- #1
TrickyDicky
- 3,507
- 27
What are the symmetries determined by FRW spacetime? I guess they include Lorentz symmetry, rotationally and translationally symmetries, but not time symmetry. Is this right?
Thanks
Thanks
TrickyDicky said:What are the symmetries determined by FRW spacetime? I guess they include Lorentz symmetry, rotationally and translationally symmetries, but not time symmetry. Is this right?
Thanks
bcrowell said:Lorentz transformations are defined locally, not globally.
I don't think conformal flatness connects in any way to Lorentz transformations.
A little addition: this translation vector generally has a different proper length in each spatial slice. What's constant is its comoving length.3 translations (homogeneity)
The FRW (Friedmann-Robertson-Walker) metric is a mathematical description of the geometry of the universe in the context of general relativity. It describes the shape, size, and evolution of the universe over time.
The symmetries of the FRW metric include homogeneity, isotropy, and spatial flatness. Homogeneity means that the universe looks the same at any point in space, while isotropy means that it looks the same in all directions. Spatial flatness refers to the overall curvature of the universe.
Exploring the symmetries of the FRW metric can help us better understand the structure and evolution of the universe. It allows us to make predictions about the behavior of the universe and test the validity of various cosmological theories.
We can measure the symmetries of the FRW metric through observations of the cosmic microwave background radiation, which is a remnant of the early universe. These observations can also be used to determine the values of the various parameters in the FRW metric, such as the Hubble constant and the density of matter and energy in the universe.
The symmetries of the FRW metric have significant implications for our understanding of the universe. They suggest a highly homogeneous and isotropic universe on large scales, with a slight spatial curvature. They also support the idea of cosmic inflation, a period of rapid expansion in the early universe, which helps to explain various cosmological observations and phenomena.