Researchers Model Scalar-induced Gravitational Waves in Spatially Covariant Gravity

The search for subtle violations of Einstein’s theory of general relativity drives much of modern gravitational wave research, and a new study explores how these violations might manifest as a stochastic background of gravitational waves. Jiehao Jiang from Sun Yat-sen University, Jieming Lin from Imperial College London, and Xian Gao et al. investigate scalar-induced gravitational waves within a framework called spatially covariant gravity, a class of theories that allows for violations of Lorentz invariance. This research develops a detailed understanding of how these modified gravity theories predict deviations from standard gravitational wave signals, specifically focusing on alterations to both the strength and the characteristic patterns of the waves. The findings demonstrate the potential for future gravitational wave detectors to not only confirm or refute these theories, but also to map out the specific ways in which gravity might deviate from Einstein’s predictions, opening a new window into the fundamental laws of the universe.

Extending earlier formulations, researchers compute the general kernel function for stochastic gravitational waves (SIGWs) on a flat Friedmann-Lemaître-Robertson-Walker background. This work focuses on polynomial-type scalar-gauge gravity Lagrangians up to third-order derivatives, allowing exploration of a wide range of gravitational modifications. Explicit expressions for the kernel are derived assuming a power-law time evolution of the coefficients, and the analysis restricts attention to operators where tensor modes propagate at the speed of light, avoiding problematic late-time divergences in the fractional energy density of SIGWs. Unlike the usual Newtonian gauge, the breaking of time reparametrization symmetry inherent in scalar-gauge gravity necessitates the adoption of a unitary gauge.

Scalar Perturbations and Gravitational Wave Generation

This collection of research papers primarily focuses on cosmology, gravitational waves, modified gravity, and related topics. A central theme is the generation and detection of Scalar-Induced Gravitational Waves, offering a unique window into the very early universe and potential new physics. Researchers investigate how scalar perturbations, originating from inflation or other early universe processes, generate a stochastic background of gravitational waves, calculating the amplitude and frequency spectrum of these signals and assessing their detectability with current and future observatories. A significant portion of the research explores theories that modify General Relativity, motivated by attempts to explain dark energy, dark matter, and to develop a consistent theory of quantum gravity.

Key areas include higher-derivative gravity, scalar-tensor theories, disformal transformations, and non-metricity gravity. X. Gao’s work is central to spatially covariant gravity, a specific framework exploring modifications to standard gravity. Several papers focus on how gravitational waves propagate through spacetime and how they can be detected, studying polarization, propagation in modified gravity, and using observations to test theories and constrain model parameters. Beyond SIGWs, researchers address broader aspects of early universe cosmology, exploring models of inflation, phase transitions, and deviations from Gaussianity in the primordial density perturbations.

Scalar Gravitational Waves in Modified Gravity

Researchers investigated scalar-induced gravitational waves (SIGWs) within the framework of spatially covariant gravity (SCG), a modified gravity theory that relaxes the strict requirements of Lorentz invariance while preserving spatial diffeomorphism invariance. Extending previous SCG formulations, the team derived the general kernel function governing SIGW production on a flat Friedmann-Lemaître-Robertson-Walker background, focusing on polynomial-type Lagrangians containing up to three derivatives. This allowed them to explore a broad class of modifications to standard gravity and their impact on gravitational wave generation. The study necessitated a shift away from the commonly used Newtonian gauge due to the breaking of time reparametrization symmetry inherent in SCG; instead, researchers employed a unitary gauge analysis.

By assuming a power-law time dependence for the coefficients within the SCG Lagrangian, they obtained explicit solutions for the kernel function, a crucial component in calculating SIGW production. Focusing on the radiation-dominated era, the team computed the energy density of SIGWs, specifically examining SCG operators that allow tensor modes to propagate at the speed of light, thereby avoiding problematic late-time divergences. Results demonstrate that SCG predicts distinctive deviations from general relativity in the fractional energy density of SIGWs, including scale-dependent modifications to both the amplitude and spectral shape of the gravitational wave signal. These findings highlight the potential of stochastic gravitational wave background measurements to probe SCG and other Lorentz-violating extensions of general relativity.

Lorentz Violation Probed by Gravitational Waves

This research presents a systematic investigation of scalar-induced gravitational waves (SIGWs) within the framework of spatially covariant gravity, a type of modified gravity theory that allows for violations of Lorentz invariance. By calculating the kernel function governing SIGW generation, the study demonstrates how deviations from general relativity can manifest as alterations to both the amplitude and spectral shape of the gravitational wave background. The results show that these modifications arise from the unique cubic interactions within spatially covariant gravity and are present even when deviations from standard gravity are small. The findings highlight the potential of stochastic gravitational wave background measurements to probe these Lorentz-violating theories. While the study focused on polynomial-type Lagrangians up to third-order derivatives and restricted analysis to operators ensuring luminal tensor propagation, the authors acknowledge that extending the work to include parity-violating operators, higher-order terms, or couplings to other fields represents a valuable avenue for future research, potentially detectable by current and future observatories like pulsar timing arrays and space-based interferometers.