[Paper Review] Gravitational waves from cosmic strings in LISA: reconstruction pipeline and physics interpretation

José J. Blanco-Pillado, Yanou Cui+7 more|arXiv (Cornell University)|May 6, 2024

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper develops a dedicated reconstruction pipeline for stochastic gravitational wave backgrounds from cosmic strings in the LISA mission, using both analytical and numerically derived templates from Nambu-Goto simulations. It demonstrates that LISA can probe cosmic string tensions as low as $G\mu \sim 10^{-16} - 10^{-17}$, enabling precision tests of early-universe physics and new relativistic degrees of freedom, though degeneracies with non-gravitational radiation fractions reduce reconstruction accuracy.

ABSTRACT

We initiate the LISA template databank for stochastic gravitational wave backgrounds sourced by cosmic strings. We include two templates, an analytical template, which enables more flexible searches, and a numerical template derived directly from large Nambu-Goto simulations of string networks. Using searches based on these templates, we forecast the parameter space within the reach of the experiment and the precision with which their parameters will be reconstructed, provided a signal is observed. The reconstruction permits probing the Hubble expansion and new relativistic DoF in the early universe. We quantify the impact that astrophysical foregrounds can have on these searches. Finally, we discuss the impact that these observations would have on our understanding of the fundamental models behind the string networks. Overall, we prove that LISA has great potential for probing cosmic string models and may reach tensions as low as $Gμ=10^{-16} - 10^{-17} $, which translates into energy scales of the order $10^{11}~ ext{GeV}$.

Motivation & Objective

• To develop a robust, flexible reconstruction pipeline for stochastic gravitational wave backgrounds (SGWB) from cosmic strings in the LISA mission.
• To enable precise parameter estimation of cosmic string energy scale $G\mu$ and non-gravitational radiation fraction $f_{\text{NG}}$ using both analytical and numerically derived templates.
• To forecast the sensitivity of LISA to cosmic string models and assess the impact of astrophysical foregrounds on detection and reconstruction.
• To investigate how SGWB observations can constrain early-universe physics, including the Hubble expansion history and new relativistic degrees of freedom.
• To quantify the degeneracy between $G\mu$ and $f_{\text{NG}}$ and its impact on reconstruction precision.

Proposed method

• The authors construct two SGWB templates: one analytical and one derived from large-scale Nambu-Goto simulations of cosmic string networks.
• They implement a modified version of the SGWBinner pipeline to perform Bayesian parameter estimation on simulated LISA data streams.
• The pipeline includes an additional parameter $f_{\text{NG}}$ to model the fraction of energy radiated gravitationally, allowing for non-maximal GW emission.
• Monte Carlo simulations with 30 trials per parameter set are used to assess average reconstruction accuracy and precision, with and without astrophysical foregrounds.
• The method accounts for the degeneracy between $G\mu$ and $f_{\text{NG}}$ by analyzing how shifts in amplitude and frequency scale with $G\mu$ and $\sqrt{G\mu}$.
• Sensitivity forecasts are derived by injecting signals across a range of $\log_{10}(G\mu)$ values from $-17.0$ to $-10.0$, with $f_{\text{NG}}$ set to 1.0 or 0.1.

Experimental results

Research questions

• RQ1 Can LISA reconstruct the cosmic string parameter $G\mu$ with high precision using realistic SGWB templates?
• RQ2 How does the inclusion of a non-gravitational radiation fraction $f_{\text{NG}}$ affect the reconstruction accuracy and precision of $G\mu$?
• RQ3 What is the minimum detectable $G\mu$ value for LISA, and what energy scale does it correspond to?
• RQ4 How do astrophysical foregrounds impact the ability to detect and reconstruct cosmic string SGWB signals?
• RQ5 To what extent can SGWB observations from cosmic strings constrain early-universe physics, such as the Hubble expansion rate and new relativistic degrees of freedom?

Key findings

• LISA can achieve a sensitivity threshold of $G\mu \sim 10^{-16} - 10^{-17}$, corresponding to energy scales of $\sim 10^{11}~\text{GeV}$.
• Reconstruction of $G\mu$ is biased toward lighter strings when $f_{\text{NG}} = 1.0$, with increased standard deviations compared to the base case.
• When $f_{\text{NG}} = 0.1$, the uncertainty in $G\mu$ increases by a factor of about ten, reflecting strong degeneracy between $G\mu$ and $f_{\text{NG}}$.
• The degeneracy is most pronounced in the LISA frequency band, where the shape of the SGWB—especially features like the radiation-to-matter transition bump—plays a critical role in fitting.
• For $\log_{10}(G\mu) = -12.0$ and $f_{\text{NG}} = 0.1$, the reconstruction shows lower uncertainty than adjacent points, though absolute error is larger, suggesting sensitivity to spectral structure in the LISA window.
• Signals below the LISA PLS (e.g., $\log_{10}(G\mu) = -17.0$) lead to wide, unreliable confidence regions due to marginal signal acceptance.