Gravitational Waves from the Big Bang

Abstract

For millennia, humanity has relied exclusively on light$\unicode{x2014}$initially visible light and, later, broader and broader portions of the electromagnetic spectrum$\unicode{x2014}$to observe the universe. In the past decade, a remarkable chapter in extending astronomy beyond electromagnetic antennas has been concretized: the dawn of gravitational-wave astronomy has opened a new observational window into the cosmos. Among the many new astronomical sources we may now look for and study through their gravitational-wave signals, the Big Bang is surely among the most fascinating. Gravitational waves give us concrete hope of directly observing the primordial universe, whose light, emitted more than 13.7 billion years ago, is blocked from reaching our telescopes. This dissertation is aimed at the study of gravitational waves from cosmic inflation, the main scientific paradigm for the very early universe. Therefore, the text is divided into chapters on gravitational waves, inflationary cosmology, and inflationary gravitational waves. More specifically, our discussion will be steered by the endeavor to explain how the gravitational-wave signal sought by the NANOGrav observatory could have originated in the primordial universe.

Figures (11)

• Figure 2.1: The distance $D$ between vectors $\Vec{x}$ and $\Vec{x}'$ in three-dimensional Euclidean space is one of the most intuitive cases to compute. Pictorially, it corresponds to the diagonal of a parallelpiped and, hence, the result $D^2=(x-x')^2+(y-y')^2+(z-z')^2$ may be derived from two sequential applications of the Pythagorean theorem.
• Figure 2.2: A qualitative depiction of the effect caused by gravitational waves with plus and cross polarizations when they pass through a region containing a ring of massive particles.
• Figure 2.3: Cartoon illustration of the LIGO interferometer reproduced from Ref. ligo_interferometer. Vertical and horizontal rectangles in the figure represent different mirrors, while the tilted rectangle represents the beam splitter. Arrows on the red lines indicate the path taken by the laser light. As noted and represented in the figure, the LIGO interferometer has sophisticated features that make it more than a basic Michelson-Morley interferometer. In the 4-km Fabry-Pérot cavities, the laser beams are reflected back and forth around three hundred times along the arm of the interferometer before being allowed to return to where they will interfere with one another, increasing photons' effective traveled distance and lasers' effective power within each arm. The power recycling mirror further enhances the lasers' power within the Fabry-Pérot cavities by ensuring that almost all light exiting them is redirected back, with only a small fraction being directed to the photodetector that will record the interference pattern.
• Figure 2.4: An artist's interpretation of a pulsar reproduced from Ref. nrao_parts_pulsar. The white sphere in the center represents the neutron star, while the blue curves represent its magnetic field lines, and the yellow tubes represent its jets of electromagnetic radiation, whose rotation follows that of the star.
• Figure 3.5: Two-dimensional patterns in green, with drawings in red that help convey points about the observer's viewpoint. The pattern on the left is homogeneous when considering scales larger than the stripe width, as the one demarcated by the red square, for otherwise there is variation between regions within light and dark stripes. The vertical direction is preferential, so it is not isotropic. The pattern in the middle is isotropic around its center since, as highlighted by the radial lines in red, the alternation of green and white along any direction extending outward from the center is exactly equal. It is, however, inhomogeneous: imagine dragging a square like the red one in the left panel around this figure and easily convince yourself that the pattern bounded by it changes around the figure. The pattern on the right is both homogeneous and isotropic in light of what has already been discussed for the first two panels.