Scalar induced gravitational waves

Abstract

The study of primordial fluctuations and their implications for the early universe has traditionally been constrained by observations of large-scale perturbations, such as those provided by the Cosmic Microwave Background (CMB).

However, Scalar-Induced Gravitational Waves (SIGWs) might offer a new way of probing small-scale fluctuations and therefore earlier phases of the universe, before the CMB. This report explores the application of advanced methods for computing the SIGW power spectrum, focusing on the adaptation of the FFT-Log approach to enhance the analysis of SIGWs and therefore primordial fluctuations. We begin by reviewing the broader context and the current state of the field, before establishing the theoretical framework, deriving key results and validating them against existing literature. We then present our modified FFT-Log method, implemented for its potential to efficiently compute the SIGW power spectrum. This approach is applied on a model involving a delta scalar power spectrum, to showcase its practical utility. Our findings suggest that the modified FFT-Log approach can enhance the analysis of SIGWs in models involving time-dependent equations of state. Its efficiency is examined in a qualitative manner but remains to be fully explored, pending the development of software for its integration. While FFT-Log generally offers faster computation for convolution integrals, its effectiveness in this context remains uncertain and further research is needed to fully assess its potential benefits compared to traditional methods.

This work ultimately introduces a new computational tool for investigating early universe physics. Future research could refine this method and explore its impact on constraining the SIGW power spectrum for different phases.