[Paper Review] Dark Energy and Dark Matter from Yang-Mills Condensate and the Peccei-Quinn mechanism

Andrea Addazi, Pietro Donà+1 more|arXiv (Cornell University)|Feb 4, 2016

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper proposes a unified model where dark energy arises from a non-perturbative Yang-Mills condensate (YMC) in a dark SU(2) gauge sector, while QCD axions—arising from a Peccei-Quinn symmetry—provide cold dark matter. The YMC acts as dark energy via a minimum in its effective Lagrangian, and through effective field theory interactions, a fraction of dark energy density is converted into dark matter over 1–10 Gyr, a process testable in next-generation dark energy experiments.

ABSTRACT

We analyze a model of cold axion Dark Matter weakly coupled with a dark gluon condensate, reproducing Dark Energy. We first review how to recover the Dark Energy behavior using the functional renormalization group approach, and ground our study on the properties of the effective Lagrangian, to be determined non-perturbatively. Then, within the context of $G_{SM}\ imes SU(2)_{D}\ imes U(1)_{PQ}$, we consider YMC interactions with QCD axions. We predict a transfer of Dark Energy density into Dark Matter density in a cosmological time that can be tested in the next generation of experiments dedicated to Dark Energy measures.

Motivation & Objective

• To establish a non-perturbative framework for Yang-Mills condensates (YMC) as a source of dark energy, overcoming limitations of perturbative approaches.
• To unify dark energy and cold dark matter within a minimal extension of the Standard Model: $G_{SM} \times SU(2)_D \times U(1)_{PQ}$, incorporating the Peccei-Quinn mechanism.
• To investigate the dynamical transfer of dark energy density into dark matter density via axion emission from the YMC, within an effective field theory framework.
• To provide testable predictions for the rate and cosmological timescale of this energy conversion, relevant for upcoming dark energy experiments.

Proposed method

• Utilizes the functional renormalization group (FRG) approach to non-perturbatively determine the effective action of a dark SU(2) Yang-Mills theory, ensuring stability in the infrared regime.
• Imposes three physical requirements on the effective Lagrangian $\mathcal{W}(\Theta)$: a non-trivial minimum at $\Theta_0 \approx \Lambda_D^4$, a perturbative one-loop limit, and UV linearity in $\Theta$.
• Introduces a minimal extension of the SM with $SU(2)_D \times U(1)_{PQ}$, where the Peccei-Quinn symmetry generates QCD axions as cold dark matter candidates.
• Models the interaction between the dark YMC and axions via an effective field theory, allowing for axion emission from the condensate.
• Estimates the axion emission rate $\Gamma \sim 10^2 \Lambda_D^3 \mathcal{M}^{-2}$, leading to a cosmological timescale $\tau \sim (\mathcal{M}/\text{GeV})^2$ Gyr for energy transfer.
• Considers thermal corrections to axion emission at early cosmological times, though these are negligible for $T \ll \Lambda_D$.

Experimental results

Research questions

• RQ1 Can a non-perturbative Yang-Mills condensate in a dark SU(2) sector reproduce the equation of state of dark energy?
• RQ2 Does the effective Lagrangian of the YMC satisfy the necessary conditions (minimum, perturbative limit, UV behavior) for a viable dark energy model?
• RQ3 Can QCD axions, arising from the Peccei-Quinn mechanism, be dynamically produced from the YMC, leading to a transfer of dark energy density into dark matter?
• RQ4 What is the cosmological timescale for this energy transfer, and can it be probed by future dark energy experiments?
• RQ5 How do thermal corrections in the early universe affect the axion emission rate from the YMC?

Key findings

• A non-perturbative functional renormalization group analysis confirms the existence of a minimum in the effective Lagrangian $\mathcal{W}(\Theta)$ at $\Theta_0 \approx \Lambda_D^4$ for SU(2), validating the YMC as a dark energy candidate.
• The model satisfies all three required conditions: a non-trivial minimum, a perturbative one-loop limit, and UV linearity in $\Theta$, ensuring consistency with known quantum field theory behavior.
• Axion emission from the YMC occurs with a rate $\Gamma \sim 10^2 \Lambda_D^3 \mathcal{M}^{-2}$, leading to a cosmological timescale $\tau \sim (\mathcal{M}/\text{GeV})^2$ Gyr for energy transfer.
• A 10% variation in dark matter density over 10 Gyr is observable if $\mathcal{M} \simeq 120$ GeV, setting a testable benchmark for future experiments.
• Axions emitted have energy $E \simeq 2\Lambda_D \simeq m_a$, making them slow and easily capturable by cold dark matter condensates, enhancing detectability.
• Thermal corrections to axion emission are negligible at $T \ll \Lambda_D$, but may be relevant at earlier times when $T \sim \text{few} \times \Lambda_D \simeq 10^{-4}$ eV, though not computed in detail here.