Constraints on typical relic gravitational waves based on data of LIGO

Abstract

Relic gravitational waves (RGWs) from early universe carry fundamental information, so it's extraordinarily important to search RGW signals from data of observatories like LIGO-Virgo network. Here, focusing on typical RGWs from inflation and first-order phase transition (by sound waves and bubble collisions), effective and targeted deep learning neural networks are established to search RGW signals among real LIGO data (O2, O3a and O3b). We construct Convolutional Neural Network (CNN) to estimate likelihood (by quantitative values and distributions) of existence of focused RGW signals in LIGO data, or provide constraints on their strengths. We find if the built CNN properly estimates the parameters of RGWs, it can accurately (about 94% to 99%) determine whether the samples contain RGW signals, and if not, the likelihood given by CNN is not reliable. After testing large amount of LIGO datasets, the results indicate no evidence of RGWs from inflation, sound waves, or bubble collisions predicted by focused theories, and it provides upper limits of their GW spectral energy densities of h^2\Omega_{gw} of 10^{-5} (for various orders of GW amplitude given specific parameter regions by reverse mapping). In short, null results and upper limits are acquire; the methods and neural networks we develop to search RGWs from LIGO data could be effective and reliable, which can be applied not only for current data but also upcoming O4 data or other observational datasets, to establish an available scheme for exploring potential RGW signals or to provide constraints on relevant theoretical models.