finally, the model does not exhibit early dark energy features, and thus it immediately passes BBN constraints, while the variation of the effective Newton's constant lies well inside the observational bounds.

Kinematics of Mg ii absorbers from the redshift-space distortion around massive quiescent galaxies

ABSTRACT The kinematics of Mg ii absorbers is the key to understanding the origin of cool, metal-enriched gas clouds in the circumgalactic medium of massive quiescent galaxies. Exploiting the fact that the cloud line-of-sight velocity distribution is the only unknown for predicting the redshift-space distortion (RSD) of Mg ii absorbers from their 3D real-space distribution around galaxies, we develop a novel method to infer the cool cloud kinematics from the redshift-space galaxy–cloud cross-correlation ξs. We measure ξs for ∼104 Mg ii absorbers around ∼8 × 105 CMASS galaxies at 0.4 &amp;lt; z &amp;lt; 0.8. We discover that ξs does not exhibit a strong Fingers-of-God effect, but is heavily truncated at velocity ${\sim }300\, \mathrm{km}\, {\rm s}^{-1}$. We reconstruct both the redshift and real-space cloud number density distributions inside haloes, $\xi ^{s}_{1h}$ and ξ1h, respectively. Thus, for any model of cloud kinematics, we can predict $\xi ^{s}_{1h}$ from the reconstructed ξ1h, and self-consistently compare to the observed $\xi ^{s}_{1h}$. We consider four types of cloud kinematics, including an isothermal model with a single velocity dispersion, a satellite infall model in which cool clouds reside in the subhaloes, a cloud accretion model in which clouds follow the cosmic gas accretion, and a tired wind model in which clouds originate from the galactic wind-driven bubbles. All the four models provide statistically good fits to the RSD data, but only the tired wind model can reproduce the observed truncation by propagating ancient wind bubbles at ${\sim }250\, \mathrm{km}\, s^{-1}$ on scales ${\sim }400\, \, h^{-1}\, \mathrm{kpc}$. Our method provides an exciting path to decoding the dynamical origin of metal absorbers from the RSD measurements with upcoming spectroscopic surveys.

Growth of structures and redshift-space distortion data in scale-dependent gravity

This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between $\Lambda$CDM and available observations as far as the value of the rms density fluctuation, $\sigma_8$, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at red-shift $z \sim 1$. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination $A=f \sigma_8$ in the framework of scale-dependent gravity, where both Newton's constant and the cosmological constant are allowed to vary with time. Upon comparison between available observational data (supernovae data as well as redshift-space distortion data) and theoretical predictions of the model, we determine the numerical value of $\sigma_8$ that best fits the data.

Measurement on the cosmic curvature using the Gaussian process method

ABSTRACT Inflation predicts that the Universe is spatially flat. The Planck 2018 measurements of the cosmic microwave background anisotropy favour a spatially closed universe at more than 2σ confidence level. We use model-independent methods to study the issue of cosmic curvature. The method reconstructs the Hubble parameter H(z) from cosmic chronometers data with the Gaussian process method. The distance modulus is then calculated with the reconstructed function H(z) and fitted by Type Ia supernovae data. Combining the cosmic chronometers and Type Ia supernovae data, we obtain Ωk0h2 = 0.102 ± 0.066 that is consistent with a spatially flat universe at the 2σ confidence level. By adding the redshift-space distortions data to the Type Ia supernovae data with a proposed novel model-independent method, we obtain $\Omega _{k0}h^2=0.117^{+0.058}_{-0.045}$ and no deviation from Λ cold dark matter (ΛCDM) model is found.

Testing the effect of H0 on fσ8 tension using a Gaussian process method

ABSTRACT Using the fσ8(z) redshift space distortion (RSD) data, the $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$ tension is studied utilizing a parametrization of growth rate f(z) = Ωm(z)γ. Here, f(z) is derived from the expansion history H(z) which is reconstructed from the observational Hubble data applying the Gaussian process method. It is found that different priors of H0 have great influences on the evolution curve of H(z) and the constraint of $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$. When using a larger H0 prior, the low redshifts H(z) deviate significantly from that of the ΛCDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the H0 tension problem. The tension between our best-fitting values of $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$ and that of the Planck 2018 ΛCDM (PLA) will disappear (less than 1σ) when taking a prior for H0 obtained from PLA. Moreover, the tension exceeds 2σ level when applying the prior H0 = 73.52 ± 1.62 km s−1 Mpc−1 resulted from the Hubble Space Telescope photometry. By comparing the $S_8\!-\!\Omega _\mathrm{ m}^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.