Contents

Definition

In an action functional on a space of pseudo-Riemannian manifolds – such as the Einstein-Hilbert action functional for gravity – a cosmological constant is a term proportional to the volume

where $\lambda \in ℝ$ is the cosmological constant .

For instance pure Einstein-Hilbert gravity with cosmological constant (and not other fields) is given by the functional

Generically it happens that one considers action functionals where $\lambda$ is in fact not a constant, but a function of other fields $\varphi$ on $X$.

In this context those solutions to the Euler-Lagrange equations are of interest in which $\lambda (\varphi )$ happens to be exactly or approximately constant. Many such models of not-really-constant-but-effectively-constant terms proportional to the volume are being proposed and considered in attempts to explain observed or speculated dynamics of the cosmos.

See in particular at FRW model for the role of the cosmologicsl constant in homogeneous and isotropic models as in the standard model of cosmology.

Related concepts

• FRW model

• cosmology

• energy

  • matter, radiation?, cosmological constant

References

On the Cosmological constant problem

A good review is in

• Stefanus Nobbenhuis, The cosmological constant problem – an inspiration for new physics PhD thesis (2006) (web pdf)