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Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity

Artur Ladeira, Rafael C. Nunes, Supriya Pan, Weiqiang Yang

Abstract

The \(w_{\dagger}\)VCDM framework provides a theoretically well-controlled extension of \(Λ\)CDM within the class of minimally modified gravity theories, allowing for flexible cosmological background evolution and linear perturbation dynamics while remaining free of pathological instabilities. In this work, we have shown that this scenario remains robust when confronted with current cosmological observations, even in the presence of an extended neutrino sector. Combining \textit{Planck} CMB data with DESI DR2 BAO and DESY5 supernovae, we obtain stringent constraints on neutrino physics, including \(\sum m_ν< 0.11~\mathrm{eV}\) (95\% CL) and \(N_{\rm eff} = 2.98^{+0.13}_{-0.14}\), fully consistent with Standard Model expectations. Crucially, the data exhibit a statistically significant preference for a late-time dark-energy transition, characterized by a robust quintessence--phantom crossing that remains stable across all dataset combinations and neutrino-sector extensions, including the presence of a sterile neutrino. The combined effects of modified late-time expansion and additional relativistic degrees of freedom systematically raise the inferred Hubble constant, substantially alleviating the \(H_0\) tension without invoking early dark energy or introducing theoretical instabilities. Overall, the \(w_{\dagger}\)VCDM scenario emerges as a compelling phenomenological framework that simultaneously accommodates current constraints on neutrino physics, provides an excellent fit to recent BAO and supernovae data, and offers a viable pathway toward resolving persistent tensions in the standard cosmological model.

Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity

Abstract

The VCDM framework provides a theoretically well-controlled extension of CDM within the class of minimally modified gravity theories, allowing for flexible cosmological background evolution and linear perturbation dynamics while remaining free of pathological instabilities. In this work, we have shown that this scenario remains robust when confronted with current cosmological observations, even in the presence of an extended neutrino sector. Combining \textit{Planck} CMB data with DESI DR2 BAO and DESY5 supernovae, we obtain stringent constraints on neutrino physics, including (95\% CL) and , fully consistent with Standard Model expectations. Crucially, the data exhibit a statistically significant preference for a late-time dark-energy transition, characterized by a robust quintessence--phantom crossing that remains stable across all dataset combinations and neutrino-sector extensions, including the presence of a sterile neutrino. The combined effects of modified late-time expansion and additional relativistic degrees of freedom systematically raise the inferred Hubble constant, substantially alleviating the tension without invoking early dark energy or introducing theoretical instabilities. Overall, the VCDM scenario emerges as a compelling phenomenological framework that simultaneously accommodates current constraints on neutrino physics, provides an excellent fit to recent BAO and supernovae data, and offers a viable pathway toward resolving persistent tensions in the standard cosmological model.
Paper Structure (7 sections, 18 equations, 4 figures, 4 tables)

This paper contains 7 sections, 18 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The $w_{\dagger}$VCDM parametrization
  3. Datasets and methodology
  4. A note on the negative neutrino mass range
  5. Main Results
  6. Constraints in presence of Sterile Neutrino
  7. Conclusion

Figures (4)

  • Figure 1: One-dimensional posterior distributions and 68% and 95% CL joint contours representing the $w_\dagger$VCDM + $\sum m_{\nu}$ scenario for several combined datasets.
  • Figure 2: One-dimensional posterior distributions and 68% and 95% CL joint contours representing the $w_\dagger$VCDM + $\sum m_{\nu}$ + $N_{\rm eff}$ scenario for several combined datasets.
  • Figure 3: The figure shows AIC versus $\Delta \chi^2_{\rm min}$ for the extended $w_{\dagger}$VDM models considering all the datasets.
  • Figure 4: One-dimensional posterior distributions and 68% and 95% CL joint contours representing the $w_\dagger$VCDM + $m_{esterile}$ scenario for several combined datasets.