Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Cosmological Principle

The Cosmological Principle assumes that the universe is homogeneous and isotropic on large scales, meaning it looks the same in all directions and locations.
📜

The statement of the theorem

The Cosmological Principle assumes that the universe is statistically homogeneous and isotropic on sufficiently large scales. Mathematically, this implies that the metric tensor gμνg_{\mu\nu} can be written in the Friedmann-Lemaître-Robertson-Walker (FLRW) form, which depends only on time tt and the scale factor a(t)a(t), but not on the spatial coordinates (x,y,z)(x, y, z): \n\nds2=−c2dt2+a2(t)[dr21−kr2+r2(dθ2+sin⁡2θdϕ2)]ds^2 = -c^2 dt^2 + a^2(t) \left[ \frac{dr^2}{1 - k r^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right]\n\nWhere kk is the spatial curvature parameter.