Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions

Abstract: We present a robust assessment of cosmological constraints on the sum of neutrino masses ($\sum m_ν$) when relaxing the standard assumption of purely adiabatic primordial initial conditions. Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the $Λ$CDM model, the 95\% upper limit weakens only marginally from $\sum m_ν< 0.052$ eV (purely adiabatic) to $< 0.057$ eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is $< 0.111$ eV, shifting to $< 0.115$ eV with NDI, yet the isocurvature mode remains undetected. While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on $\sum m_ν$. Notably, the adiabatic $Λ$CDM limit of $0.052$ eV lies below the minimum sum required by the normal neutrino mass hierarchy ($0.05878$ eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to $< 0.092$ eV. Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on $\sum m_ν$ and NDI using the full CMB-SPA+DESI DR2+DES dataset.

• The paper presents a Bayesian framework that jointly fits adiabatic and NDI modes to constrain the sum of neutrino masses.
• It shows that including neutrino density isocurvature yields only a minor relaxation of neutrino mass upper limits, emphasizing prior dependence.
• The study demonstrates that dark energy parameterization critically affects mass bounds, motivating joint analyses with upcoming surveys.

Neutrino Mass Constraints and Primordial Isocurvature: Insights from ACT DR6 and DESI DR2

Introduction

The determination of absolute neutrino masses and their ordering remains a central unresolved topic intersecting particle physics and cosmology. Laboratory oscillation experiments constrain squared mass splittings but not the absolute scale or mass hierarchy. In contrast, cosmological datasets, through their sensitivity to structure growth and the cosmic microwave background (CMB), provide the most stringent upper limits on the sum of neutrino masses ($\sum m_\nu$), with current claims approaching the normal hierarchy floor. However, these limits depend on assumptions about the early universe, most critically the nature of primordial perturbations. While the standard model assumes purely adiabatic initial conditions, mixed scenarios with non-negligible neutrino density isocurvature (NDI) can occur in multi-field inflationary models or with non-standard neutrino physics. This work (“Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions” (2606.17994)) presents a comprehensive Bayesian analysis of $\sum m_\nu$ that for the first time jointly fits both adiabatic and NDI modes and confronts cosmological data with physically motivated priors.

Theoretical Framework and Parameterization

Massive neutrinos imprint themselves onto the CMB and large-scale structure primarily by free-streaming effects that suppress power on sub-degree angular scales and on wavenumbers $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$. The standard analysis is typically performed with the $\Lambda$CDM model, adiabatic initial conditions, and degenerate mass (DH) or normal/inverted hierarchy (NH/IH) priors.

In this work, the initial condition sector is generalized via a basis of adiabatic and neutrino density isocurvature modes, with the primordial power spectrum described by a symmetric matrix with independent amplitudes at two physically motivated pivots ($k=0.002$ and $0.1\,\mathrm{Mpc}^{-1}$). This parameterization captures both the scale-dependent effects of NDI and allows for explicit tests of their detectability with current data. The isocurvature power component $\mathcal{P}_{\mathcal{I}\mathcal{I}}(k)$ can in principle be correlated with the adiabatic part, but in this analysis only the uncorrelated regime is considered. The NDI amplitude $\beta(k)$ is left fully free at both pivots.

Extensions to the late universe, specifically the Chevallier–Polarski–Linder (CPL) dynamical dark energy model, are analyzed in parallel to $\Lambda$CDM in order to quantify model-dependence.

Data and Methodology

The analysis exploits the synergy of the latest high-resolution CMB datasets—ACT DR6, SPT-3G, and Planck 2018—as assembled by the CMB-SPA likelihood construction. This CMB data is complemented with DESI DR2's percent-level BAO measurements (which span a broad redshift range and include Ly$\alpha$), and the DES Year 5 supernovae sample for additional leverage on expansion history. Parameter inference is carried out via MontePython using the CLASS Boltzmann solver. Both the sum of neutrino masses and the full set of isocurvature/adiabatic amplitude parameters are sampled, with hierarchical priors and lower bounds on $\sum m_\nu$0 varied for thoroughness.

Figure 1: Lensed CMB TT and polarization power spectra at fixed $\sum m_\nu$1 and varying NDI fraction $\sum m_\nu$2 (right panels), demonstrating the distinct scales at which isocurvature alters the observables.

Physical Degeneracies and the Role of NDI

The analysis makes explicit the scale separation between the effects of massive neutrinos and NDI. Increasing $\sum m_\nu$3 (under fixed adiabaticity) suppresses the CMB and matter power spectra at relatively fine angular scales (large $\sum m_\nu$4) and high $\sum m_\nu$5. NDI, in contrast, induces features on larger angular scales (low multipoles, particularly $\sum m_\nu$6) and distinct modulations of the first acoustic peaks. This separation is visualized in Figure 1; the distinct signatures mean that high-resolution CMB data and large-volume LSS surveys can efficiently break degeneracies between the two physical effects.

Main Results: Posterior Distributions and Robustness of Neutrino Mass Bounds

The posterior for $\sum m_\nu$7 in various modeling scenarios reveals several key features, as shown in the following figures:

Figure 2: Posterior distributions for $\sum m_\nu$8 under adiabatic and mixed (adiabatic$\sum m_\nu$9NDI) scenarios in $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$0CDM, showing marginal shifts in the upper bound in the presence of NDI modes.

• $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$1CDM, Adiabatic: The 95% CL upper limit is $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$2 eV (with prior lower bound at zero).
• $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$3CDM, +NDI: Including a free NDI amplitude degrades the limit only slightly, to $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$4 eV, and the amplitude of NDI is driven to zero by the data.
• CPL Dark Energy, Adiabatic: The upper bound weakens to $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$5 eV.
• CPL, +NDI: The bound shifts to $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$6 eV, again with the NDI amplitude consistent with no signal.

The triangle plots of the cosmological parameter posteriors support that the inclusion of NDI has only a minor effect on correlated parameters, indicating that current data robustly restrict the shape of the primordial spectrum (see Figure 3).

Figure 3: Triangle plot of cosmological parameters in $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$7CDM, showing tight posteriors and little impact from the inclusion of NDI.

Crucially, the dependence of the upper bound on $k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$8 on prior choice is highlighted. The lowest physically meaningful value for the sum is set by the NH limit ($k \gtrsim 0.01\,h\,\mathrm{Mpc}^{-1}$9 eV); imposing this as a lower bound increases the 95% CL upper limit to $\Lambda$0 eV in $\Lambda$1CDM, demonstrating how choices in parameter space definition can appear as artificial improvements in the mass constraint if not stated clearly.

Implications for Early Universe Physics and Future Cosmological Analyses

The main implications are:

• Absence of Evidence for NDI: The NDI amplitude is always driven toward zero, indicating that primordial perturbations are consistent with adiabatic initial conditions. Cosmological neutrino mass bounds are therefore robust to isocurvature sector extensions (within current instrument sensitivity).
• Sensitivity to Dark Energy Parameterization: Allowing for time-varying dark energy (as in CPL) degrades neutrino mass constraints by almost a factor of two, illustrating that late-time model-dependence is currently a greater systematic than initial conditions.
• Prior Dependence: The explicit demonstration that the minimal prior for $\Lambda$2 dramatically alters the apparent bound if the data are peaking near the physically allowed floor signals the necessity to always quote prior assumptions, especially as cosmological constraints continue to improve.

These results suggest that, with the current generation of CMB and LSS data, the upper bounds on $\Lambda$3 are statistical and systematic-limited and cannot break through the floor set by the minimal mass allowed by the mass hierarchy without new physics or more precise data.

Prospects

Upcoming surveys, including CMB-S4, LiteBIRD, and Euclid, will further reduce both isocurvature and neutrino mass error bars (possibly to $\Lambda$4 eV). Simultaneous constraints on NDI modes, $\Lambda$5 and neutrino self-interactions will be a necessity to ensure astrophysical robustness. Model-independent bounds may require breaking remaining degeneracies in late-universe physics, motivating joint analyses and stronger control of systematic uncertainties.

Conclusion

The paper provides a stringent and physically nuanced analysis of cosmological neutrino mass limits, quantifying their sensitivity to isocurvature, dark energy, hierarchy, and prior choice. The findings confirm that current cosmological datasets show no indication of neutrino density isocurvature modes and that upper bounds on $\Lambda$6 are generically robust to plausible extensions of the initial conditions sector. However, these bounds remain sensitive to late-time DE parameterizations and to the details of the likelihood priors, which must be contextually specified in future work and for robust comparisons with laboratory experiments and cosmological forecasts.