2019•Cambridge University Press eBooksRequires access

Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution

Horaƫiu Năstase

Abstract

The Friedmann-Lemaître-Robinson-Walker (FLRW) cosmological solution for the expanding (time dependent) Universe is found. We start with an ansatz for a homogenous and isotropic space in comoving coordinates, and define various coordinate systems and analyze the geometry. The Einstein equations reduce to the Friedmann equation for the “Hubble constant” and the acceleration equation for the scale factor, related through the conservation of the energy-momentum tensor. Given an equation of state for matter, we can solve the Friedmann equation.

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Key concepts: Friedmann–Lemaître–Robertson–Walker metric, Friedmann equations, Scale factor (cosmology), Physics, Mathematical physics, Equation of state, Ansatz, Classical mechanics