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arxiv: 2510.10439 · v2 · submitted 2025-10-12 · 🌌 astro-ph.CO

Constraints of dynamical dark energy models from different observational datasets

Peiyuan Xu , Lu Chen , Guohao Li , Yang Han This is my paper

Pith reviewed 2026-05-18 08:15 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords dynamical dark energylogarithmic modelDESI DR2DES-Y5SNIa samplescosmological constraintsequation of stateBayesian evidence
0
0 comments X

The pith

The logarithmic dark energy model fits observations from CMB, BAO, and DES-Y5 better than other parameterizations and provides evidence for dynamical dark energy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines seven different ways to let dark energy's equation of state change over time, using the latest data from the Planck satellite, DESI survey, and several supernova catalogs. It tests these models against a baseline constant-dark-energy model and finds that a logarithmic form gives the best match to the data in most combinations. This matters because if dark energy is not constant, it changes how we understand the universe's expansion and could ease some disagreements between different measurements of the cosmos. The study shows that results depend on which supernova sample is used, with the DES-Y5 sample favoring dynamical models most strongly.

Core claim

By constraining parameters with Planck PR4 and DESI DR2 data plus various SNIa samples, the analysis demonstrates that the Logarithmic model has the best fitting performance among the tested forms. With the CMB+BAO+DES-Y5 combination, it yields strong evidence in favor of dynamical dark energy, while other models like CPL are not optimal in all cases.

What carries the argument

The central mechanism is the Bayesian evidence and Akaike Information Criterion comparison across seven parameterization models of the dark energy equation of state w(z), applied to four different dataset combinations including CMB, BAO from DESI, and three SNIa compilations.

If this is right

  • The linear Chevallier-Polarski-Linder parameterization is not the optimal choice in all cases.
  • The Logarithmic model provides strong evidence to support dynamical dark energy when using CMB+BAO+DES-Y5.
  • All two-parameter dynamical dark energy models perform most prominently in the CMB+BAO+DES-Y5 dataset.
  • With CMB+BAO(without LRG1 and LRG2)+DES-Y5, Jassal-Bagla-Padmanabhan and Chevallier-Polarski-Linder models gain more obvious preference.
  • The results may relatively reduce sigma8 tension but do not effectively alleviate H0 tension.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If confirmed, this suggests that future high-precision surveys could distinguish between specific functional forms for dark energy evolution.
  • The dependence on supernova samples indicates that systematic uncertainties in distance measurements play a key role in model selection.
  • This approach could be extended to include other probes like weak lensing to test consistency.

Load-bearing premise

The chosen parameterization forms for dark energy are assumed to be appropriate and the datasets are treated as independent after handling covariances.

What would settle it

A new dataset combination or larger survey that shows no improvement in fit for the logarithmic model over LambdaCDM would challenge the claim of strong evidence for dynamical dark energy.

Figures

Figures reproduced from arXiv: 2510.10439 by Guohao Li, Lu Chen, Peiyuan Xu, Yang Han.

Figure 1
Figure 1. Figure 1: FIG. 1: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key param [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key param [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key pa [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key pa [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key param [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key param [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key pa [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key pa [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The one-dimensional posterior distributions and two-dimensional marginalized contours for the main key pa [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Comparison of constraints obtained for the models using combined CMB + BAO + PantheonPlus observational [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Comparison of constraints obtained for the models using combined CMB + BAO + DES-Y5 observational datasets. [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Comparison of constraints obtained for the models using combined CMB + BAO + Union3 observational datasets. [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
read the original abstract

The measurements of baryon acoustic oscillation by the Dark Energy Spectroscopic Instrument Data Release 2 indicate that dark energy may be dynamical with a time-varying equation of state. This has challenged the core assumptions of the $\Lambda$CDM model and aroused widespread discussion. Existing work has achieved fruitful results in the dark energy models, exploring various parameterization forms, but it lacks systematic parameter constraints based on the latest dataset combinations. We use $\Lambda$CDM as a baseline model and carry out rigorous statistical constraints on key cosmological parameters for seven representative parameterization models. The Planck PR4 and DESI DR2 observations are incorporated into our study. We use four datasets: CMB+BAO+PantheonPlus, CMB+BAO+DES-Y5, CMB+BAO+Union3, and CMB+BAO(without LRG1 and LRG2)+DES-Y5. Our results may not effectively alleviate ${H}_{0}$ tension, but may relatively reduce ${\sigma }_{8}$ tension. By comparing the Akaike Information Criterion and the Bayesian evidence obtained for each model, we demonstrate that the linear Chevallier-Polarski-Linder parameterization is not the optimal choice in all cases. The Logarithmic model shows the best fitting performance among three different SNIa samples. However, with CMB+BAO(without LRG1 and LRG2)+DES-Y5, Jassal-Bagla-Padmanabhan and Chevallier-Polarski-Linder models gain more obvious preference. All two-parameter dynamical dark energy models perform most prominently in the CMB+BAO+DES-Y5 dataset, with the Logarithmic model providing strong evidence to support dynamical dark energy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper performs Bayesian parameter constraints and model selection for seven dynamical dark energy parameterizations (including Logarithmic, CPL, and JBP) against a ΛCDM baseline. It uses Planck PR4 CMB, DESI DR2 BAO, and three SNIa compilations (PantheonPlus, DES-Y5, Union3) in four dataset combinations, one of which excludes LRG1/LR G2 BAO points. Model ranking relies on AIC and Bayesian evidence; the central claim is that the Logarithmic model yields the best performance across SNIa samples and supplies strong evidence for dynamical dark energy when combined with CMB+BAO+DES-Y5, while the results only modestly alleviate σ8 tension and do not resolve H0 tension.

Significance. If the reported evidence ratios and dataset independence assumptions hold after the clarifications requested below, the work supplies timely constraints from DESI DR2 and demonstrates that the CPL parameterization is not uniformly preferred. Credit is due for the systematic use of both AIC and Bayesian evidence on well-documented Planck PR4 and DESI DR2 likelihoods.

major comments (3)
  1. [Abstract and §3] Abstract and §3 (dataset definitions): the CMB+BAO(without LRG1 and LRG2)+DES-Y5 combination drops two BAO points without an explicit justification or test of whether their removal alters the evidence ranking; because the Logarithmic and JBP models gain preference precisely in this combination, the central claim of 'strong evidence' for dynamical dark energy is load-bearing on this choice and requires a dedicated robustness check.
  2. [§4] §4 (results and evidence tables): the abstract asserts that the Logarithmic model 'provides strong evidence' with CMB+BAO+DES-Y5, yet the numerical ΔAIC and ΔlnZ values that would allow verification against conventional thresholds (e.g., |ΔlnZ| > 5) are not quoted in the summary; the tables must report these differences explicitly so the strength of the model preference can be assessed independently of the chosen parameterization.
  3. [§2.2 and §4.1] §2.2 and §4.1 (likelihood construction): it is not stated whether the full cross-covariance matrices between Planck PR4, DESI DR2, and the SNIa samples were propagated in every joint fit; if only diagonal or approximate covariances were used, the Bayesian evidence ratios that underpin the model ranking could be biased, directly affecting the claim that two-parameter dynamical models perform most prominently with CMB+BAO+DES-Y5.
minor comments (2)
  1. [§2] Notation for the seven models should be collected in a single table with explicit functional forms for w(a) to improve readability.
  2. [Figure captions] Figure captions for the posterior contours should state the exact dataset combination and whether the contours are marginalized over all nuisance parameters.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and have revised the manuscript to improve clarity, add requested checks, and strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (dataset definitions): the CMB+BAO(without LRG1 and LRG2)+DES-Y5 combination drops two BAO points without an explicit justification or test of whether their removal alters the evidence ranking; because the Logarithmic and JBP models gain preference precisely in this combination, the central claim of 'strong evidence' for dynamical dark energy is load-bearing on this choice and requires a dedicated robustness check.

    Authors: We agree that the exclusion of the LRG1 and LRG2 points requires explicit justification and a robustness test, as these points influence the model ranking for the Logarithmic and JBP parameterizations. The motivation for their removal stems from known potential systematics in those DESI DR2 measurements, but we acknowledge this was not sufficiently documented. In the revised manuscript we will add a dedicated robustness subsection (or appendix) that recomputes the Bayesian evidence and AIC rankings both with and without LRG1/LR G2 for all seven models and all dataset combinations. This will allow direct assessment of whether the preference for dynamical dark energy remains stable. revision: yes

  2. Referee: [§4] §4 (results and evidence tables): the abstract asserts that the Logarithmic model 'provides strong evidence' with CMB+BAO+DES-Y5, yet the numerical ΔAIC and ΔlnZ values that would allow verification against conventional thresholds (e.g., |ΔlnZ| > 5) are not quoted in the summary; the tables must report these differences explicitly so the strength of the model preference can be assessed independently of the chosen parameterization.

    Authors: We accept that the abstract and tables should quote the explicit numerical differences. We will revise the abstract to state the specific ΔAIC and ΔlnZ values (relative to ΛCDM) for the Logarithmic model in the CMB+BAO+DES-Y5 combination. The tables in §4 will be updated to include columns or rows explicitly listing ΔAIC and ΔlnZ for every model and every dataset combination, enabling readers to evaluate the evidence strength against standard thresholds such as |ΔlnZ| > 5. revision: yes

  3. Referee: [§2.2 and §4.1] §2.2 and §4.1 (likelihood construction): it is not stated whether the full cross-covariance matrices between Planck PR4, DESI DR2, and the SNIa samples were propagated in every joint fit; if only diagonal or approximate covariances were used, the Bayesian evidence ratios that underpin the model ranking could be biased, directly affecting the claim that two-parameter dynamical models perform most prominently with CMB+BAO+DES-Y5.

    Authors: The joint likelihoods were formed by multiplying the individual likelihoods supplied by each collaboration, which is the standard practice when public cross-covariance matrices between CMB, BAO, and SNIa are unavailable. We will add an explicit statement in §2.2 clarifying this construction and noting that cross-covariances between these independent probes are expected to be small. While we agree that unaccounted cross-correlations could in principle affect the evidence ratios, the current public data releases do not provide the necessary joint covariance information. We will also add a brief discussion of this assumption as a potential limitation in §4.1. revision: partial

Circularity Check

0 steps flagged

No significant circularity: standard fits and evidence comparison on external data

full rationale

The paper constrains parameters of seven dark energy parameterizations (including Logarithmic, CPL, JBP) against four combinations of Planck PR4, DESI DR2, and SNIa samples, then ranks them by AIC and Bayesian evidence. All steps are direct likelihood evaluations on the supplied datasets; no claimed 'prediction' reduces to a fitted quantity by construction, no self-citation supplies a uniqueness theorem, and no ansatz is smuggled in. The central claim that the Logarithmic model supplies 'strong evidence' for dynamical dark energy is simply the outcome of those computed evidences, which remain falsifiable against the same external data and do not tautologically reproduce the inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard cosmological assumptions plus several free parameters per model and the choice of parameterization forms themselves.

free parameters (2)
  • w0, wa (or equivalent) for each of seven models
    Two free parameters per dynamical dark energy model are fitted to the data; these are the central quantities being constrained.
  • Omega_m, H0, sigma8, etc.
    Standard cosmological parameters are varied jointly with the dark-energy parameters.
axioms (2)
  • domain assumption The chosen parameterization forms (CPL, logarithmic, JBP, etc.) adequately capture possible time evolution of dark energy.
    The paper tests these specific forms without deriving them from a fundamental theory.
  • domain assumption The four dataset combinations can be combined with standard covariance matrices.
    Independence and covariance treatment between CMB, BAO, and SNIa are assumed.

pith-pipeline@v0.9.0 · 5842 in / 1521 out tokens · 27614 ms · 2026-05-18T08:15:46.776137+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith.Foundation.RealityFromDistinction reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We use the publicly available cosmological calculation code CAMB, and make specific modifications for different models. Then we perform Markov Chain Monte Carlo (MCMC) analysis with the publicly available sampler Cobaya.

  • IndisputableMonolith.Cost.FunctionalEquation washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    By comparing the Akaike Information Criterion and the Bayesian evidence obtained for each model, we demonstrate that the linear Chevallier-Polarski-Linder parameterization is not the optimal choice in all cases. The Logarithmic model shows the best fitting performance among three different SNIa samples.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

Works this paper leans on

75 extracted references · 75 canonical work pages · cited by 1 Pith paper · 30 internal anchors

  1. [1]

    The parameter constraints obtained by ΛCDM in three different datasets do not change much, showing high stability

    ΛCDM The ΛCDM is included as the standard model in our work, where w0 = -1, wa = 0, to compare with other models. The parameter constraints obtained by ΛCDM in three different datasets do not change much, showing high stability. We compare our H0 results with H0 = 67 .36 ± 0.54 km /s/Mpc given by Planck PR3 TTTEEE+lowE+lensing (hereafter Planck PR3) [8] a...

    work page

  2. [2]

    This model, as the smallest extension of the ΛCDM, is the only single-parameter DDE model included in our study

    wCDM In wCDM model, w0 is a variable constant and wa = 0. This model, as the smallest extension of the ΛCDM, is the only single-parameter DDE model included in our study. w0 describes the evolution of DE EOS and shows the lowest 6 value under the constraints of three different datasets. Specifically, w0 = −0.992+0.025 −0.023 in CMB+BAO+PantheonPlus; w0 = ...

    work page

  3. [3]

    (3) X(a) under CPL parameterization is: X(a) = a−3−3w0−3waExp[3wa(a − 1)]

    CPL Chevallier-Polarski-Linder (CPL) parametrization [41, 42] is the most basic and widely applicable two-parameter extension model, and its DE EOS is: w(a) = w0 + wa(1 − a). (3) X(a) under CPL parameterization is: X(a) = a−3−3w0−3waExp[3wa(a − 1)]. (4) The values of our w0 show a consistent pattern: the 1σ confidence interval excludes the current value o...

    work page 2018

  4. [4]

    (5) Its X(a) is : X(a) = a−3−3w0Exp 3 2 wa(a − 1)2

    Jassal-Bagla-Padmanabhan parametrization We consider the Jassal-Bagla-Padmanabhan (JBP) [44] form for the DE EOS: w(a) = w0 + waa(1 − a). (5) Its X(a) is : X(a) = a−3−3w0Exp 3 2 wa(a − 1)2 . (6) In CMB+BAO+PantheonPlus and CMB+BAO+Union3 datasets, the results for w0 at the 1σ level. are very close to the standard value -1, with values of −0.979+0.006 −0.0...

    work page 2018

  5. [5]

    and the locally measured Hubble constant H0 = 73.04 ± 1.04 km/s/Mpc [6]. In CMB+BAO+PantheonPlus, H0 = 67.49+0.45 −0.40 km/s/Mpc, which has a difference of 0.19σ for Planck PR3, 4.90σ for Local; H0 = 67.11+0.51 −0.45 km/s/Mpc from CMB+BAO+DES-Y5, 0.34 σ for Planck PR3 and 5.12 σ for Local; and based on CMB+BAO+Union3, H0 = 67.38+0.54 −0.41 km/s/Mpc, with ...

    work page 2018

  6. [6]

    It has two cases: FSLL I : w(a) = w0 − wa a(1 − a) a2 + (a − 1)2 , (7) 8 FSLL II : w(a) = w0 − wa (a − 1)2 a2 + (a − 1)2

    Feng–Shen–Li–Li parametrization The next model we study is the Feng–Shen–Li–Li (FSLL) parametrization [47]. It has two cases: FSLL I : w(a) = w0 − wa a(1 − a) a2 + (a − 1)2 , (7) 8 FSLL II : w(a) = w0 − wa (a − 1)2 a2 + (a − 1)2 . (8) Corresponding X(a) can be described as: FSLL I : X(a) = a−3−3w0Exp 3 8 wa(π + 4 arctan(1− 2a) + 2 ln (2a2 − 2a + 1)) , (9)...

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    (11) 9 X(a) can be written as: X(a) = a−3−3w0−3wa(2a2 − 2a + 1) 3 2 wa

    Barboza-Alcaniz parameterization The Barboza-Alcaniz (BA) parameterization [49] is characterized by the form: w(a) = w0 + wa 1 − a a2 + (1 − a)2 . (11) 9 X(a) can be written as: X(a) = a−3−3w0−3wa(2a2 − 2a + 1) 3 2 wa . (12) The DE EOS parameters of the BA model show the most significant variations, with w0 being the largest across all three datasets. Spe...

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    (13) We can also obtain: X(a) = a−3−3w0+ 3 2 wa ln a

    Logarithmic parametrization Going a step further, the logarithmic (LOG) parametrization [51] is: w(a) = w0 − wa ln a. (13) We can also obtain: X(a) = a−3−3w0+ 3 2 wa ln a. (14) The constraints of DE EOS parameters for LOG model show the same trend as the BA model, but its performance is slightly weaker. Under CMB+BAO+PantheonPlus and CMB+BAO+Union3, w0 de...

    work page 2018

  9. [9]

    (15) We can get its X(a) as: X(a) = a−3−3w0+3waExp [3ewa(Ei(−1) − Ei(−a))]

    Exponential parametrization The exponential (EXP) parametrization [54, 55] has the following form: w(a) = w0 + wa [Exp(1 − a) − 1] . (15) We can get its X(a) as: X(a) = a−3−3w0+3waExp [3ewa(Ei(−1) − Ei(−a))] . (16) Here Ei(x) = − R ∞ −x e−x x dx (for x < 0) is the exponential integral function. We can find in Fig. 9 that the EXP model exhibits strong cons...

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    Then we discuss the parameters in wCDM, CPL, JBP, and FSLL models: the w0 and Ω m are larger, while the H0, and σ8 are relatively small

    In CMB+BAO+DES-Y5, there are differences in Ω ch2 between the ΛCDM and wCDM models: the Ω ch2 of the former is relatively high while the Ω ch2 of the latter is lower. Then we discuss the parameters in wCDM, CPL, JBP, and FSLL models: the w0 and Ω m are larger, while the H0, and σ8 are relatively small. The above models are very close under the constraints...

    work page 2087

  11. [11]

    Here, w0 and Ω m are lead to lower values, while H0 and σ8 are driven to higher values

    In contrast, when the CMB+BAO+PantheonPlus dataset is used with the BA, LOG, and EXP models, the trend of parameters is reversed. Here, w0 and Ω m are lead to lower values, while H0 and σ8 are driven to higher values. CMB+BAO+DES-Y5 and CMB+BAO+Union3 provide similar constraints for the BA and EXP models, while LOG 13 1.05 1.00 0.95 0.90 w0 0.77 0.78 0.79...

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    However, we find that the σ8 values of all DDE models are smaller than ΛCDM, which is of positive significance for alleviating σ8 tension

    The H0 values of all DDE models are smaller than ΛCDM, which is not helpful to alleviate the Hubble tension [5]. However, we find that the σ8 values of all DDE models are smaller than ΛCDM, which is of positive significance for alleviating σ8 tension. The most significant improvement comes from the BA model under the CMB+BAO+Union3 dataset. Secondly, taki...

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    In CPL, JBP, FSLL I and FSLL II models, the w0 exhibit a nonsmooth one-dimensional posterior distribution, suggesting a possible multimodal structure in their parameter space

    In the CMB+BAO+PantheonPlus dataset, w0 is significantly larger in the BA and LOG models, with the BA value being higher than the LOG value. In CPL, JBP, FSLL I and FSLL II models, the w0 exhibit a nonsmooth one-dimensional posterior distribution, suggesting a possible multimodal structure in their parameter space. However, when we change SNIa to DES-Y5, ...

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    Under CMB+BAO+PantheonPlus, only the BA, LOG, and EXP models deviate from -1 at 95% C.L

    The degree of deviation for w0 from the standard value -1 in different models may be related to the SNIa data. Under CMB+BAO+PantheonPlus, only the BA, LOG, and EXP models deviate from -1 at 95% C.L.. When SNIa is replaced with Union3, the LOG model remains unchanged, but the BA and EXP models can deviate from -1 at 14 1.0 0.9 0.8 w0 0.76 0.78 0.80 0.82 8...

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    Under the constraints of CMB+BAO+DES-Y5, the H0 tension of all DDE models reached the maximum value among the three datasets

    We also analyze the impact of the three datasets on H0 tension. Under the constraints of CMB+BAO+DES-Y5, the H0 tension of all DDE models reached the maximum value among the three datasets. With the exception of the wCDM model, the H0 tension of all models exceeded 5 σ. Switching from SNIa to PantheonPlus improved the situation, with H0 tension of all mod...

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    Only σ8 is relatively low in the BA, EXP and LOG models and exhibits an increasing trend

    When using the CMB+BAO+Union3 dataset, the overall distribution of model parameters remains stable. Only σ8 is relatively low in the BA, EXP and LOG models and exhibits an increasing trend. 15 1.00 0.95 0.90 w0 0.77 0.78 0.79 0.80 0.81 0.82 8 0.30 0.31 0.32 m 66 67 68 H0 0.115 0.116 0.117 0.118 0.119 ch2 0.1 0.0 0.1 0.2 0.3 wa 0.1 0.0 0.1 0.2 0.3 wa 0.115...

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    This indicates that compared with the CPL model, the FSLL II, BA, LOG, and EXP models remain more favorable

    In the CMB+BAO+PantheonPlus datasets, the AIC values of the FSLL II, BA, LOG and EXP models are lower than the CPL model. This indicates that compared with the CPL model, the FSLL II, BA, LOG, and EXP models remain more favorable

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    Moreover, the AIC value of the BA model is smaller than that of the wCDM model, which shows a certain superiority

    For the CMB+BAO+Union3 datasets, the FSLL II, BA, LOG, and EXP models also have lower AIC values than the CPL model. Moreover, the AIC value of the BA model is smaller than that of the wCDM model, which shows a certain superiority

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    The FSLL II model still has a slight advantage in the AIC value over the CPL model

    Then, let us focus on the CMB+BAO+DES-Y5 datasets. The FSLL II model still has a slight advantage in the AIC value over the CPL model. Meanwhile, the BA, LOG, and EXP models have made significant progress and generated more favorable evidence. All three models have lower AIC values than the CPL, wCDM, and ΛCDM models, especially compared to the ΛCDM model...

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    We find that the AIC value of the BA model has a certain advantage in any dataset, being the minimum value among all two-parameter DDE models, which fully demonstrates the strong fitting ability of the BA model to these observational data. VI. SUMMAR Y In this paper, we analyze the ΛCDM model and DDE parameterized models, placing strict constraints on key...

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    S. Perlmutter et al. [Supernova Cosmology Project], Astrophys. J. 517 (1999), 565-586 doi:10.1086/307221 [arXiv:astro- ph/9812133 [astro-ph]]. 19 1.00 0.95 0.90 0.85 0.80 w0 0.76 0.77 0.78 0.79 0.80 0.81 0.82 8 0.30 0.31 0.32 0.33 0.34 m 65 66 67 68 H0 0.115 0.116 0.117 0.118 0.119 ch2 0.2 0.1 0.0 0.1 wa 0.2 0.1 0.0 0.1 wa 0.115 0.116 0.117 0.118 0.119 ch...

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