Searches of a Cosmological Gravitational-Wave Background with 3G Detectors: Probing the Very Early Universe

Gravitational-wave detection from compact binary coalescences with current gravitational-wave detectors has made a tremendous impact on our understanding of astrophysical sources and look forward to the stochastic gravitational-wave background (SGWB) signal detection. An SGWB comprises superpositions of numerous astrophysical and cosmological sources, providing a direct window to study early universe phenomena and fundamental physics. Observation of the early universe gravitational-wave background signal would be paramount. Till yet, there is no direct or statistical evidence of stochastic cosmological gravitational-wave background (SCGWB) signal apart from upper limits has placed on the associated parameters after analyzing the advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) and advanced Virgo (AdV) data. With the proposed third-generation ground-based gravitational-wave detectors, Einstein Telescope and Cosmic Explorer, we might be able to detect evidence of an SCGWB. However, digging out these prime signals would be a challenging quest as the dominance of the astrophysical foreground from compact binary coalescences will mask the SCGWB. This idea to deal with the foreground signal and increase future gravitational-wave detector's sensitivity toward SCGWB searches led to the foundation of the work presented in the thesis. In this work, I study a subtraction-noise projection method with future ground-based detectors, which first subtracts the dominating foreground signals from compact binary coalescences and then makes it possible to reduce the residuals left after subtraction of a foreground of compact binary coalescences, significantly improving our chances to detect an SCGWB. The subtraction of the foreground signal depends upon the accurate parameter estimation of individual binary signals present in the detector data. I carried out the analysis using posterior sampling for the parameter estimation of binary black hole mergers. The removal of an astrophysical foreground in future detectors with potentially several $10^5$ signals per year will be computationally very challenging. I extended state-of-the-art Bayesian parameter estimation and detector modeling software (Bilby) to incorporate foreground reduction methods based on geometric interpretations of matched filtering. I also developed a numerical approach for the calculation of Fisher matrices that allows the implementation of arbitrary waveform models, i.e. not only the analytical ones. As a result, I demonstrate the sensitivity improvement of SCGWB searches and find that the ultimate sensitivity of SCGWB searches will not be limited due to residuals left after subtracting the estimated binary black holes foreground. However, the fraction of the astrophysical foreground that cannot be detected even with third-generation instruments, or the possible presence of other signals (non-deterministic astrophysical stochastic background signals) can further impact the sensitivity towards the SCGWB searches. To search for an isotropic SGWB and their statistical evidence in aLIGO and AdV data, I am involved in research activities with the stochastic group of LIGO VIRGO Collaboration contributing to data analysis and isotropic SGWB searches. The main objective of my contribution is, to analyze the whole third observation run data of aLIGO and AdV, and look for variations in the signal if present, i.e. coherence between the different baselines of aLIGO and AdV detectors. And then to use a stochastic energy density spectrum following a power-law distribution to check for SGWBs either of astrophysical or cosmological origin based on the power-law index, which characterizes the background signal and then helps to put upper limits on the respective SGWB. I, therefore, present the upper limits on isotropic SGWB searches from the third observation run of aLIGO and AdV detectors data. The limits on the isotropic SGWB from the third observation run stochastic data analysis improved by a significant factor in comparison to the upper limits from the first and the second observation run stochastic data analysis.