Volume 87, Number 5, September 2009
Article Number 59001
Number of page(s) 2
Section Geophysics, Astronomy and Astrophysics
Published online 24 September 2009
EPL, 87 (2009) 59001
DOI: 10.1209/0295-5075/87/59001

Global definition and physical interpretation of the cosmological constant

G. Rosen

Department of Physics, Drexel University - Philadelphia, PA 19104, USA

received on 10 June 2009; accepted in final form by R. A. Treumann on 28 August 2009; published September 2009
published online 24 September 2009

Defined as a global physical entity, the cosmological constant $\Lambda $ appears here as a stationary functional of the metric, the matter (dark as well as visible) and the radiation fields. Subject to compact-support variations of the fields, $\delta \Lambda =0$ gives the metric, matter and radiation field equations. With this rigorous physical formulation, the empirical relation $\Lambda \cong 2.7\kappa \rho _{0}$, where $\rho _{0}$ is the average energy-density of matter and radiation, follows from the spacetime average of $\kappa (L-g^{\mu \nu} \partial L/\partial g^{\mu \nu })$ through the observable four-volume of the Universe on the homogeneity scale $({\sim }100\,{\rm Mpc}),$ where L is the Lagrangian of the matter and radiation fields. Hence, the notion of negative-pressure dark energy is obviated in favor of an energy-density relationship for the cosmological constant that derives from the physical principle $\delta \Lambda =0$. Moreover, this formulation can be employed practically to rule out certain common-suspect free fields as the dominant component of dark matter. In particular, it is readily shown that a massive spin-zero scalar free field or a massive spin-one vector free field are precluded as the dominant component of dark matter.

98.80.Jk - Mathematical and relativistic aspects of cosmology.
98.90.+s - Other topics on stellar systems; interstellar medium; galactic and extragalactic objects and systems; the Universe.

© EPLA 2009