Some Tests of General Relativity Using Gravitational Wave Observations

Samajdar, Anuradha (2018) Some Tests of General Relativity Using Gravitational Wave Observations. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

This thesis deals with some approaches to test General Relativity using gravitational waves and a brief discussion of a parameter estimation technique. The dawn of gravitational wave astronomy has provided fresh impetus for both these purposes. We have used gravitational wave data for constraining Lorentz violation in the gravity sector. A Bayesian analysis enabling this has been introduced. An interpretation of an apparent deviation from general relativity as resulting from a non-negligible residual eccentricity has been made. This is done using analytical expressions, thus making it computationally inexpensive. A discussion of Particle Swarm Optimisation is made in the context of extracting parameters from signals from an inspiralling binary system. Chapter 1 is a general introduction to gravitational wave astronomy. We start with a discussion of the gravitational wave discovery in 2015 and it’s impact in the field of gravitational wave astronomy. We give a brief background of the foundations of the subject, especially in light of initial e↵orts to detect these elusive waves. The theory of the existence of gravitational radiation starting from Einstein’s equations and its solutions in approximate scenarios are discussed. We also discuss the detectors and their operational principles, which results in output of data used for analysis by the LIGO pipelines. Chapter 2 introduces the existing techniques used for data analysis by the LIGO pipelines. The main pipelines for parameter estimation and testing general relativity are introduced. The main principles of Bayesian inference, which is used extensively by both these pipelines are presented. A description of existing methods to test theories of gravity is given. These methods have been established and used on the gravitational signals seen so far. Prevailing methods to verify Lorentz invariance are discussed to form a basis for testing Lorentz invariance with gravitational waves, which forms a central topic of this thesis. Chapter 3 presents the method we have developed to include verification of Lorentz invariance using gravitational waves in the standard LIGO data analysis pipeline. We have used Bayesian analysis and focussed on propagation e↵ect of these waves. Our analysis is based on the modification of the dispersion relation of gravitational waves without invoking any specific Lorentz violating theory. This method, introduced by Mirshekari et al., has been generalised to be include spins and used with full waveform models describing all stages of a binary coalescence. We have presented the first constraints on Lorentz violation from the gravitational wave observations made so far, published by the LIGO and Virgo collaborations this year. A comparison with the constraints prevailing on Lorentz violation from sectors other than gravity is also being made. Chapter 4 extends the method developed in the previous chapter to constrain the dispersion of gravitational waves using advanced detectors. We focus on an advanced configuration of the current second generation detectors, a third generation detector, and a space-based gravitational wave observatory. Of these, we find the best constraints with the third-generation or space-based detector, depending on the order at which the dispersion relation is modified. For the analysis of this chapter however, we restrict ourselves to using a Fisher matrix approach. We make some comparisons of our bounds from those existing in the literature using the same modified dispersion approach. Chapter 5 discusses a method to constrain the residual eccentricity of a binary source when entering a detector’s band. We recast results from parameterised tests in terms of eccentricity using analytical expressions from a frequency domain waveform model developed in a PN-consistent fashion. Explicit expressions connecting the parameterised coefficients at each phase order and eccentricity are included. We have discussed simulations where the signal has a non-negligible residual eccentricity and we try to constrain this parameter from parameterised recovery made at different phase orders. We discuss future plans to make more extensive simulations which might lead to better understanding of eccentric systems. Chapter 6 discusses an alternative method to extract parameters from a binary’s coalescence. We use particle swarm optimisation for this, which is a fast technique to locate the global maxima in multidimensional parameter space. We compare estimates obtained using this algorithm and those obtained from the standard Bayesian pipeline.

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