Improved estimation of radiated axions from cosmological axionic strings

TL;DR

The paper tackles the challenge of estimating radiated axions from a cosmological network of axionic strings by performing large-scale field-theoretic simulations on a $512^3$ lattice and implementing a novel string-identification method alongside a pseudo power spectrum estimator (PPSE) to extract the free-axion spectrum. The main findings show the global string network reaches a scaling regime with $ξ ≈ 0.87$ and that the radiated spectrum is peaked at horizon scales with an exponential cutoff, leading to a bound $f_a \le 3\times 10^{11}$ GeV. This work tightens previous constraints on the axion decay constant, informs the modeling of axion dark matter, and provides robust methods for disentangling string-core contamination from the radiated axion signal. Overall, the study delivers a first-principles, high-precision assessment of axion production from cosmological strings and its cosmological implications.

Abstract

Cosmological evolution of axionic string network is analyzed in terms of field-theoretic simulations in a box of 512^3 grids, which are the largest ever, using a new and more efficient identification scheme of global strings. The scaling parameter is found to be ξ=0.87 +- 0.14 in agreement with previous results. The energy spectrum is calculated precisely using a pseudo power spectrum estimator which significantly reduces the error in the mean reciprocal comoving momentum. The resultant constraint on the axion decay constant leads to f_a <= 3*10^11 GeV. We also discuss implications for the early Universe.

Figures (7)

• Figure 1: Schematic view of our method for string identification. (Left) Shown is a quadrate in real space penetrated by a string (green point). The loci of $\phi_1=0$ and $\phi_2=0$ (red lines) intersect with each other at the string. Note that the string does not necessarily penetrate the quadrate perpendicularly. When the phase of $\Phi$ continuously changes around the string isotropically, phases at the opposite sides of an arbitrary line on the quadrate intersecting the penetration point differ by $\pi$. Greek numbers (I), (II), (III) and (IV) in the left panel shows the quadrants of $(\phi_1,\phi_2)$ in these regions. (Right) Shown is the mapping of four vertices in the field space. The minimal phase range containing the images of these four vertices is indicated with a red arrow. By observing whether the phase difference $\Delta\theta$ in this minimal range is larger than $\pi$, we identify quadrates penetrated by strings.
• Figure 2: Schematic overview of our pipeline.
• Figure 3: Validity check of our estimation method using PPSE. Three different spectra are plotted (See text for details). Only statistical errors are shown; bars corresponds to the square root of the diagonal components of covariance matrices.
• Figure 4: Visualization of one realization from our field theoretic simulation. Red line corresponds to axionic string identified by our method discussed in Section \ref{['sec:id']}. $\tau$ in the top right of each panel is the conformal time of each time slice, which can be translated into the proper time $t$ via a relation in radiation domination $t/t_\mathrm{crit}=\tau^2/\tau_\mathrm{crit}^2$. The spatial scale shows a comoving length in unit of the horizon size at $t_\mathrm{end}=25t_\mathrm{crit}$.
• Figure 5: Time evolution of the scaling parameter $\xi$ obtained by averaging over 20 realizations. Note that data points are not homogeneously placed in $t$, but in $\tau\propto \sqrt t$.