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However, Friedmann abandoned the idea in his first paper "On the curvature of space". Starting with Einstein's 10 equations of relativity, Friedmann applies the symmetry of an isotropic universe and a simple model for mass-energy density to derive a relationship between that density and the curvature of spacetime.
The Friedmann–Lemaître–Robertson–Walker metric (FLRW; / ˈ f r iː d m ə n l ə ˈ m ɛ t r ə ... / ) is a metric that describes a homogeneous , isotropic , expanding (or otherwise, contracting) universe that is path-connected , but not necessarily simply connected .
Removing the cosmological constant term from the Friedmann equations on the grounds that it was both unsatisfactory and unnecessary, Einstein arrived at a model of a universe that expands and then contracts, a model that was later denoted the Friedmann–Einstein model of the universe. [3] [4] In the model, Einstein derived simple expressions ...
According to the Friedmann–Lemaître–Robertson–Walker metric which is used to model the expanding universe, if at present time we receive light from a distant object with a redshift of z, then the scale factor at the time the object originally emitted that light is () = +. [7] [8]
Friedmann's model gave rise to three different types of models for the evolution of the universe. First, the universe would expand for a given amount of time, and if the expansion rate is less than the density of the universe (leading to gravitational attraction), it would ultimately lead to the collapse of the universe at a later stage.
The spacetime of the universe is, unlike the diagrams, four-dimensional. The flatness problem (also known as the oldness problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special ...
Λ is positive and has a magnitude greater than gravity. Universe has initial high-density state ("primeval atom"). Followed by a two-stage expansion. Λ is used to destabilize the universe. (Lemaître is considered the father of the Big Bang model.) Oscillating universe (Friedmann-Einstein) Favored by Friedmann 1920s Expanding and contracting ...
He was the earliest to employ Alexander Friedmann's and Georges Lemaître's non-static solutions of Einstein's gravitational equations describing a universe of uniform matter density and constant spatial curvature. Gamow's crucial advance would provide a physical reification of Lemaître's idea of a unique primordial quantum.