[Paper Review] Cosmological Signatures of the Interaction between Dark-Energy and Massive Neutrinos

Kiyotomo Ichiki, Yong-Yeon Keum|ArXiv.org|Mar 21, 2008

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates a cosmological model in which massive neutrinos interact with a quintessence scalar field, causing their mass to vary over time and driving late-time cosmic acceleration. Using cosmological perturbation theory, the authors compute CMB anisotropies and matter power spectra, finding a 95% confidence level upper bound of $\sum m_{\nu} < 0.87\,\text{eV}$ on the sum of neutrino masses, with the scattering term in the Boltzmann equation playing a critical role in preserving energy-momentum conservation and stabilizing the ISW effect.

ABSTRACT

We investigate whether interaction between massive neutrinos and quintessence scalar field is the origin of the late time accelerated expansion of the universe. We present cosmological perturbation theory in neutrinos probe interacting dark-energy models, and calculate cosmic microwave background anisotropies and matter power spectrum. In these models, the evolution of the mass of neutrinos is determined by the quintessence scalar field, which is responsible for the cosmic acceleration today. We consider several types of scalar field potentials and put constraints on the coupling parameter between neutrinos and dark energy. Assuming the flatness of the universe, the constraint we can derive from the current observation is $\sum m_ν &lt; 0.87 eV$ at the 95 % confidence level for the sum over three species of neutrinos. We also discuss on the stability issue of the our model and on the impact of the scattering term in Boltzmann equation from the mass-varying neutrinos.

Motivation & Objective

• To explore the cosmological implications of a time-varying neutrino mass induced by coupling to a quintessence scalar field.
• To investigate how such an interaction affects cosmic microwave background (CMB) anisotropies and large-scale structure (LSS) power spectra.
• To derive observational constraints on the neutrino mass sum and coupling strength in interacting dark energy models.
• To examine the stability of the model under perturbations and the role of the scattering term in the neutrino Boltzmann equation.

Proposed method

• Formulates a cosmological perturbation theory framework for neutrino-probe interacting dark-energy models with a time-dependent neutrino mass.
• Derives equations of motion for the quintessence scalar field, including effective potential terms from neutrino self-energy contributions.
• Incorporates a scattering term in the geodesic equation of neutrinos, proportional to $\partial m_\nu / \partial x$, to ensure energy-momentum conservation at linear order.
• Considers three types of quintessence potentials: inverse power law, SUGRA-type, and exponential, to explore different cosmological evolutions.
• Solves the Boltzmann equation for neutrinos with a time-varying mass $m_\nu(\phi) = \bar{m}_i e^{\beta \phi / M_{\text{pl}}}$, including the impact of the scattering term.
• Performs likelihood analysis using CMB and LSS data to constrain the neutrino mass sum and coupling parameter.

Experimental results

Research questions

• RQ1 How does the interaction between massive neutrinos and a quintessence scalar field affect the cosmic microwave background anisotropy power spectrum?
• RQ2 What is the impact of the scattering term in the neutrino Boltzmann equation on the integrated Sachs-Wolfe effect and large-scale structure?
• RQ3 Can the model remain stable against adiabatic perturbations, and what conditions on the scalar field potential ensure this?
• RQ4 What observational constraints can be placed on the total neutrino mass in this interacting dark-energy scenario?
• RQ5 How do different quintessence potentials (inverse power law, SUGRA-type, exponential) affect the cosmological evolution and observable signatures?

Key findings

• The inclusion of the scattering term in the neutrino Boltzmann equation is essential for preserving energy-momentum conservation at linear order, preventing unphysical enhancements in the late-time integrated Sachs-Wolfe effect.
• Neglecting the scattering term leads to anomalously large ISW effects, particularly at large angular scales, due to violation of energy-momentum conservation.
• The model remains stable against adiabatic instabilities, as the effective mass of the scalar field $m_{\text{eff}}$ remains below the Hubble scale $H$ throughout cosmic history.
• The sound speed of neutrinos remains positive and evolves from $1/3$ (relativistic) to lower values, indicating stability against density fluctuations.
• The 95% confidence level upper bound on the sum of neutrino masses is $\sum m_\nu < 0.87\,\text{eV}$, derived from current CMB and LSS data.
• Models with $M_\nu = 1.0\,\text{eV}$ significantly deviate from observational data in the matter power spectrum, while $M_\nu = 0.3\,\text{eV}$ remains consistent when other parameters are adjusted.