When Geometry Radiates Review: Gravitational Waves in Theory, Cosmology, and Observation

TL;DR

This review comprehensively covers the theory, cosmological implications, and observational methods of gravitational waves, connecting foundational physics with current and future detection strategies.

Contribution

It provides a unified pedagogical framework linking gravitational wave theory, cosmology, and observations, including recent developments and future directions.

Findings

Derived gravitational wave solutions in linearized general relativity.

Analyzed gravitational waves in expanding universes and inflation.

Surveyed observational strategies across multiple detection platforms.

Abstract

Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that bridges foundational theory with observational frontiers. We begin by developing the theory of gravitational radiation within linearized general relativity, deriving gravitational waves as solutions to the linearized Einstein equations and clarifying their physical interpretation, polarization states, and key properties. We then deepen the discussion through a geometric perspective, tracing the connection between gravitational radiation and the algebraic structure of the Weyl tensor and its role in defining energy and angular momentum in asymptotically flat spacetimes. Extending beyond flat backgrounds, we examine gravitational waves in an expanding universe, following their evolution across cosmological epochs and their generation during inflation. Within this setting, we discuss adiabatic modes and consistency relations that reveal universal properties of long-wavelength perturbations, and derive the inflationary spectrum of vacuum gravitational waves together with their contribution to the integrated Sachs-Wolfe effect. We also survey the main observational strategies for detecting gravitational waves across a broad frequency range, including cosmic microwave background polarization, pulsar timing arrays, ground- and space-based laser interferometers, and resonant cavity detectors. We then discuss the astrophysical and cosmological mechanisms responsible for generating gravitational radiation. We conclude by summarizing the current status of the field and outlining promising directions for future theoretical and observational developments.