E2 Cosmological General Relativity

Topic

At the heart of this model lie Einstein's field equations—incorporating the cosmological constant—which serve as the foundation for all modern cosmology.

The standard cosmological metric derived from these equations describes a homogeneous and isotropic universe possessing its own intrinsic spatial curvature.

The Friedmann equations are, in turn, derived as components of those same Einstein equations applied to a perfect cosmic fluid: the first is an energy equation linking the universe's expansion rate to its total density and curvature, while the continuity equation expresses the local conservation of that energy.

The standard model assumes this spatial curvature is exactly zero—meaning the universe is flat—an assumption confirmed by anisotropies in the cosmic microwave background with a precision of just four-tenths of a percentage point; this is not merely a convenient assumption, but a prediction verified with great accuracy. Thus, from the Einstein field equations that open this document to the verified zero curvature that concludes it—encompassing the standard cosmological metric and the Friedmann equations—cosmological general relativity demonstrates how a single set of equations, originally formulated to describe gravity in general, ultimately predicts the exact geometric shape of the entire universe with remarkable precision.

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