High-resolution cosmological simulations of primordial dark matter clustering under long-range and fractional forces

TL;DR

This work investigates how long-range attractive fifth forces, realized via a Yukawa coupling between fermions and a light scalar, can induce a fractional, scale-dependent force in the early Universe. By implementing oscillation-averaged fractional Yukawa forces within a high-resolution P$^3$M N-body framework, the authors compare density statistics to Newtonian gravity and find that halos formed under the fractional force are significantly denser at the same mass scale. They further show that nonlinear scalar fluctuations become important when halo sizes approach the effective Compton length $\ell$, potentially modifying clustering and leading to screening effects that could cap halo growth. These results imply that early-universe structure formation can be markedly altered by scale-dependent forces, with possible observational consequences for primordial black holes, gravitational waves, and relic correlations, and highlight the need to model radiative and nonlinear scalar dynamics in future work.

Abstract

Long-range attractive fifth forces can lead to exponential instabilities in the early Universe. For fermions with a Yukawa coupling to a sufficiently light scalar mediator, rapid oscillations of the scalar field can lead to a conservative force law with fractional behaviour on sufficiently large scales. We study cosmological systems evolving under both this fractional potential and the Newtonian potential using high-resolution N-body simulations. We find that, at the same mass scale, halos that form under the fractional potential are much more dense than those that from the Newtonian potential. However, we also find that the perturbed scalar field may have large fluctuations once halo sizes become comparable to an effective Compton length, which will modify subsequent clustering and collapse.

Figures (19)

• Figure 1: Scale-dependence of the Newtonian interaction ($\mathcal{G}$), the Yukawa interaction ($\mathcal{Y}$), and various fractional interactions ($\mathcal{Q}$). The values of $\xi/\ell$ are chosen for each $m$ to match the fifth force arising in scalar-fermion systems.
• Figure 2: Background evolution of a scalar field for various scalar self-interactions $\propto\phi^{2m}$. When the scalar field is large ($\nu_0\ll0$) it's potential is dominated by self-interactions ($\propto\nu_0^{2m}$), whereas when it is small ($\nu_0\sim0$) it is dominated by the Yukawa interactions and the scalar field behaves parabolically $\nu_0\approx-\theta^2/2$.
• Figure 3: Ratio of approximate potential $\mathcal{Q}$ in Eq. \ref{['eq:qpotential']} to the numerical evaluation of Eq. \ref{['eq:oscavgF']}. The top panel shows the Fourier space calculation whereas the lower panel shows the corresponding real space calculation. For large $m$ the real space curves are truncated due to numerical oscillations when evaluating $_1F_2$ with large arguments.
• Figure 4: (Top) P$^3$M force calculation for an inverse square law (green) and the oscillation averaged scalar force (blue). Solid lines show the mean of 1000 repetitions, while shaded regions show the $1\sigma$ standard deviation. The vertical grey line shows the softening length, while the shaded grey region indicates where the grid geometry affects whether the PP force is calculated. (Bottom) Shaded regions show the standard deviation without the mean. The solid curves show the fluctuation between the mean force and the approximate force based on Eq. \ref{['eq:qpotential']} (purple) and an exact oscillation averaged force calculation (black). Both theoretical and numerical errors are around $\sim 1\%$ (shown as dotted horizontal lines).
• Figure 5: Initial power spectra at $s_i=10^{-2}$. While the two $n_0=2$ simulations have the same initial power spectrum, the $n_0=1$ simulations are different at $s_i$ but have the same linear power at a later redshift.