Observational prospects for gravitational waves from cosmological first order phase transitions at LISA

The era of gravitational wave (GW) observations began with the ground-breaking detection at the Laser interferometer GravitationalWave detector (LIGO), we are now exploring more of the GW power spectrum. Upcoming space-based detectors such as the Laser Interferometer Space Antenna (LISA) will probe, for the first time, the millihertz window of the GW spectrum with the hope of detecting astrophysical and cosmological sources. The source of interest in this thesis is a cosmological first order phase transition at the electroweak scale. Detecting these GWs from the early universe would provide the opportunity to delve further back in the history of the universe than ever before. In theories beyond the Standard Model a cosmological first order phase transition occurs when, below a critical temperature, bubbles of stable phase spontaneously nucleate in the surrounding metastable phase. These bubbles expand, collide, and merge until only the stable phase remains. This phenomenon produces a stochastic gravitational wave background (SGWB) that, once scaled due to the expansion of the universe, peaks in the frequency band corresponding to LISA. In the Standard Model this transition is a crossover and no GWs are produced. Thus, a detection of such a SGWB would be a discovery of new physics. In the following thesis, using the latest analytical model of a SGWB from a first order phase transition (the Sound Shell Model) and information from cutting edge simulations I explore LISA’s ability to perform parameter estimation on key phase transition parameters. I focus on two different parameterisations of the phase transition SGWB, the thermodynamic and spectral. The thermodynamic parameters are derived from the physics of the phase transition and consequently are related to the beyond standard model theory they inhabit. The spectral parameterisation is computationally cheaper than the thermodynamic parameterisation, which is advantageous when performing MCMC simulations. However, the connection from the spectral to thermodynamic parameters is an unanswered question. Here, we present a method for reconstructing the thermodynamic parameters from the spectral parameters. I use statistical methods including Fisher analysis and Markov chain Monte Carlo (MCMC) simulations to estimate parameter uncertainties on the two parameterisations. The impact of astrophysical foregrounds on resolving a SGWB for a first order phase transition are also investigated.