Scalar induced gravitational waves review (2109.01398v2)

Abstract: We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advances in the cosmology of induced gravitational waves, as well as becoming familiar with the calculations behind.

• The paper introduces a rigorous analytical framework for deriving the scalar-induced gravitational wave spectrum from second-order perturbations during the inflationary epoch.
• It details numerical evaluations of spectral indices under varying cosmological conditions, benchmarking findings against observational prospects from detectors like LISA.
• The review highlights open challenges such as gauge dependence and non-gaussian effects, paving the way for future research in early universe cosmology.

An Overview of Scalar Induced Gravitational Waves

The paper "Scalar Induced Gravitational Waves Review" serves as a comprehensive examination of the theoretical foundations and implications of gravitational waves (GWs) induced by primordial curvature perturbations. It explores the physical understanding, analytical formulations, and observational prospects of these induced gravitational waves (IGWs), bringing to light the complex dynamics of the early universe through GWs as a probe. The review acknowledges the likenesses and complexities associated with the concept and dynamics of IGWs, emphasizing their potential to explore the unexplored epochs of the universe’s history.

Physics and Formulation

IGWs are generated from second-order perturbations of scalar fields that arise during the inflationary epoch of the universe. These scalar perturbations, particularly those with large amplitude, can induce GWs upon horizon re-entry. The paper explicates the intuitive physics behind this phenomenon, using the action formalism to derive relevant equations in different cosmological settings, particularly focusing on parameters such as equation of state and sound speed. The induced tensor spectrum is influenced by these primordial fluctuations, and the corresponding transfer functions for the induced gravitational waves are derived analytically, allowing for deeper insight into the dynamics governing them.

Analytical and Numerical Results

An important contribution of the paper is its detailed derivation of analytical kernels needed to compute the IGW spectrum across various cosmological backgrounds. The results are segregated for radiation domination and epochs with different equation of states (EoS), providing comprehensive spectral indices for different primordial spectrum shapes. The consistency and validity of these analytic results are benchmarked cleanly against potential observational data, covering both sharp peaks and broad spectrum scenarios in the primordial power spectrum.

Observational Prospects and Implications

The review forecasts the role of IGWs in future gravitational wave observations, as we stand on the cusp of a significant leap in GW detector capabilities. It speculates on using data from upcoming detectors like LISA and potential observables in spectral distortions to reverse-engineer constraints on the primordial curvature power spectra. Through such observations, specific epochs such as those dominated by primordial black holes (PBH) become amenable to paper, offering insights into the universe before standard Big Bang nucleosynthesis.

Open Questions and Theoretical Challenges

From an analytical perspective, an intriguing aspect explored in the paper is the gauge dependence in defining the tensor spectrum at second order. This remains an open theoretical challenge, invoking further investigation into the descriptions of gauge-invariant gravitational radiation in cosmological perturbation theory. The paper also discusses the effects of non-gaussianities and the challenges they pose due to their potential impact on making precise predictions about the IGWs spectrum.

Conclusion and Future Directions

The paper provides a thorough investigation into the state-of-the-art research on IGWs, detailing intricate methodologies for Igw spectral analysis and elucidating their potential significance in fundamental cosmology. As the cosmic microwave background has allowed cosmologists to peer into the infant universe, IGWs are poised to unlock mysteries from even earlier times, fostering novel understandings as observational, numerical, and theoretical techniques evolve. Future research is bound to focus on resolving outstanding theoretical ambiguities, optimizing cross-correlation analysis with cosmological data, and maximizing the scientific return of future GW detection initiatives in providing windows into the earliest eras of cosmic evolution.