Probing the gravitational wave background from cosmic strings with Alternative LISA-TAIJI network

Last updated on Feb 11, 2026 Gravitational-Wave Detection
DOI

Highlights

  • Multi-Detector Network Analysis: First comprehensive study comparing the performance of individual space-based detectors (LISA, TAIJI) and joint detector networks (LISA-TAIJI) for detecting stochastic gravitational wave background from cosmic strings.

  • Three TAIJI Configurations: Systematically investigates three different orbital configurations for TAIJI (TAIJIm, TAIJIp, TAIJIc) to identify optimal network design for SGWB detection, providing crucial input for mission planning.

  • Superior Sensitivity with LISA-TAIJIc: Demonstrates that the LISA-TAIJIc network configuration achieves the best sensitivity for detecting cosmic string SGWB, significantly outperforming individual detectors and alternative network configurations.

  • Cosmic String Constraints: Shows the potential to constrain cosmic string tension to Gμ = O(10^-17), providing stringent tests of early universe physics and fundamental theories predicting topological defects.

  • Power-Law Sensitivity Analysis: Develops comprehensive power-law sensitivity (PLS) curves for all detector configurations, enabling direct comparison with theoretical SGWB spectra from cosmic string loop networks.

Key Contributions

1. Comprehensive Network Configuration Study

This work systematically evaluates multiple detector architectures:

Individual Detectors:

  • LISA (ESA/NASA flagship mission)
  • TAIJI in three different orbital configurations

Joint Networks:

  • LISA-TAIJIm (moderate separation)
  • LISA-TAIJIp (parallel configuration)
  • LISA-TAIJIc (complementary configuration)

2. Cosmic String SGWB Modeling

The analysis incorporates sophisticated cosmic string physics:

  • Loop formation and evolution throughout cosmic history
  • Gravitational wave emission from oscillating loops
  • Cosmological evolution of the string network
  • Resulting stochastic background spectrum in the millihertz band

3. Power-Law Sensitivity Methodology

Development of PLS curves for multi-detector networks:

  • Accounts for correlated and uncorrelated noise between detectors
  • Considers detector separation and orbital configurations
  • Enables model-independent sensitivity characterization
  • Facilitates comparison across different SGWB sources

4. Optimal Configuration Identification

Rigorous comparison identifies LISA-TAIJIc as optimal because:

  • Maximizes baseline diversity for cross-correlation
  • Provides complementary sky coverage
  • Enhances discrimination between signal and detector noise
  • Achieves best overall sensitivity in the target frequency band

Methodology

Cosmic String SGWB Calculation

1. String Network Dynamics

Cosmic strings form topological defects in the early universe:

  • Network reaches scaling regime with characteristic string density
  • Strings continuously form loops through self-intersection
  • Loops oscillate and emit gravitational waves until evaporation

2. Loop Population Evolution

The cosmic string loop population evolves according to:

  • Formation rate from long string network
  • Gravitational wave emission and energy loss
  • Loop decay and disappearance
  • Resulting distribution in loop size and redshift

3. GW Spectrum from Loops

Each loop emits GWs at harmonics of its fundamental frequency:

  • Harmonic emission pattern characteristic of string loops
  • Spectrum depends on loop oscillation modes
  • Cusps and kinks produce distinctive frequency dependence

4. Stochastic Background

The SGWB is the sum over all loops throughout cosmic history:

  • Integration over loop sizes and redshifts
  • Cosmological redshift effects
  • Resulting energy density spectrum Ωgw(f)

Multi-Detector Network Analysis

1. Individual Detector Sensitivity

For each detector (LISA, TAIJIm, TAIJIp, TAIJIc):

  • Noise power spectral density based on mission design
  • Instrumental noise (laser, acceleration, position)
  • Confusion noise from galactic binaries
  • Detector response function

2. Cross-Correlation Analysis

For joint LISA-TAIJI networks:

  • Cross-correlation statistic between detector outputs
  • Overlap reduction function (ORF) depends on detector separation
  • Different configurations yield different ORFs
  • Network sensitivity depends on correlation and individual sensitivities

3. Power-Law Sensitivity Curves

PLS curves represent sensitivity to power-law SGWB spectra:

  • Assumes Ωgw(f) ∝ f^α for some spectral index α
  • Computed for various α values
  • Enables model-independent comparison with theoretical predictions
  • Identifies frequency regions of optimal sensitivity

4. Signal-to-Noise Ratio

SNR calculation for cosmic string SGWB:

  • Compare theoretical spectrum with PLS curves
  • Integration over observation time (typically years)
  • Determines detectability for given string tension Gμ

Results

Comparative Sensitivity Analysis

Individual Detector Performance:

  • LISA provides baseline sensitivity in millihertz band
  • TAIJI configurations offer comparable but slightly different sensitivities
  • Single detectors limited by inability to distinguish signal from detector noise

Network Advantages:

  • LISA-TAIJI networks achieve significantly better sensitivity than individual detectors
  • Cross-correlation enables discrimination between correlated signal and uncorrelated noise
  • Network sensitivity improvements of factor ~2-3 in some frequency ranges

Configuration Comparison:

  • LISA-TAIJIm: Moderate improvement over single detectors
  • LISA-TAIJIp: Parallel orbits provide some enhancement
  • LISA-TAIJIc: Complementary configuration achieves best performance

LISA-TAIJIc Superiority:

The complementary configuration (TAIJIc) provides:

  • Optimal overlap reduction function across frequency band
  • Best cross-correlation sensitivity
  • Maximum network SNR for cosmic string SGWB
  • Superior ability to constrain string tension

Cosmic String Constraints

Current Constraints:

  • Pulsar timing arrays: Gμ ≲ 10^-11 (at lower frequencies)
  • LIGO/Virgo SGWB searches: Gμ ≲ 10^-15 (at higher frequencies)
  • CMB observations: Gμ ≲ 10^-7 (from initial conditions)

LISA-TAIJIc Prospects:

  • Potential to constrain Gμ ≲ 10^-17
  • Probes gap between CMB and ground-based limits
  • Most sensitive to loops formed at intermediate cosmic times
  • Distinguishes between cosmic string models

Frequency Dependence

Sensitivity varies across the millihertz band:

  • Optimal sensitivity in range ~0.1 mHz to 10 mHz
  • Cosmic string spectrum peaks in this range for certain parameters
  • Complementary to ground-based and pulsar timing array frequencies

Impact

Advancing Space-Based GW Astronomy

This work provides critical insights for mission design:

For TAIJI Mission Planning:

  • Identifies optimal orbital configuration (complementary to LISA)
  • Quantifies scientific benefits of different design choices
  • Supports Chinese space-based GW mission development

For LISA-TAIJI Collaboration:

  • Demonstrates value of international multi-detector network
  • Establishes science case for coordinated observations
  • Motivates collaboration between ESA/NASA and Chinese missions

Probing Fundamental Physics

Cosmic string detection would have profound implications:

Cosmology:

  • Direct evidence for phase transitions in early universe
  • Constraints on symmetry breaking scales and particle physics beyond Standard Model
  • Tests of cosmic string formation scenarios

String Theory:

  • Some string theory models predict fundamental or cosmic superstrings
  • GW observations probe high-energy physics inaccessible to colliders
  • Complements theoretical predictions with observational tests

Alternative to Inflation:

  • Cosmic strings arise naturally in some alternatives to cosmic inflation
  • SGWB spectrum shape distinguishes between cosmological scenarios

Complementary to Other SGWB Sources

The millihertz band may contain multiple SGWB components:

  • Cosmic strings
  • Phase transitions in early universe
  • Primordial black hole formation
  • Astrophysical backgrounds (unresolved compact binaries)

Network observations enable:

  • Disentangling multiple SGWB components
  • Spectral shape characterization
  • Discrimination between source types

Methodological Contributions

This analysis provides:

  • Template for multi-detector network studies
  • PLS methodology applicable to other SGWB sources
  • Quantitative comparison framework for mission architectures
  • Tools for optimizing detector network configurations

Resources

Publication Information

  • Journal: The European Physical Journal C, Volume 83, Issue 11, Article 1010 (2023)
  • DOI: 10.1140/epjc/s10052-023-12129-y
  • Publication Date: November 7, 2023
  • Open Access: Available through EPJC open access policy

Space-Based GW Missions

LISA (Laser Interferometer Space Antenna):

  • ESA-led with NASA participation
  • Three spacecraft in heliocentric orbit
  • Launch target: mid-2030s
  • Official Website

TAIJI:

  • Chinese Academy of Sciences mission
  • Three spacecraft constellation
  • Multiple configurations under study
  • Complementary to LISA

TianQin:

  • Complementary Chinese mission
  • Geocentric orbit design
  • Focus on MBHBs at specific sky location

Cosmic String Physics

Theoretical Background:

  • Topological defects in field theory and cosmology
  • Formation through symmetry breaking phase transitions
  • String dynamics and network evolution
  • Gravitational wave emission mechanisms

Observational Constraints:

  • Cosmic Microwave Background observations
  • Pulsar timing array limits
  • LIGO/Virgo SGWB searches
  • Compilations of current limits on Gμ

Stochastic GW Background

General Resources:

  • Reviews on SGWB sources and detection methods
  • Multi-detector cross-correlation techniques
  • Power-law sensitivity formalism
  • Separation of signal from detector noise

Other SGWB Sources:

  • Phase transitions in early universe
  • Astrophysical backgrounds (compact binary populations)
  • Primordial gravitational waves from inflation

Multi-Detector GW Astronomy

Network Analysis:

  • Overlap reduction functions for separated detectors
  • Sky localization and source characterization benefits
  • Synergies between space and ground-based detectors

International Collaboration:

  • Opportunities for LISA-TAIJI joint observations
  • Complementary capabilities of different missions
  • Multi-messenger astronomy with GW networks

Technical Resources

  • Detector noise models for LISA and TAIJI
  • Galactic foreground confusion noise estimates
  • Time-delay interferometry for space-based detectors
  • Data analysis pipelines for SGWB searches

Further Reading

  • Reviews on cosmic strings and gravitational waves
  • Space-based gravitational wave detector design
  • Stochastic background searches in current GW data
  • Early universe phase transitions and their observational signatures
Gravitational Waves SGWB Cosmic String LISA Taiji
He Wang
He Wang
Research Associate

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