Pulsar Timing Arrays And The Detection Of Gravitational-wave Background

Different inflationary models predict the existence of Relic Gravitational Waves (RGWs) which have a broad spectrum. The strength of RGWs, on one hand, depends on the exact inflationary models. When parameterized, different models predict a variety of tensor-scalar ratios and tensorial indices. On the other hand, the strength also depends on the evolution of the universe after inflationary epoch, such as the rate of expansion. Therefore, RGWs provide perfect probes for both inflation and the evolution of the universe.In the theory of hierarchical clustering, elliptical galaxies form through the coales-cences of small galaxies. Observations show that Super Massive Black Holes (SMBHs) exist in many galactic centers. During the process of galactic merging, the central SMBHs may become closer enough and emit gravitational waves in the nano-Hz band. The Gravitational-Wave Background (GWB) from the merging SMBHs presents useful method for the research of galactic mass distribution, galactic dynamics and the inter-action of SMBHs.RGWs and those gravitational waves from SMBHs form two different categories of GWBs, becoming the import targets of Pulsar Timing Arrays (PTAs). When pass-ing through the space between the Earth and the millisecond pulsars, GWBs affect the space-time of the background, leading to the irregularities in the timing of pulsars. Tim-ing towards a series of quiescent millisecond pulsars in a long duration, consisting of the PTAs, could reduce the timing noise and raise the detection sensitivity. Therefore, in the frequency band of nano-Hz, PTAs are convenient for the detection and research of GWBs.In Chapter 2 of this thesis, we firstly investigate the propagation effects that affect the strength of RGWs, including the accelerated expansion, cosmic phase transitions (e.g. e+e-, phase transitions of quantum chromodynamics), the free-streaming of rel-ativistic gases and the unusual equation of state before the nucleosynthesis during big bang. After that, in Chapter 3, combining with the recent observations from different PTAs, we set constraints on the tensor-scalar ratio and tensorial index and compare the results from other observations like cosmic microwave background, nucleosynthesis and laser interferometers. In Chapter 4, based on the relation of signal-noise ratio of detection and the observational parameters, we estimate the detection ability of future PTAs and the constraints on the early universe. Chapter 5 combines the observational data of galactic evolution and performs a kind of semi-analytic method to calculate the strength of GWB from SMBHs before discussing the challenges facing current theories. Finally, Chapter 6 summaries the results of the thesis.