[论文解读] Gravitational Waves Produced by Domain Walls During Inflation

Haipeng An, Yang Chen|arXiv (Cornell University)|Apr 5, 2023

Cosmology and Gravitation Theories被引用 8

一句话总结

本论文研究在没有网络的情况下，在膨胀期间由域壁形成的随机引力波背景，使用 1000^3 格点的格点模拟，并推导出一个经验谱公式以评估未来引力波探测器和宇宙微波背景 B 模（CMB B-mode）的可探测性，与 PTA 信号可能相关。

ABSTRACT

We study the properties of the stochastic gravitational wave background (SGWB) produced by domain walls (DWs) during inflation without forming a network. We numerically simulate the DW production caused by a second-order phase transition and calculate the SGWB spectrum using a $1000 imes1000 imes1000$ lattice. We show that the SGWB can be observed directly by future terrestrial and spatial gravitational wave detectors and through the B-mode spectrum in CMB. This signal can also explain the common noise process observed by pulsar timing array experiments. With numerical simulations, we derive an empirical formula for the strength and qualitative features of the SGWB spectrum. The details of the SGWB spectrum also contain information about the later evolution of the universe.

研究动机与目标

• Motivate and investigate gravitational waves generated by domain walls formed during inflation without forming a network.
• Simulate the tachyonic growth and nonlinear evolution of a spectator sector field undergoing a second-order phase transition during inflation.
• Compute the resulting gravitational wave spectrum and derive an empirical formula for its peak strength.
• Assess detectability of the signal across terrestrial, space-based GW detectors and CMB B-mode observations, and discuss links to pulsar timing arrays.

提出的方法

• Model a spectator sector with a Landau-Ginzburg potential undergoing a second-order phase transition during de Sitter inflation.
• Study two scenarios for DW formation: (A) temperature-triggered transition at the start of inflation, (B) inflaton-driven transition.
• Use tachyonic growth of long-wavelength modes and then nonlinear classical lattice evolution on a 1000^3 grid to form domain walls.
• Compute the GW spectrum using the transverse-traceless part of the energy-momentum tensor and a Green’s-function formalism with a kernel that highlights the dominant contribution around kτ′≈−2.
• Incorporate lattice discretization with a sixth-order symplectic integrator and a lattice-improved projection to suppress unphysical modes.
• Derive a semi-analytical expression for the peak of the GW spectrum and explore dependence on post-inflationary expansion histories (instant reheating, MD, KD).

Figure 1: The evolutions of the root mean square of $\sigma$ for scenario (A) (green) and (B) (yellow). The dashed curves show the corresponding the temporary expectation of $\sigma$ . For both cases we use $H=10^{-4}M_{\rm pl}$ , $m=5\times 10^{-3}M_{\rm pl}$ . For (A) we have $\lambda=0.0625$ , $m

实验结果

研究问题

• RQ1 Can domain walls formed during inflation, without forming a network, generate a detectable stochastic gravitational wave background?
• RQ2 What is the shape and peak strength of the SGWB produced by such domain walls, and how does it depend on inflationary and post-inflationary evolution?
• RQ3 Can the inflationary DW-induced SGWB imprint be observed in CMB B-modes or explained the common PTA noise?
• RQ4 How does the subsequent evolution of the universe after inflation affect the SGWB spectrum?
• RQ5 How can one distinguish DW-induced SGWB from quantum tensor fluctuations with future observations?

主要发现

• The SGWB from inflationary domain walls without a network can be directly observable by future terrestrial and space-based GW detectors and via CMB B-modes.
• DWs produced during inflation dominate GW production in the simulations, with signals ceasing around four e-folds after the phase transition in the models studied.
• The authors derive an empirical formula for the peak GW energy density that encodes the dependence on wall thickness and the redshift history, linking the peak to the post-inflationary expansion era.
• Depending on the e-folds N_c between the phase transition and the end of inflation, the signal can fall into PTA sensitivity (N_c ≈ 40), space-based detectors (N_c ≈ 20−25), terrestrial detectors (N_c ≈ 10), or CMB B-modes (N_c ≈ 60).
• The shape of the B-mode spectrum induced by this GW source differs from the quantum-generated tensor spectrum, enabling potential discrimination with future CMB observations.
• The study provides a framework to relate the SGWB spectrum to the later evolution of the universe and to explore connections to the NANOGrav common-noise hints.

Figure 2: Evolution of the $\sigma$ field in scenario (A) for $\ln a/a_{c}=1.3,2.3,3.3$ and $4.3$ , where the $x$ and $y$ axes show the comoving coordinates in the unit of $a_{c}^{-1}m_{\rm KZ}^{-1}$ , and the $z$ axis shows $\sigma/v$ . The parameters in the potential are the same as in Fig. 1 .