Cosmological constant: Difference between revisions

Latest revision as of 14:37, 18 May 2010

Definition

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

$R_{i j} = λ g_{i j}$

where $R$ 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.

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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 ~~subspcae~~ of the tangent space.		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.