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Statistical consistency of sign-switching vacuum energy with cosmological observations

Sehjal Khandelwal, Abraão J. S. Capistrano, Suresh Kumar

Abstract

We assess dataset agreement and late-time predictive adequacy in $Λ$CDM and its sign-switching extension, $Λ_{\rm s}$CDM, using a suite of Gaussian and exact non-Gaussian consistency diagnostics. Both models are constrained with cosmic microwave background measurements from Planck, ACT, and SPT, baryon acoustic oscillation data from DESI DR2, and low-redshift Type Ia supernova data from PantheonPlus+SH0ES. We find that commonly used Gaussian tension metrics can significantly overstate inconsistencies when broad, non-Gaussian posteriors are combined with tightly constrained datasets. In contrast, the exact non-Gaussian parameter shift indicates excellent consistency between CMB and BAO observations in both models. The $Λ_{\rm s}$CDM extension modestly improves geometric compatibility at intermediate redshifts, although reductions in parameter-level tension do not necessarily imply improved predictive consistency. These results highlight the importance of exact, non-Gaussian, and predictive diagnostics for robust assessments of cosmological model consistency.

Statistical consistency of sign-switching vacuum energy with cosmological observations

Abstract

We assess dataset agreement and late-time predictive adequacy in CDM and its sign-switching extension, CDM, using a suite of Gaussian and exact non-Gaussian consistency diagnostics. Both models are constrained with cosmic microwave background measurements from Planck, ACT, and SPT, baryon acoustic oscillation data from DESI DR2, and low-redshift Type Ia supernova data from PantheonPlus+SH0ES. We find that commonly used Gaussian tension metrics can significantly overstate inconsistencies when broad, non-Gaussian posteriors are combined with tightly constrained datasets. In contrast, the exact non-Gaussian parameter shift indicates excellent consistency between CMB and BAO observations in both models. The CDM extension modestly improves geometric compatibility at intermediate redshifts, although reductions in parameter-level tension do not necessarily imply improved predictive consistency. These results highlight the importance of exact, non-Gaussian, and predictive diagnostics for robust assessments of cosmological model consistency.
Paper Structure (13 sections, 15 equations, 8 figures, 4 tables)

This paper contains 13 sections, 15 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Cosmological Framework and Models
  3. Datasets
  4. Methodology
  5. Statistical Analysis and Results for Various Tension Metrics
  6. Rule Of Thumb
  7. Posterior Means of Two Datasets in Standard Form
  8. Posterior Means of Two Datasets in Updated Form
  9. Goodness-of-fit type test
  10. Exact Parameter Shift in Non-Gaussian Metrics
  11. Posterior Predictive Consistency Tests
  12. Discussion
  13. Conclusion

Figures (8)

  • Figure 1: Triangular plots for the $\Lambda$CDM model. (Left) Comparison between CMB (red), DESI DR2 (blue), and their combination (black). (Right) Comparison between the combined CMB+DESI DR2 dataset (black), PPS (blue), and the full combination (red). Diagonal panels show 1D posteriors; off-diagonal panels show 68% and 95% contours.
  • Figure 2: Triangular plots for the $\Lambda_{\rm s}$CDM model. (Left) Comparison between CMB (red), DESI DR2 (blue), and their combination (black). (Right) Comparison between CMB+DESI DR2 (red), PPS (blue), and the full combination (black). Diagonal panels show 1D posteriors; off-diagonal panels show 68% and 95% credible regions.
  • Figure 3: Posterior predictive residual distributions for the $\Lambda$CDM model. Histograms show replicated discrepancies in $H_0$ and $\mu(z=0.01)$ generated from posterior samples constrained by CMB and DESI DR2 data. The vertical line denotes the observed value in each case.
  • Figure 4: Posterior predictive distribution of the maximum joint discrepancy statistic for $\Lambda$CDM. Replicated values are obtained from posterior draws, and the vertical line indicates the observed statistic.
  • Figure 5: Posterior predictive replicated distributions for $\Lambda$CDM showing $H_0$, $\mu(z=0.01)$, and the joint $\chi^2$ statistic. Replicated values are generated from posterior samples; vertical lines mark the observed quantities.
  • ...and 3 more figures