Cosmology of Einstein-de Sitter Universe

The graphs show the expansion of a flat, matter-dominated universe as described by the Friedmann equation. In a flat universe, the cosmological parameters, matter density and vacuum density , are related by . Therefore it is sufficient to vary only . The "shift" slider allows you vary the expansion rate of the initial curve toward the actual value .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The Friedmann equation in its simplest form (flat universe, cosmological constant ) is . It describes the Einstein–de Sitter universe, in which the expansion depends sensitively on the density . The so-called critical density is given by . Cosmologists prefer the dimensionless parameter . Using , the expansion rate is and the relation implies that the amount of matter in the universe remains constant. Friedmann's equation can be transformed into , with the solution , since here. In the present epoch, , so . The Hubble time would give the age of the universe if were constant, so the graph must be shifted until the line through the point and the origin is tangent to the graph.

Einstein–de Sitter space was the favorite model for an expanding universe until the 1980s. After the inflation theory was proposed, vacuum energy or dark energy had to be considered. This can be represented by a cosmological constant , which Einstein inserted into his theory of general relativity to achieve a static universe but later rejected. With the vacuum density , the Friedmann equation becomes .
The solution believed to be most accurate today takes and . For , becomes negative, which would imply a contracting universe.
[1] B. A. Jordaan. "Cosmology and the Engineer." (Jan 9, 2015). www.einsteins-theory-of-relativity-4engineers.com/cosmology.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+