# Difference between revisions of "Cosmological constant"

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where <math>R</math> denotes the [[Ricci curvature tensor]]. | where <math>R</math> denotes the [[Ricci curvature tensor]]. | ||

− | Equivalently the cosmological constant for an Einstein metric can be defined as the [[Ricci curvature]] associated with any one-dimensional | + | Equivalently the cosmological constant for an Einstein metric can be defined as the [[Ricci curvature]] associated with any one-dimensional subspace of the tangent space. |

## Latest revision as of 14:37, 18 May 2010

## Definition

Let be a manifold equipped with an Einstein metric. Then the cosmological constant of is defined as the constant of proportionality for which:

where denotes the Ricci curvature tensor.

Equivalently the cosmological constant for an Einstein metric can be defined as the Ricci curvature associated with any one-dimensional subspace of the tangent space.