4.1 A cosmological constant

The cosmological constant arises as an adjustment to Einstein’s field equations of general relativity, and therefore the Friedmann equations, to describe the evolution of the Universe. has a gravitational effect in the opposite direction to that of matter and radiation, and therefore could in principle enable a static Universe; however, in the favoured cosmological model it must dominate over matter and radiation to enable accelerated expansion.

The equation of state for a cosmological fluid is given as follows:

where is the pressure of the fluid, is its density, is the speed of light, and is known as the equation of state parameter. The equation of state parameter is therefore the ratio between the pressure of a fluid and its energy density. Ordinary matter has , and radiation has . The peculiar property of dark energy models is that , so that the fluid has a negative pressure. This is what enables it to act in the opposite direction to the gravitational effect of ordinary matter.

In the case of a cosmological constant, . Therefore the pressure and the energy density have the same magnitude but opposite signs, and – as the name suggests – these quantities remain constant with time despite the expansion of the Universe. In this model it is therefore the decrease in the energy density of other components (e.g. or ) with time that causes to dominate the evolution of the Universe at late times.