A new diagnostic for the null test of dynamical dark energy in light of DESI 2024 and other BAO data

To elucidate the robustness of the baryon acoustic oscillation (BAO) data measured by the dark energy spectroscopic instrument (DESI) in capturing the dynamical behavior of dark energy, we assess the model dependence of the evidence for dynamical dark energy inferred from the DESI BAO data. While the DESI BAO data slightly tightens the constraints on model parameters and increases the tension between the Chevallier–Polarski–Linder (CPL) model and the ΛCDM model, we find that the influence of DESI BAO data on the constraint of w0 is small in the SSLCPL model. In comparison to the CPL model, the tension with the ΛCDM model is reduced for the SSLCPL model, suggesting that the evidence for dynamical dark energy from DESI BAO data is dependent on cosmological models. The inclusion of spatial curvature has little impact on the results in the SSLCPL model.

Recent measurements of baryon acoustic oscillations (BAO) by the Dark Energy Spectroscopic Instrument (DESI) exhibit a mild-to-moderate tension with cosmic microwave background (CMB) and Type Ia supernova (SN) observations when interpreted within the ΛCDM framework. This discrepancy has been cited as evidence for dynamical dark energy (DDE). Given the profound implications of DDE for fundamental physics, we explore whether the tension can instead be resolved by modifying the physics of recombination. We find that a phenomenological model of modified recombination can effectively reconcile the BAO and CMB datasets and, unlike DDE, also predicts a higher Hubble constant H 0, thereby partially alleviating the Hubble tension. A global fit to BAO, CMB, and calibrated SN data favors modified recombination over DDE.

We present baryon acoustic oscillation (BAO) measurements from more than 14 million galaxies and quasars drawn from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), based on three years of operation. For cosmology inference, these galaxy measurements are combined with DESI Lyman- α forest BAO results presented in a companion paper (M. Abdul-Karim , companion paper, .). The DR2 BAO results are consistent with DESI DR1 and the Sloan Digital Sky Survey, and their distance-redshift relationship matches those from recent compilations of supernovae (SNe) over the same redshift range. The results are well described by a flat Λ cold dark matter ( Λ CDM ) model, but the parameters preferred by BAO are in mild, 2.3 σ tension with those determined from the cosmic microwave background (CMB), although the DESI results are consistent with the acoustic angular scale θ * that is well measured by Planck. This tension is alleviated by dark energy with a time-evolving equation of state parametrized by w 0 and w a , which provides a better fit to the data, with a favored solution in the quadrant with w 0 > − 1 and w a < 0 . This solution is preferred over Λ CDM at 3.1 σ for the combination of DESI BAO and CMB data. When also including SNe, the preference for a dynamical dark energy model over Λ CDM ranges from 2.8 − 4.2 σ depending on which SNe sample is used. We present evidence from other data combinations which also favor the same behavior at high significance. From the combination of DESI and CMB we derive 95% upper limits on the sum of neutrino masses, finding ∑ m ν < 0.064 eV assuming Λ CDM and ∑ m ν < 0.16 eV in the w 0 w a model. Unless there is an unknown systematic error associated with one or more datasets, it is clear that Λ CDM is being challenged by the combination of DESI BAO with other measurements and that dynamical dark energy offers a possible solution.

In light of the evidence for dynamical dark energy (DE) found from the most recent Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) measurements, we perform a nonparametric, model-independent reconstruction of the DE density evolution. To do so, we develop and validate a new framework that reconstructs the DE density through a third-degree piecewise polynomial interpolation, allowing for direct constraints on its redshift evolution without assuming any specific functional form. The strength of our approach resides in the choice of directly reconstructing the DE density, which provides a more straightforward relation to the distances measured by BAO than the equation of state parameter. We investigate the constraining power of cosmic microwave background (CMB) observations combined with supernovae (SNe) and BAO measurements. In agreement with results from other works, we find a preference for deviations from ΛCDM, with a significance of 2.4σ when using the Dark Energy Survey Year 5 (DESY5) SNe data, and 1.3σ with PantheonPlus. In all the cases we consider, the derived DE equation of state parameter presents evidence for phantom crossing. By investigating potential systematic effects in the low-redshift samples of DESY5 observations, we confirm that correcting for the offset in apparent magnitude with respect to PantheonPlus data, as suggested in previous studies, completely removes the tension. Furthermore, we assess the risk of potentially overfitting the data by changing the number of interpolation nodes. As expected, we find that with lesser nodes we get a smoother reconstructed behavior of the DE density, although with similar overall features. The pipeline developed in this work is ready to be used with future high-precision data to further investigate the evidence for a nonstandard background evolution.

Understanding whether cosmic acceleration arises from a cosmological constant or a dynamical component is a central goal of cosmology, and the Dark Energy Spectroscopic Instrument (DESI) enables stringent tests with high-precision distance measurements. Here we analyse measurements of baryon acoustic oscillations in DESI Data Release 1 and Data Release 2 and consider type Ia supernovae and a distance prior for the cosmic microwave background. With the larger statistical power and wider redshift coverage of Data Release 2, the preference for dynamical dark energy does not diminish relative to Data Release 1. Using both a shape-function reconstruction and non-parametric approaches with a Horndeski-motivated correlation prior, we find that the equation of state for dark energy w(z) varies with redshift. Baryon acoustic oscillation data alone yield modest constraints, but in combination with independent supernova compilations and the prior for the cosmic microwave background, they strengthen the evidence for dynamics. A Bayesian comparison of models shows moderate support for departures from Λ cold dark matter (ΛCDM) when several degrees of freedom in w(z) are allowed, corresponding to ~3σ tension with ΛCDM (and higher for some datasets). Despite methodological differences, our results are consistent with companion DESI papers, underscoring the complementarity of the approaches. Possible systematics remain under study; forthcoming DESI, Euclid and next-generation cosmic microwave background data will provide decisive tests.

In this article we compare a variety of well-known dynamical dark energy models using the cosmic microwave background measurements from the 2018 Planck legacy and 2015 Planck data releases, the baryon acoustic oscillations measurements and the local measurements of H0 obtained by the SH0ES (Supernovae, H0, for the Equation of State of Dark energy) collaboration analysing the Hubble Space Telescope data. We discuss the alleviation of H0 tension, that is obtained at the price of a phantom-like dark energy equation of state. We perform a Bayesian evidence analysis to quantify the improvement of the fit, finding that all the dark energy models considered in this work are preferred against the ΛCDM scenario. Finally, among all the possibilities analysed, the CPL model is the best one in fitting the data and solving the H0 tension at the same time. However, unfortunately, this dynamical dark energy solution is not supported by the baryon acoustic oscillations (BAO) data, and the tension is restored when BAO data are included for all the models.

We investigate the null tests of cosmic accelerated expansion by using the Baryon Acoustic Oscillation (BAO) data measured by the Dark Energy Spectroscopic Instrument (DESI) and reconstruct the dimensionless Hubble parameter E ( z ) from the DESI BAO Alcock-Paczynski (AP) data using Gaussian process to perform the null test. We find strong evidence of accelerated expansion from the DESI BAO AP data. By reconstructing the deceleration parameter q ( z ) from the DESI BAO AP data, we find that accelerated expansion persisted until z ≲ 0.7 with a 99.7% confidence level. Additionally, to provide insights into the Hubble tension problem, we propose combining the reconstructed E ( z ) with D H / r d data to derive the model-independent result r d h = 99.8 ± 3.1 Mpc. This result is consistent with measurements from cosmic microwave background (CMB) anisotropies using the ΛCDM model. We also propose a model-independent method for reconstructing the comoving angular diameter distance D M ( z ) from the distance modulus μ using SNe Ia data and combining this result with DESI BAO data of D M / r d to constrain the value of r d . We find that the value of r d derived from this model-independent method is smaller than that obtained from CMB measurements, with a significant discrepancy of at least 4.17 σ . All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.

New insights from the Dark Energy Spectroscopic Instrument (DESI) 2024 baryon acoustic oscillations (BAO) data, in conjunction with cosmic microwave background (CMB) and Type Ia supernova (SN) data, suggest that dark energy may not be a cosmological constant. In this work, we investigate the cosmological implications of holographic dark energy (HDE) and interacting holographic dark energy (IHDE) models, utilizing CMB, DESI BAO, and SN data. By considering the combined DESI BAO and SN data, we determine that in the IHDE model, the parameter c>1 1$$\\end{document}]]> and the dark-energy equation of state w does not cross -1 at the 1σ confidence level, whereas in the HDE model, it marginally falls below this threshold. Upon incorporating CMB data, we observe that in the HDE model, the parameter c<1 and w crosses -1 at a level beyond 10σ. Conversely, for the IHDE model, the likelihood of w crossing -1 is considerably diminished, implying that the introduction of interaction within the HDE model could potentially resolve or mitigate the cosmic big rip conundrum. Furthermore, our analysis reveals that the HDE and IHDE models are statistically as viable as the ΛCDM model when assessing Bayesian evidence with DESI BAO data combined with SN data. However, when CMB data are added, the HDE and IHDE models are significantly less favored than the ΛCDM model. Our findings advocate for further exploration of the HDE and IHDE models using forthcoming, more precise late-universe observations.

Recent baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) collaboration, combined with the cosmic microwave background (CMB) and type Ia supernovae observations, suggest a preference for dynamical dark energy (DDE) with w 0 &gt; −1 and w a &lt; 0. Given the cosmological origin of fast radio bursts (FRBs), the combination of their dispersion measures (DMs) and host galaxy redshifts makes localized FRBs a valuable tool for probing cosmology. Using an updated sample of 92 localized FRBs, along with DESI BAO, PlantheonPlus, and CMB data, we constrain the dark energy (DE) equation of state (EoS) under the Chevallier–Polarski–Linder parameterization. We find that even without incorporating CMB data, DDE remains preferred with w 0 = − 0.85 5 − 0.084 + 0.084 and w a = − 1.17 4 − 0.491 + 0.462 at a confidence level of ∼2.5σ. A joint analysis constrains these to be w 0 = − 0.78 4 − 0.064 + 0.064 and w a = − 0.87 2 − 0.278 + 0.269 , showing a discrepancy with ΛCDM at a ∼3.1σ level. Furthermore, using localized FRBs alone, we estimate the Hubble constant H 0 to be 69.0 4 − 2.07 + 2.30 and 75.6 1 − 2.07 + 2.23 km s − 1 Mpc − 1 , assuming the Galactic electron density models to be NE2001 and YMW16, respectively. Thus, accurate accounting of the Galactic DM is crucial for resolving the Hubble tension with FRBs. Future BAO measurements, next-generation CMB experiments, and more localized FRBs will further constrain the DE EoS and the cosmological parameters.

Baryon acoustic oscillation measurements by the Dark Energy Spectroscopic Instrument (Data Release 1) have revealed exciting results that show evidence for dynamical dark energy at ∼ 3σ when combined with cosmic microwave background and type Ia supernova observations. These measurements are based on the w 0 w a CDM model of dark energy. The evidence is less in other dark energy models such as the wCDM model. In order to avoid imposing a dark energy model, we reconstruct the distance measures and the equation of the state of dark energy independent of any dark energy model and driven only by observational data. Our results show that the model-agnostic (in terms of late-time models) evidence for dynamical dark energy from DESI is not significant. Our analysis also provides model-independent constraints on cosmological parameters such as the Hubble constant and the matter-energy density parameter at present. Although we used CMB distance priors (not full CMB data) from a ΛCDM early-time model, our results remain largely similar for other cosmological models, provided that these models do not differ significantly from the standard model.

Within the standard six-parameter Lambda cold dark matter ($\Lambda$CDM) model, a 2σ–3σ tension persists between baryon acoustic oscillation (BAO) measurements from the Dark Energy Spectroscopic Instrument (DESI) and observations of the cosmic microwave background (CMB). Although this tension has often been interpreted as evidence for dynamical dark energy or a sum of neutrino masses below the established minimum, recent studies suggest it may instead originate from an underestimation of the reionization optical depth, particularly when inferred from large-scale CMB polarization. Jhaveri et al. propose that a suppression of large-scale primordial curvature power could partially cancel the contribution of $\tau$ to the CMB low-$\ell$ polarization power spectrum, leading to a biased low $\tau$ measurement in standard analyses. In this work, we investigate whether punctuated inflation – which generates a suppression of primordial power on large scales through a transient fast-roll phase – can raise the inferred $\tau$ value and thereby reconcile the consistency between CMB and BAO. For simple models with step-like features in the inflaton potential, we find that the constraint on $\tau$ and the CMB–BAO tension remain nearly identical to those in the standard six-parameter $\Lambda$CDM model. We provide a physical explanation for this negative result.

Scattered hints of dynamical dark energy (DE) have emerged in various contexts over the past decade. Recent observations from multiple supernova catalogs and the Dark Energy Spectroscopic Instrument (DESI), when combined with CMB data, suggest a highly non-trivial evolution of DE at the 2.5 -4σ CL. This evidence is typically quantified using the well-known Chevallier-Polarski-Linder (CPL) parametrization of the DE equation-of-state parameter, w DE, which corresponds to a first-order Taylor expansion of w DE(a) around a = 1. However, this truncation is to some extent arbitrary and may bias our interpretation of the data, potentially leading us to mistake spurious features of the best-fit CPL model for genuine physical properties of DE. In this work, we apply the Weighted Function Regression (WFR) method to eliminate the subjectivity associated with the choice of truncation order. We assign Bayesian weights to the various orders and compute weighted posterior distributions of the quantities of interest. Using this model-agnostic approach, we reconstruct some of the most relevant cosmological background quantities, namely w DE(z), the DE density ρ DE(z), and several cosmographical functions, including the Hubble function H(z), the deceleration parameter q(z) and the jerk j(z). This allows us to identify which DE features are genuinely preferred by the data, rather than artifacts of a specific parametrization of w DE(z). We examine the robustness of our results against variations in the CMB and SNIa likelihoods. Furthermore, we extend our analysis by allowing for negative DE. Our results corroborate previous indications of dynamical DE reported in the literature, now confirmed for the first time using the WFR method. The combined analysis of CMB, BAO, and SNIa data favors an effective DE component that transitions from phantom to quintessence behavior at redshift z cross ∼ 0.4. The probability of phantom crossing lies between 96.21% and 99.97%, depending on the SNIa data set used, and hence a simple monotonic evolution of the DE density is excluded at the ∼ 2-4σ CL. Moreover, applying Occam's razor, we find no significant evidence for a negative dark energy density below z ∼ 2.5-3. Our reconstructions do not address the Hubble tension, yielding values of H 0 consistent with the Planck/ΛCDM range. If SH0ES measurements are not affected by systematic biases, the evidence for dynamical dark energy may need to be reassessed.

Baryonic Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI), in combination with Cosmic Microwave Background (CMB) data and Type Ia Supernovae (SN) luminosity distances, suggests a dynamical evolution of the dark energy equation of state with a phantom phase (w < -1) in the past when the so-called w 0 wa parametrization w(a) = w 0 + w a (1-a) is assumed. In this work, we investigate more general dark energy models that also allow a phantom equation of state. We consider three cases: an equation of state with a transition feature, a model-agnostic equation of state with constant values in chosen redshift bins, and a k-essence model. Since the dark energy equation of state is correlated with neutrino masses, we reassess constraints on the neutrino mass sum focusing on the model-agnostic equation of state. We find that the combination of DESI BAO with Planck 2018 CMB data and SN data from Pantheon, Pantheon+, or Union3 is consistent with an oscillatory dark energy equation of state, while a monotonic behavior is preferred by the DESY5 SN data. Performing model comparison techniques, we find that the w 0 wa parametrization remains the simplest dark energy model that can provide a better fit to DESI BAO, CMB, and all SN datasets than ΛCDM. Constraints on the neutrino mass sum assuming dynamical dark energy are relaxed compared to ΛCDM and we show that these constraints are tighter in the model-agnostic case relative to w 0 wa model by 70%–90%.

We obtain constraints in a 12 parameter cosmological model using the recent Dark Energy Spectroscopic Instrument Data Release (DR) 2 Baryon Acoustic Oscillations (BAO) data, combined with cosmic microwave background (CMB) power spectra (Planck Public Release, PR, 4) and lensing (Planck PR4 + Atacama Cosmology Telescope DR 6) data, uncalibrated Type Ia supernovae (SNe) data from Pantheon+ and Dark Energy Survey (DES) Year 5 (DESY5) samples, and Weak Lensing (WL; DES Year 1) data. The cosmological model consists of six Λ cold dark matter parameters and additionally, the dynamical dark energy parameters (w 0, w a ), the sum of neutrino masses (∑m ν ), the effective number of non-photon radiation species (N eff), the scaling of the lensing amplitude (A lens), and the running of the scalar spectral index (α s ). Our major findings are the following: (i) With CMB+BAO+DESY5+WL, we obtain the first 2σ+ detection of a non-zero ∑ m ν = 0.1 9 − 0.18 + 0.15 eV (95%). Replacing DESY5 with Pantheon+ still yields a ∼1.9σ detection. (ii) The cosmological constant lies at the edge of the 95% contour with CMB+BAO+Pantheon+ but is excluded at 2σ+ with DESY5, leaving evidence for dynamical dark energy data-set dependent and inconclusive. (iii) With CMB+BAO+SNe+WL, A lens = 1 is excluded at &gt;2σ, while it remains consistent with unity without WL data—suggesting that the existence of lensing anomaly with Planck PR4 likelihoods may depend on non-CMB data sets. (iv) The Hubble tension persists at 3.6σ–4.2σ with CMB+BAO+SNe; WL data have minimal impact.

We present an updated reconstruction of the dark energy equation of state, w(a), using the newly released DESI DR2 Baryon Acoustic Oscillation (BAO) data in combination with Pantheon+ and DES5Y Type Ia supernovae measurements, respectively. Building on our previous analysis, which employed a non-parametric flexknot reconstruction approach, we examine whether the evidence for dynamical dark energy persists with the improved precision of the DESI DR2 dataset. We find that while the overall qualitative structure of w(a) remains consistent with our earlier findings, the statistical support for dynamical dark energy is reduced when considering DESI DR2 data alone, particularly for more complex flexknot models with higher numbers of knots. However, the evidence for simpler dynamical models, such as wCDM and CPL (which correspond to n = 1 and n = 2 knots respectively), increases relative to ΛCDM with DESI DR2 alone, with CPL being the preferred dynamical model, consistent with previous DESI analyses. When combined with Pantheon+ data, the conclusions remain broadly consistent with our earlier work, but when instead combined with DES5Y supernovae data, there is an increased preference for flexknot models for all values of n considered. This results in all such models being preferred over ΛCDM, with the CPL model being the most favoured by a Bayes factor of ∼2.3 relative to ΛCDM.