Formalism
Definition
Spacetime configurations
Properties
Spacetimes
black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Quantum theory
The Friedmann–Lemaître–Robertson–Walker models (often FRW-models) are class of models in cosmology. These are solutions to Einstein's equations describing a spatially homogeneous and isotropic expanding or contracting spacetime. Hence these are solutions used as models in cosmology. Indeed, an FRW-model is part of the standard model of cosmology. (In contrast to inhomogeneous cosmology.)
The plain FRW model parameterizes a homogenous and isotropic spacetime after diffeomorphism gauge fixing with a single parameter , the scale factor of the universe depending on coordinate time (fixed by some gauge condition).
The equations of motion of the FRW model are then
where
is called the Hubble parameter?;
and
of a “perfect fluid” of matter and radiation filling the universe.
Moreover, the ratio
is part of the experimental/phenomenological input into the model, which describes which kind of matter/radiation is assumed to fill spacetime
w | source of energy-density filling spacetime |
---|---|
1/3 | radiation or relativistic matter |
0 | dust matter |
1 | stiff fluid |
-1 | cosmological constant |
The first equation may be rewritten as
where the density parameter consists of the contribution
Named after Alexander Friedmann?, Georges Lemaître, Howard Robertson?, Arthur Walker.
Introduction and survey:
Matthias Blau, chapter 33 and 34 of Lecture notes on general relativity (web)
Jorge L. Cervantes-Cota, George Smoot, Cosmology today – A brief review (2011)(arXiv:1107.1789)
Konstantinos Xenos, An Introduction to FRW Cosmology and dark energy models (arXiv:2101.06135)
(emphasis on dark energy and inflation)
See also:
Discussion in Regge calculus:
Last revised on June 7, 2024 at 09:11:30. See the history of this page for a list of all contributions to it.