insight - Computational Complexity - # Gravitational Wave Production from Nonlinear Structure Formation in Early Matter-Dominated Eras

Core Concepts

Nonlinearities significantly enhance the production of stochastic gravitational waves during early matter-dominated eras, with the dominant contribution coming from the collapse of the largest and latest-forming gravitationally-bound structures.

Abstract

This work presents a comprehensive calculation of the stochastic gravitational wave (GW) background generated during an early matter-dominated era (EMDE) in the universe. The authors use a hybrid N-body and lattice simulation approach to study GW production from both the metastable matter species and the radiation produced in its decay.

Key highlights:

- The authors find that nonlinearities significantly enhance GW production up to frequencies at least as large as the inverse light-crossing time of the largest halos that form prior to reheating.
- The dominant contribution to the GW spectrum comes from the collapse of the largest and latest-forming gravitationally-bound structures, rather than the radiation produced in the decay of the metastable matter.
- The amplitude of the GW spectrum scales as A^(7/4), where A is the amplitude of the primordial curvature power spectrum, while the frequency spectrum is independent of A and set by the reheating timescale.
- Depending on the reheating temperature and the amplitude of primordial curvature perturbations, the induced SGWB may be within reach of future GW observatories.
- The authors caution that a fully relativistic treatment is required to resolve the GW spectrum at frequencies above the inverse light-crossing time of the largest halos.

To Another Language

from source content

arxiv.org

Stats

The typical mass scale of the latest-forming halos prior to reheating is set by the amplitude of the primordial curvature power spectrum, A.
The number density of such halos at reheating scales as A^(3/2).
The amplitude of the GW energy density spectrum scales as A^(7/4), independent of the Hubble parameter at reheating.

Quotes

"Nonlinearities significantly enhance GW production up to frequencies at least as large as the inverse light-crossing time of the largest halos that form prior to reheating."
"The dominant contribution to the GW spectrum comes from the collapse of the largest and latest-forming gravitationally-bound structures, rather than the radiation produced in the decay of the metastable matter."
"Depending on the reheating temperature and the amplitude of primordial curvature perturbations, the induced SGWB may be within reach of future GW observatories."

Key Insights Distilled From

by Nicolas Fern... at **arxiv.org** 10-01-2024

Deeper Inquiries

If the decay radiation (DR) were not modeled as a perfect fluid and instead allowed to develop anisotropic stress, the gravitational wave (GW) spectrum would likely experience significant modifications. Anisotropic stress is a crucial source of tensor perturbations, which are responsible for generating GWs. In the context of the simulations presented, the treatment of DR as a perfect fluid simplifies the dynamics and neglects the potential contributions from anisotropic stress that could enhance GW production.
Allowing for anisotropic stress in the DR would introduce additional source terms in the equations governing GW production, particularly in the transverse-traceless (TT) components of the stress-energy tensor. This could lead to an increase in the amplitude of the GW spectrum, especially at frequencies associated with the dynamics of the collapsing structures. The presence of anisotropic stress would also affect the coherence of GW emission from collapsing halos, potentially leading to a more complex frequency spectrum with enhanced power at certain scales.
Moreover, the interaction between the anisotropic stress and the scalar perturbations could result in a more efficient transfer of energy from small-scale fluctuations to larger scales, thereby amplifying the GW signal. This could make the SGWB more detectable by future observatories, as the enhanced GW production would be more pronounced in the nonlinear regime of structure formation.

The findings from this work have significant implications for models of early universe physics that predict enhanced small-scale curvature perturbations, such as those arising from axion-like dark matter (ALDM) or secluded dark sectors. These models often involve mechanisms that can amplify the primordial curvature power spectrum on small scales, leading to the formation of dense structures that can influence the dynamics of the universe during the early matter-dominated era (EMDE).
The enhanced small-scale curvature perturbations predicted by these models can lead to a more pronounced stochastic gravitational wave background (SGWB) due to the nonlinear dynamics of structure formation. As the simulations indicate, the GW spectrum is sensitive to the amplitude of the primordial curvature power spectrum, (A_s), with the energy density of GWs scaling as (\Omega_{GW} \propto A_s^{7/4}). This suggests that models with larger (A_s) could produce a more detectable SGWB, particularly if the reheating temperature is low enough to allow for significant GW production before the transition to radiation domination.
Furthermore, the results indicate that the GW spectrum is dominated by the collapse of the largest and latest-forming halos, which are influenced by the underlying physics of the early universe. This means that observational signatures of GWs could provide insights into the nature of dark matter and the dynamics of early universe processes, potentially validating or constraining models involving ALDM or secluded dark sectors.

Yes, the gravitational wave (GW) signal from early structure formation could provide valuable insights into the particle physics of post-inflationary reheating. The production of GWs during the transition from an early matter-dominated era (EMDE) to radiation domination is closely linked to the dynamics of the fields responsible for reheating, including the decay of metastable particles and the subsequent generation of radiation.
The characteristics of the SGWB, such as its amplitude and frequency spectrum, are influenced by the properties of the reheating process, including the reheating temperature and the nature of the decaying matter. For instance, the simulations suggest that the GW spectrum is sensitive to the amplitude of the primordial curvature perturbations, which can be affected by the dynamics of reheating. If the reheating occurs at a low temperature, it may allow for the production of a detectable SGWB, providing a unique window into the conditions of the early universe.
Moreover, the detection of GWs could help distinguish between different models of reheating, such as those involving rapid decay processes or more gradual transitions. By analyzing the SGWB, researchers could infer properties of the underlying particle physics, such as the mass and decay rates of the particles involved in reheating, as well as the interactions between different fields.
In summary, the GW signal from early structure formation not only serves as a probe of the dynamics of the early universe but also offers a potential means to explore the fundamental particle physics that governs the post-inflationary epoch, thereby enhancing our understanding of the universe's evolution.

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