Dynamical Dark Energy Models Research Articles

Robust preference for Dynamical Dark Energy in DESI BAO and SN measurements

Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when combined with Cosmic Microwave Background (CMB) data from Planck and two different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a preference for Dynamical Dark Energy (DDE) characterized by a present-day quintessence-like equation of state that crossed into the phantom regime in the past. A core ansatz for this result is assuming a linear Chevallier-Polarski-Linder (CPL) parameterization w(a) = w 0 + wa (1-a) to describe the evolution of the DE equation of state (EoS). In this paper, we test if and to what extent this assumption impacts the results. To prevent broadening uncertainties in cosmological parameter inference and facilitate direct comparison with the baseline CPL case, we focus on 4 alternative well-known models that, just like CPL, consist of only two free parameters: the present-day DE EoS (w0 ) and a parameter quantifying its dynamical evolution (wa ). We demonstrate that the preference for DDE remains robust regardless of the parameterization: w0 consistently remains in the quintessence regime, while wa consistently indicates a preference for a dynamical evolution towards the phantom regime. This tendency is significantly strengthened by DESY5 SN measurements. By comparing the best-fit χ2 obtained within each DDE model, we notice that the linear CPL parameterization is not the best-fitting case. Among the models considered, the EoS proposed by Barboza and Alcaniz consistently leads to the most significant improvement.

The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing ΛCDM and a dynamical dark energy model ( w0waCDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available.

Cosmological constraints on a dynamical dark energy model in F(Q) gravity

Extended teleparallel gravity, characterized by function F(Q), where Q is the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable 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 at the present time and exhibits a special event in the future, within F(Q) gravity. To constrain the free parameters of the model, we perform Markov chain Monte Carlo (MCMC) analysis, using the last data from Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Pantheon}^{+}$$\\end{document} and the latest measurements of the H(z) parameter, combined. On the basis of this analysis, we find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime, as in the case of general relativity. Furthermore, this behavior affects the future expansion of the Universe, as it becomes decelerating at a 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} confidence level for z<-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z<-0.5$$\\end{document}, showing a bounce at zB≈-0.835\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{\ ext {B}}\\approx -0.835$$\\end{document}. We support our conclusion with a cosmographic analysis.

Exploring the dark energy equation of state with JWST

Observations from the James Webb Space Telescope (JWST) have unveiled several galaxies with stellar masses M∗≳1010M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_*\\gtrsim 10^{10} M_\\odot$$\\end{document} at redshifts 7.4≲z≲9.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.4\\lesssim z\\lesssim 9.1$$\\end{document}. These remarkable findings indicate an unexpectedly high stellar mass density, which contradicts the prediction of the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \\rm{CDM}$$\\end{document} model. Our study utilizes the Chevallier–Polarski–Linder (CPL) parameterization, one of the dynamic dark energy models, to probe the role of dark energy on shaping galaxy formation. By considering varying star formation efficiencies within this framework, our analysis demonstrates that in a universe with a higher proportion of dark energy, more massive galaxies are formed at high redshifts, given a fixed perturbation amplitude observed today. These intriguing results highlight the promising prospect of revealing the nature of dark energy by analyzing the high-redshift massive galaxies.

Semi-symmetric metric gravity: From the Friedmann–Schouten geometry with torsion to dynamical dark energy models

In this paper, we develop a geometric generalization of General Relativity based on the semi-symmetric metric connection introduced by Friedmann and Schouten in 1924. Although the mathematical properties of this connection, which allows for torsion, have been extensively studied, its physical implications remain underexplored. We provide a detailed exposition of the differential geometric aspects of semi-symmetric connections and formulate the corresponding field equations induced by the specific form of torsion we are investigating. We consider the cosmological applications of the theory by deriving the generalized Friedmann equations in a flat, homogeneous and isotropic geometry. The Friedmann equations also include some supplementary terms as compared to their general relativistic counterparts, which can be interpreted as a geometric type dark energy. To evaluate the proposed theory, we consider three cosmological models — the first with constant effective density and pressure, the second with the dark energy satisfying a linear equation of state, and a third one with a polytropic equation of state. We also compare the predictions of the semi-symmetric metric gravitational theory with the observational data for the Hubble function, and with the predictions of the ΛCDM model. Our findings indicate that the semi-symmetric metric cosmological models give a good description of the observational data, and for certain values of the model parameters, they can reproduce almost exactly the predictions of the ΛCDM paradigm. Consequently, Friedmann’s initially proposed geometry emerges as a credible alternative to standard general relativity, in which dark energy has a purely geometric origin.

Evaluating a sigmoid dark energy model to explain the Hubble tension

AbstractIn this study, we analyze Type Ia supernovae (SNe Ia) data sourced from the Pantheon+ compilation to investigate late‐time physics effects influencing the expansion history, , at redshifts . Our focus centers on a time‐varying dark energy (DE) model that introduces a rapid transition in the equation of state, at a specific redshift, , from the baseline, , value to the present value, . The change in the equation of state is implemented as a transition in the DE density scale factor driven by a sigmoid function. The constraints obtained for the DE sigmoid phenomenological parametrization have broad applicability for dynamic DE models that invoke late‐time physics. Our analysis indicates that the sigmoid model provides a slightly better, though not statistically significant, fit to the SNe Pantheon+ data compared to the standard cold dark matter () model. The fit results, assuming a flat geometry and maintaining constant at the 2018‐Planck value of , are as follows: km s Mpc, , . The errors represent statistical uncertainties only. The available SN dataset lacks sufficient statistical power to distinguish between the baseline model and the alternative sigmoid models. A feature of interest offered by the sigmoid model is that it identifies a specific redshift, , where a potential transition in the equation of state could have occurred. The sigmoid model does not favor a DE in the phantom region (). Further constraints to the dynamic DE model have been obtained using CMB data to compute the distance to the last scattering surface. While the sigmoid DE model does not completely resolve the tension, it offers a transition mechanism that can still play a role alongside other potential solutions.

Negative cosmological constant in the dark energy sector: tests from JWST photometric and spectroscopic observations of high-redshift galaxies

Early observations with the James Webb Space Telescope (JWST) have revealed the existence of an unexpectedly large abundance of extremely massive galaxies at redshifts z ≳ 5: these are in tension with the predictions not only of the standard ΛCDM cosmology, but also with those of a wide class of dynamical dark energy (DE) models, and are generally in better agreement with models characterized by a phantom behaviour. Here we consider a model, inspired by string theory and the ubiquity of anti-de Sitter vacua therein, featuring an evolving DE component with positive energy density on top of a negative cosmological constant, argued in an earlier exploratory analysis to potentially be able to explain the JWST observations. We perform a robust comparison of this model against JWST data, considering both photometric observations from the CEERS program, and spectroscopic observations from the FRESCO survey. We show that the model is able to accommodate the JWST observations, with a consistency probability of up to 98%, even in the presence of an evolving component with a quintessence-like behaviour (easier to accommodate theoretically compared to phantom DE), while remaining consistent with standard low-redshift probes. Our results showcase the potential of measurements of high-redshift galaxy abundances in tests of fundamental physics, and their complementarity with standard cosmological probes.

Constraining fundamental constants with fast radio bursts: unveiling the role of energy scale

ABSTRACT Understanding physical mechanisms relies on the accurate determination of fundamental constants, although inherent limitations in experimental techniques introduce uncertainties into these measurements. This paper explores the uncertainties associated with measuring the fine-structure constant ($\alpha$) and the proton-to-electron mass ratio ($\mu$) using observed fast radio bursts (FRBs). We select 50 localized FRBs to quantify the effects of varying this fundamental coupling on the relation between dispersion measure and redshift. By leveraging independent measurements of dispersion measures and redshifts of these FRBs, we constrain the uncertainties in $\alpha$ and $\mu$ approximately to $\Delta \alpha /\alpha =1.99\times 10^{-5}$ and $\Delta \mu /\mu =-1.00\times 10^{-5}$ within the standard $\Lambda$CDM cosmological framework. Remarkably, these constraints improve nearly an order-of-magnitude when considering a dynamical dark energy model. This investigation not only yields one of the most stringent constraints on $\alpha$ and $\mu$ to date but also emphasizes the criticality of accounting for the energy scale of the system when formulating constraints on fundamental parameters.

Cosmological fluids with boundary term couplings

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown’s formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a scalar field, and boundary terms. We describe three different coupling models, one of which turns out to be particularly relevant for cosmology. Its behaviour is similar to that of models in which dark matter decays into dark energy. In particular, for a constant coupling, the model mimics well-known dynamical dark energy models while the non-constant couplings offer a rich dynamical structure, unseen before. We are able to achieve this richness whilst working in a two-dimensional phase space. This is a significant advantage which allows us to provide a clear physical interpretation of the key features and draw analogies with previously studied models.

Dynamical Dark Energy in Light of Cosmic Distance Measurements. II. A Study Using Current Observations

Abstract We extract key information on dark energy from current observations of BAO, OHD and H 0, and find hints of dynamical behavior of dark energy. In particular, a dynamical dark energy model whose equation of state crosses −1 is favored by observations. We also find that the Universe has started accelerating at a lower redshift than expected.

Euclid preparation

In this paper we investigate the impact of lensing magnification on the analysis of Euclid’s spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead.

Current and future cosmological impact of microwave background temperature measurements

The redshift dependence of the cosmic microwave background temperature, T(z)=T0(1+z), is a key prediction of standard cosmology, but this relation is violated in many extensions thereof. Current astrophysical facilities can probe it in the redshift range 0≤z≤6.34. We extend recent work by Gelo et al. (2022) showing that for several classes of models (all of which aim to provide alternative mechanisms for the recent acceleration of the universe) the constraining power of these measurements is comparable to that of other background cosmology probes. Specifically, we discuss constraints on two classes of models not considered in the earlier work: a model with torsion and a recently proposed phenomenological dynamical dark energy model which can be thought of as a varying speed of light model. Moreover, for both these models and also for those in the earlier work, we discuss how current constraints may be improved by next-generation ground and space astrophysical facilities. Overall, we conclude that these measurements have a significant cosmological impact, mainly because they often constrain combinations of model parameters that are orthogonal, in the relevant parameter space, to those of other probes.

Structure formation in various dynamical dark energy scenarios

This research investigates the impact of the nature of Dark Energy (DE) on structure formation, focusing on the matter power spectrum and the Integrated Sachs–Wolfe effect (ISW). By analyzing the matter power spectrum at redshifts z=0 and z=5, as well as the ISW effect on the scale of ℓ=10−100, the study provides valuable insights into the influence of DE equations of state (EoS) on structure formation. The findings reveal that dynamical DE models exhibit a stronger matter power spectrum compared to constant DE models, with the JBP model demonstrating the highest amplitude and the CPL model the weakest. Additionally, the study delves into the ISW effect, highlighting the time evolution of the ISW source term F(a) and its derivative dF(a)/da, and demonstrating that models with constant DE EoS exhibit a stronger amplitude of F(a) overall, while dynamical models such as CPL exhibit the highest amplitude among the dynamical models, whereas JBP has the lowest. The study also explores the ISW auto-correlation power spectrum and the ISW cross-correlation power spectrum, revealing that dynamical DE models dominate over those with constant DE EoS across various surveys. Moreover, it emphasizes the potential of studying the non-linear matter power spectrum and incorporating datasets from the small scales to further elucidate the dynamical nature of dark energy. This comprehensive analysis underscores the significance of both the matter power spectrum and the ISW signal in discerning the nature of dark energy, paving the way for future research to explore the matter power spectrum at higher redshifts and in the non-linear regime, providing deeper insights into the dynamical nature of dark energy.

Cosmic energy density: particles, fields and the vacuum

We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the in vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

Possible combinations of early and late time cosmologies through BAO scales

The theoretical scenarios of early universe and late time accelerated expansion constitute an open problem in cosmology. Relative Baryon Acoustic Oscillation (BAO) scales measured by 6dFGS, mathrm SDSS+2dFGRS, BOSS DR11 Lyalpha and BOSS DR11 QSO Lyalpha are used to investigate the parameter spaces of combinations of pre-recombination physics and late time cosmology. For pre-recombination physics we fix mathrm N_{eff}=3 and 4 and incorporate an Early Dark Energy (EDE) component. For late time cosmologies we consider curved Lambda CDM model, Dynamical Dark Energy (DDE) model with CPL parameterisation (omega _0,omega _1) of equation of state, Coupled Dark Energy (CDE) model with constant coupling and curved DGP brane-world scenario. Combination of a curved Lambda CDM (Omega _{textrm{k}}Lambda CDM) model with mathrm N_{eff}-EDE cosmology is found to be possible. For DDE, the relative BAO scales are achievable through omega _1 preferring the region omega _1< 0. For mathrm N_{eff}-EDE-CDE, the BAO scales are generated for both dark energy-dark matter and dark matter-dark energy conversion, however with exceptionally large value of dark energy density parameter and constant equation of state with omega _0 > -1. Curved DGP cosmology (Omega _textrm{k}DGP) is found to join with N_{textrm{eff}}-EDE cosmology through curvature parameter Omega _{mathrm{k(0)}}in [-0.002, -0.1] and cross-over parameter Omega _{mathrm{r_c}} in [0.08, 0.45]. Cosmic ages are calculated for the derived parameters of Omega _{textrm{k}}Lambda CDM, flat DDE and Omega _{textrm{k}}DGP models and compared with the ages of few globular clusters available in literature. Curved cosmologies are found to be promising.

Smoothing the [formula omitted] tension with a phantom dynamical dark energy model

The discrepancy between Planck data and direct measurements of the current expansion rate H0 and the matter fluctuation amplitude S8 has become one of the most intriguing puzzles in cosmology nowadays. The H0 tension has reached 5σ in the context of standard cosmology i.e ΛCDM. Therefore, explanations to this issue are mandatory to unveil its secrets. Despite its success, ΛCDM is unable to give a satisfying explanation to the tension problem. Unless some systematic errors are hidden in the observable measurements, physics beyond the standard model of cosmology must be advocated. In this perspective, we study a phantom dynamical dark energy model as an alternative to ΛCDM in order to explain the aforementioned issues. This phantom model is characterized by one extra parameter, Ωpdde, compared to ΛCDM. We obtain a strong positive correlation between H0 and Ωpdde, for all data combinations. Using Planck18 measurements together with BAO and Pantheon, we find that the H0 and the S8 tensions are 3.4σ and 2.75σ, respectively. By introducing a prior on the absolute magnitude, MB, of the SN Ia, the H0 tension decreases to 2.49σ with H0=69.7−0.86+0.83 km s−1 Mpc−1 and the S8 tension reaches the value 2.51σ with S8=0.82650.012+0.011.

Prospects for measuring dark energy with 21 cm intensity mapping experiments: A joint survey strategy

The 21 cm intensity mapping (IM) technique provides us with an efficient way to observe the cosmic large-scale structure (LSS). From the LSS data, one can use the baryon acoustic oscillation and redshift space distortion to trace the expansion and growth history of the universe, and thus measure the dark energy parameters. In this paper, we make a forecast for cosmological parameter estimation with the synergy of three 21 cm IM experiments. Specifically, we adopt a novel joint survey strategy, FAST ($0<z<0.35$)+SKA1-MID ($0.35<z<0.8$)+HIRAX ($0.8<z<2.5$), to measure dark energy. We simulate the 21 cm IM observations under the assumption of excellent foreground removal. We find that the synergy of three experiments could place quite tight constraints on cosmological parameters. For example, it provides $\sigma(\Omega_{\rm m})=0.0039$ and $\sigma(H_0)=0.27\ \rm km\ s^{-1}\ Mpc^{-1}$ in the $\Lambda$CDM model. Notably, the synergy could break the cosmological parameter degeneracies when constraining the dynamical dark energy models. Concretely, the joint observation offers $\sigma(w)=0.019$ in the $w$CDM model, and $\sigma(w_0)=0.085$ and $\sigma(w_a)=0.32$ in the $w_0w_a$CDM model. These results are better than or equal to those given by CMB+BAO+SN. In addition, when the foreground removal efficiency is relatively low, the strategy still performs well. Therefore, the 21 cm IM joint survey strategy is promising and worth pursuing.

H0=69.8±1.3 km s−1 Mpc−1 , Ωm0=0.288±0.017 , and other constraints from lower-redshift, non-CMB, expansion-rate data

We use updated Type Ia Pantheon+ supernova, baryon acoustic oscillation, and Hubble parameter (now also accounting for correlations) data, as well as new reverberation-measured C IV quasar data, and quasar angular size, H II starburst galaxy, reverberation-measured Mg II quasar, and Amati-correlated gamma-ray burst data to constrain cosmological parameters. We show that these data sets result in mutually consistent constraints and jointly use them to constrain cosmological parameters in six different spatially-flat and non-flat cosmological models. Our analysis provides summary model-independent determinations of two key cosmological parameters: the Hubble constant, $H_0=69.8\pm1.3$ $\rm{km \ s^{-1} \ Mpc^{-1}}$, and the current non-relativistic matter density parameter, $\Omega_{m0}=0.288\pm0.017$. Our summary error bars are 2.4 and 2.3 times those obtained using the flat $\Lambda$CDM model and Planck TT,TE,EE+lowE+lensing cosmic microwave background (CMB) anisotropy data. Our $H_0$ value is very consistent with that from the local expansion rate based on the Tip of the Red Giant Branch data, is 2$\sigma$ lower than that from the local expansion rate based on Type Ia supernova and Cepheid data, and is 2$\sigma$ higher than that in the flat $\Lambda$CDM model based on Planck TT,TE,EE+lowE+lensing CMB data. Our data compilation shows at most mild evidence for non-flat spatial hypersurfaces, but more significant evidence for dark energy dynamics, 2$\sigma$ or larger in the spatially-flat dynamical dark energy models we study.

Correlation of structure growth index with current cosmic acceleration: Constraints on dark energy models

We study dynamical dark energy (DE) models within Einstein’s theory by means of matter perturbations and the growth index [Formula: see text]. Within four-dimensional General Relativity, we assume that DE does not cluster, and we adopt a linear ansatz for the growth index to investigate its impact on the deceleration parameter, [Formula: see text], and on the DE equation-of-state parameter, [Formula: see text]. Following this approach, we identify a relationship between [Formula: see text] (today’s value of [Formula: see text]) and [Formula: see text], which to the best of our knowledge is new. For [Formula: see text], we find that in most of the cases considered it crosses the [Formula: see text] line (quintom) ending at a present day value [Formula: see text]. Furthermore, we show that an analytic expression for [Formula: see text] may be obtained in the form of order (4,4) (or higher) Padé parametrizations.

Joint constraints on cosmological parameters using future multi-band gravitational wave standard siren observations* *Supported by the National SKA Program of China (2022SKA0110200, 2022SKA0110203) and the National Natural Science Foundation of China (11975072, 11875102, 11835009)

Gravitational waves (GWs) from compact binary coalescences can be used as standard sirens to explore the cosmic expansion history. In the next decades, it is anticipated that we could obtain the multi-band GW standard siren data (from nanohertz to a few hundred hertz), which are expected to play an important role in cosmological parameter estimation. In this work, we provide, for the first time to the best of our knowledge, joint constraints on cosmological parameters using the future multi-band GW standard siren observations. We simulate the multi-band GW standard sirens based on the SKA-era pulsar timing array (PTA), Taiji observatory, and Cosmic Explorer (CE) to perform cosmological analysis. In the ΛCDM model, we find that the joint PTA+Taiji+CE data could provide a tight constraint on the Hubble constant with a precision. Moreover, PTA+Taiji+CE could break the cosmological parameter degeneracies generated by CMB, especially in the dynamical dark energy models. When combining the PTA+Taiji+CE data with the CMB data, the constraint precisions of and are and , respectively, meeting the standard of precision cosmology. The joint CMB+PTA+Taiji+CE data give in the wCDM model and and in the CDM model, which are comparable with or close to the latest constraint results by CMB+BAO+SN. In conclusion, the future multi-band GW observations are expected to be used for exploring the nature of dark energy and measuring the Hubble constant.