Axions from Strings: the Attractive Solution (1806.04677v1)

Abstract: We study the system of axion strings that forms in the early Universe if the Peccei-Quinn symmetry is restored after inflation. Using numerical simulations, we establish the existence of an asymptotic solution to which the system is attracted independently of the initial conditions. We study in detail the properties of this solution, including the average number of strings per Hubble patch, the distribution of loops and long strings, the way that different types of radiation are emitted, and the shape of the spectrum of axions produced. We find clear evidence of logarithmic violations of the scaling properties of the attractor solution. We also find that, while most of the axions are emitted with momenta of order Hubble, most of the axion energy density is contained in axions with energy of order the string core scale, at least in the parameter range available in the simulation. While such a spectrum would lead to a negligible number density of relic axions from strings when extrapolated to the physical parameter region, we show that the presence of small logarithmic corrections to the spectrum shape could completely alter such a conclusion. A detailed understanding of the evolution of the axion spectrum is therefore crucial for a reliable estimate of the relic axion abundance from strings.

• The paper confirms an attractor solution in axion string evolution, indicating predictable dynamics regardless of initial conditions.
• It identifies a logarithmic scaling violation and a UV-dominated power-law emission (q ∼ 0.75), revealing complex radiation behavior.
• The analysis shows a significant fraction of string energy channels into radial modes, challenging standard assumptions about decoupling.

Analyzing Axion String Dynamics in the Early Universe

This paper presents an in-depth investigation into the evolution and behavior of axion strings that develop in the early Universe when Peccei-Quinn (PQ) symmetry undergoes a phase transition post-inflation. The authors explore the dynamics of these strings using extensive numerical simulations, aiming to unpack how they influence the production and characteristics of cosmological axion dark matter.

Axion strings, which form due to the spontaneous breaking of the global $U(1)_{\text{PQ}}$ symmetry, represent critical elements in the cosmology of the QCD axion—a candidate for solving the strong CP problem and providing dark matter. When the PQ symmetry breaks, cosmic axion strings form, evolving and radiating axions as the Universe expands. The evolution and properties of the string network significantly impact the relic abundance and distribution of axions, necessitating a precise understanding of their dynamics.

Key Findings

1. Existence of an Attractor Solution: One of the central findings is the confirmation of an attractor solution in the string network, which the system approaches regardless of initial conditions. This result is vital as it suggests the possibility of predicting axion string dynamics at the time of the QCD crossover independently of the string configurations present just after PQ breaking.
2. Scaling Violation: The authors identify a logarithmic scaling violation when they observe that the average string length per Hubble patch $\xi(t)$ increases logarithmically with respect to the ratio $m_r/H$, where $m_r$ is the radial mode mass and $H$ the Hubble parameter. This scaling violation suggests that the string tension and coupling to axions do not fit the expected simple scaling laws, denoting complex underlying string interactions.
3. String Network Energy Distribution: An analysis of the energy budget of the string system shows a significant proportion of the energy is distributed into high momentum axions despite the energy spectrum being peaked at around Hubble-scale momentum. This contradicts some expectations that predicted a spectrum more strictly peaked in the IR, indicating complex radiation dynamics possibly influenced by interactions at the string core scale.
4. Instantaneous Emission Spectrum: The authors compute the instantaneous emission spectrum of the string network, finding it follows a power law characteristic of $1/k^q$ with $q \sim 0.75$. This sub-$1$ power law implies a UV-dominated emission, contradicting classical expectations of softer spectra often assumed in analytical estimates.
5. Energy Loss into Radials: A notable portion of energy emitted by the string network is found to convert into radial modes, presenting a surprise given radial modes were expected to decouple faster in cosmic evolution. This observation illustrates the nuanced interaction dynamics at play within the string network, which defies simpler models.

Implications and Future Directions

The outcomes of this paper have significant implications for axion dark matter production estimates. With considerable uncertainty remaining due to potential scale separation effects untested in this regime, refining the simulations to larger lattices or developing adaptive mesh methods might be required. Moreover, further efforts to analyze the late-time dynamics of strings, possibly using effective field theory approaches adapted for UV behavior, could provide deeper insights.

In conclusion, this paper underscores the profound dependence of axion relic abundance estimation on the string network's dynamics and spectral characteristics. The work invites further computational and theoretical exploration in the field of cosmological axion dynamics, signaling possible pathways to enhance the precision of predicting axion dark matter based on these complex early Universe phenomena.