The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is a solution to Einstein's field equations of general relativity that describes a homogeneous and isotropic universe. The FLRW metric is the foundation for the standard model of cosmology, often referred to as the Big Bang model. It provides the mathematical framework for understanding the expanding cosmos and includes key parameters such as the scale factor, which measures how distances in the universe expand or contract over time. This model assumes that on large scales, the universe looks the same in all directions (isotropic) and at any given location (homogeneous), which aligns well with observations of the cosmic microwave background radiation.
The FLRW metric is named after the scientists Alexander Friedmann, Georges Lemaître, Howard Percy Robertson, and Arthur Geoffrey Walker, who independently derived various forms of this cosmological model in the 1920s and 1930s. Friedmann was the first to derive the equations in 1922, demonstrating that the universe could be expanding, a notion that was revolutionary at the time. Lemaître later independently reached similar conclusions and proposed the idea of an initial "primeval atom" from which the universe expanded. Robertson and Walker further generalized these solutions, incorporating different geometries which could describe the universe's overall shape as either open, closed, or flat.
The FLRW model uses three possible types of spatial curvature: positive, negative, and zero, corresponding to closed, open, and flat universes, respectively. These curvatures are integral in understanding the overall geometry of space-time and have implications for the fate of the universe. A closed universe eventually recollapses, an open universe expands forever, and a flat universe delicately balances between the two. Observational data, particularly from the cosmic microwave background, suggest that our universe is very close to flat, with a total density near the critical density that separates these scenarios.
In modern cosmology, the FLRW metric underpins many aspects of our understanding of the universe's dynamics and structure. It is central to the study of cosmological phenomena such as the age of the universe, the cosmic microwave background, dark_energy, and dark_matter. Additionally, it provides a crucial framework for the inflationary model, which proposes a period of rapid exponential expansion in the early moments following the Big Bang. This framework is essential for explaining the observed uniformity and flatness of the universe and for predicting the distribution of galaxies and cosmic structures observed today. The continuing refinement and challenge to the FLRW model represent the dynamic and evolving nature of cosmological research.