Curvature of the Universe

This page is designed to illustrate the relationship between the energy density and curvature of the universe.

  • Use the slider labeled Omega to vary the energy density of the universe, and then observe how it's curvature changes.
  • Use the overlay buttons to observe how the curvature affects different geometric properties.
  • Hover over the
    symbols to learn more about a specific topic.
  • When you're done, click here to learn how the universe evolves!

This frame depicts a two dimensional universe in three dimensional space. It models our own three-dimensional universe thought to exist inside a higher dimensional space.

Although the universe bends into the third dimension, it remains a 2D surface. People travelling through it wouldn't notice moving in the third dimension. Sorf of like how when you move along the surface of the Earth, you don't notice the Earth's curvature!

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The shape of the universe is determined by how much stuff (in the form of energy) is in it. We describe the amount of stuff by Omega (Omega), known as the density parameter. More stuff (energy) means a larger value for Omega, and less stuff means a smaller value. The exact relationship is given by something called the Friedmann equations.

Omega is defined as the ratio between the energy density (epsilon) of the universe and the critical energy density, epsilon_c, where epsilon_c is the exact amount of energy necessary to make the universe flat.

Thus, for Omega = 1 the universe is flat!

When Omega > 1, the universe is said to have positive curvature, or be closed. This is because in the absence of dark energy, this kind of universe will eventually collapse down on itself

When Omega < 1, the universe is said to have negative curvature, or be open. This kind of universe will expand forever even without dark energy.

Experiment with the evolution of the universe here

So what is the value of Omega in our universe?

According to the most recent (2015) results of the Planck Survey, Omega is within 0.005 of 1. So we live in a flat universe!

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