Dark energy from neutrino interactions in Unimodular Gravity

Technical Summary: Dark energy from neutrino interactions in Unimodular Gravity

Problem and Motivation
Recent cosmological analyses, particularly those involving the DESI collaboration combined with Planck CMB and Type Ia supernovae data, suggest that dark energy may be an evolving function rather than a constant cosmological constant ($\Lambda$). These datasets favor an evolving dark energy component, especially when the sum of neutrino masses ($\Sigma m_\nu$) is treated as a free parameter. However, standard $\Lambda$CDM fits often result in tensions, such as favoring unphysical negative neutrino masses or conflicting with ground-based neutrino mass experiments. Furthermore, non-standard neutrino interactions have been proposed to resolve oscillation anomalies and the Hubble tension, often involving light scalar mediators that induce effective neutrino masses dependent on the thermal history of the Universe.

This paper investigates a specific mechanism where dark energy arises from non-standard interactions between relic neutrinos mediated by a light scalar field ($m_\phi < \mathcal{O}(\text{eV})$). The authors propose that these interactions, within the framework of Unimodular Gravity (UG), generate a dynamical dark energy component. In UG, the energy-momentum tensor is not strictly conserved, allowing for a current density that can source a time-varying effective cosmological term.

Methodology and Model Construction
The authors construct a model where the effective neutrino mass ($m_{\text{eff},j}$) receives finite-temperature corrections due to forward-scattering processes in the cosmic medium, mediated by a scalar field $\phi$. The effective mass is given by:
$$m_{\text{eff},j} = m_j + \sum_{i=1}^3 G_{s,ij} \Delta m(m_i, T)$$
where $G_{s,ij} = g_i g_j / m_\phi^2$ represents the effective coupling, and $\Delta m$ is the thermal scalar density dependent on the neutrino temperature $T_\nu$.

Within Unimodular Gravity, the non-conservation of the energy-momentum tensor ($\nabla_\nu T^{\mu\nu} \neq 0$) generates a current $J_\mu$. This current modifies the Einstein equations, turning the cosmological constant $\Lambda$ into a dynamical quantity:
$$\Lambda(x^\mu) = \Lambda_0 + \int J_\mu dx'^\mu$$
The authors derive the time-component of this current, $J_0$, which depends on the rate of change of the effective neutrino mass ($\dot{m}_{\text{eff}}$). This leads to a time-dependent dark energy density $\rho_\Lambda(T_\nu)$ that evolves as the Universe expands and neutrinos transition from relativistic to non-relativistic regimes.

Two specific realizations are analyzed:

1. Single-neutrino model: Coupling is restricted to the lightest neutrino eigenstate ($m_1$).
2. Two-neutrino model: Couplings involve the two lightest eigenstates ($m_1$ and $m_2$), allowing for interference effects between the terms.

Cosmological Constraints and Analysis
The authors constrain the model using Bayesian inference with a combination of late- and early-Universe datasets:

• Low-redshift probes (LzP): Megamasers, Cosmic Chronometers, DES-Dovekie Type Ia supernovae, and DESI DR2 Baryon Acoustic Oscillations (BAO).
• High-redshift prior: Planck 2018 distance priors (acoustic scale $\theta_*$, shift parameter $R$, and $\Omega_b h^2$).

The analysis explores lightest neutrino masses in the range $0.05 \text{ meV} \leq m_1 \leq 1 \text{ meV}$.

Key Results

1. Evolution of Dark Energy:

   • In the single-neutrino model, the dark energy density evolves monotonically, increasing toward the present epoch. The interaction strength $G_{s1}$ is constrained to be positive.
   • In the two-neutrino model, the interplay between the two couplings (which can have opposite signs) allows for non-monotonic evolution. The model predicts a dark energy density that can reach a maximum at intermediate redshifts ($z \sim 0.6 - 1$) before decreasing toward the present day. This behavior mimics the "transient" dark energy suggested by some DESI analyses.

2. Interaction Strength Constraints:

   • Using only LzP data, the models show a preference for non-zero interaction strengths at approximately the $2\sigma$ level.
   • For the single-neutrino model, preferred values are $G_{s1} \sim (2 - 25) \times 10^{11} \text{ eV}^{-2}$, with the preferred coupling decreasing as the neutrino mass increases.
   • For the two-neutrino model, preferred values are $G_{s2} \sim 4 \times 10^{11} \text{ eV}^{-2}$ and $G_{s1} \sim (-55, -5) \times 10^{11} \text{ eV}^{-2}$.
   • The inclusion of Planck distance priors ($\theta_*$) significantly tightens constraints, reducing the preference for non-zero couplings. For larger neutrino masses, the interaction strength becomes consistent with zero at the $1\sigma$ level, driving the solution closer to standard $\Lambda$CDM.

3. Mediator Mass:

   • Assuming perturbative neutrino couplings of order unity ($g_i \sim \mathcal{O}(1)$), the inferred interaction scale corresponds to an ultralight scalar mediator with a mass $m_\phi \sim 10^{-6} \text{ eV}$. This mass scale falls within the range often discussed for axion-like particles and ultralight scalar mediators in extensions of the Standard Model.

Significance and Claims
The paper claims that neutrino interactions mediated by a light scalar field, within the framework of Unimodular Gravity, can generate viable dynamical dark energy scenarios that are consistent with current cosmological observations.

• The model provides a phenomenological extension to $\Lambda$CDM that naturally recovers the standard limit when interactions become negligible.
• It offers a mechanism to explain the potential evolution of dark energy suggested by recent data, particularly the non-monotonic behavior (a peak followed by a decline) achievable in the two-neutrino scenario.
• The results suggest that while the statistical significance of non-zero interactions is modest (around $2\sigma$ with LzP data and reduced with CMB priors), the framework remains a viable candidate for explaining dark energy dynamics without requiring exotic new physics beyond light scalar mediators and modified gravity.
• The authors note that the current analysis is an effective late-time description; a full microscopic realization suppressing interactions in the early Universe is required for a complete theory, and future work should include perturbations and large-scale structure observables to further test the model's viability.