[Paper Review] Halo Formation from Yukawa Forces in the Very Early Universe

Guillem Domènech, Derek Inman+2 more|arXiv (Cornell University)|Apr 25, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates halo formation in the very early universe driven by long-range Yukawa forces from scalar-mediated interactions between dark matter fermions. Using self-consistent scalar field dynamics and N-body simulations, it demonstrates that halos form exponentially fast on larger scales than predicted, with potential implications for primordial black holes, dark stars, or galaxy-sized halos at matter-radiation equality.

ABSTRACT

If long-range attractive forces exist and are stronger than gravity then cosmic halo formation can begin in the radiation-dominated era. We study a simple realization of this effect in a system where dark matter fermions have Yukawa interactions mediated by scalar particles, analogous to the Higgs boson in the standard model. We develop a self-consistent description of the system including exact background dynamics of the scalar field, and precise modelling of the fermion density fluctuations. For the latter, we provide accurate approximations for the linear growth as well as quantitative modelling of the nonlinear evolution using N-body simulations. We find that halo formation occurs exponentially fast and on scales substantially larger than simple estimates predict. The final fate of these halos remains uncertain, but could be annihilation, dark stars, primordial black holes, or even the existence of galaxy-sized halos at matter-radiation equality. More generally, our results demonstrate the importance of mapping scalar-mediated interactions onto structure formation outcomes and constraints for beyond the standard model theories.

Motivation & Objective

• To investigate the role of long-range Yukawa forces in triggering early cosmic structure formation during the radiation-dominated era.
• To model the nonlinear evolution of fermion density fluctuations under scalar-mediated interactions, beyond linear approximations.
• To assess the viability of halo formation as a precursor to primordial black hole formation or other early compact objects.
• To establish a self-consistent framework coupling scalar field background dynamics with fermion clustering in cosmological N-body simulations.
• To evaluate the robustness of results against numerical artifacts from finite grid resolution and force softening in simulations.

Proposed method

• Develops a self-consistent model coupling the background dynamics of a scalar field mediating Yukawa interactions with fermion density fluctuations.
• Employs N-body simulations with particle-mesh methods to model nonlinear evolution of fermion halos under Yukawa forces.
• Uses a finite grid with adjustable softening length $ n_{ ext{ℓ}} $ to test numerical convergence and minimize artifacts from periodic boundary conditions.
• Applies rescaling techniques to test invariance of results to physical length scale $ \ell $, ensuring numerical robustness.
• Compares simulations with varying $ n_{ ext{ℓ}} $ and time-dependent $ \ell $ to assess sensitivity to force law truncation and resolution effects.
• Uses dimensionless power spectra and halo mass functions to quantify structure growth and convergence across simulation setups.

Experimental results

Research questions

• RQ1 Can Yukawa forces from scalar-mediated interactions trigger halo formation in the radiation-dominated early universe?
• RQ2 How does the nonlinear evolution of fermion density fluctuations under Yukawa forces compare to linear growth predictions?
• RQ3 What is the impact of numerical resolution and force softening on the formation of halos in N-body simulations of Yukawa interactions?
• RQ4 How do time-varying scalar mediator masses affect the effective force law and structure formation outcomes?
• RQ5 What are the implications of early halo formation for the formation of primordial black holes or other compact objects?

Key findings

• Halo formation occurs exponentially fast and on scales substantially larger than simple linear estimates predict, due to strong Yukawa attraction.
• Simulations with $ n_{\ell} = 12 $ and $ n_{\ell} = 16 $ show converged results in both power spectra and halo mass functions, indicating numerical stability.
• The power spectrum at $ s = 200 $ shows virialized halos with higher concentrations than linear theory predicts, indicating nonlinear collapse.
• Lower power in the nonlinear regime for low-frequency $ \ell $ oscillations suggests reduced force effectiveness near $ \ell \sim \bar{\ell}/2 $, possibly due to insufficient resolution.
• Halo mass functions show deviations for $ n_{\ell} \leq 8 $, and a suppression of massive halos at $ n_{\ell} = 20 $, indicating insufficient dynamic range.
• The results are robust to changes in $ n_{\ell} $ when properly rescaled, confirming the physical invariance of the force law and numerical convergence.