The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.
•Examine the Friedmann equation and its impact on our understanding of the evolution of the universe • Produce numerical and analytical solutions to the Friemann equation •The results will provide us with the geometry, current age, and ultimate fate of the universe
The Friedmann Equation Alexander Friedmann of Russia is credited with developing a dynamic equation for the expanding universe in the 1920s. This was a time when Einstein, Willem de Sitter of the Netherlands, and Georges Lemaitre of Belgium were also working on equations to model the universe.
Note that the limiting case here is when the universe collapses from infinity to bounce at exactly the condition for an Einstein universe, thereby following the red curve away from the de Sitter point. The third and fourth families of solutions mathematically form two branches of the same solution of the Friedmann equation.
Einstein’s equations which relate the scale factor a(t), energy density ρ and the pressure P for ﬂat, open and closed Universe (as denoted by curvature constant k = 0,1,−1). Today we are going to solve Friedmann equations for the matter-dominated and radiation-dominated Universe and obtain the form of the scale factor a(t).
HOMEWORK Problems; Sticking with our Newtonian expanding universe, we will now derive the Friedmann equation that relates how the scale factor changes in time to the mass/energy density.. We will proceed by using the Newtonian concept of energy conservation.
Friedmann Equation Calculator. A set of equations that describes the expansion of the universe is called as the friedmann equations. This is a calculator for a friedmann equation based on the curvature.
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Given an additional formula for the pressure, a numerical solution of the Friedmann equations is possible. You may specify freely k and the values of a and ρ at an initial time. Then a can be updated with the first Friedmann equation; and ρ with the continuity
Some cosmologists call the second of these two equations the Friedmann acceleration equation and reserve the term Friedmann equation for only the first equation. Density parameter . The density parameter, , is defined as the ratio of the actual (or observed) density to the critical density of the Friedmann universe. The relation between the ...