Einstein Field Equations - The Cosmological Constant

The Cosmological Constant

Einstein modified his original field equations to include a cosmological term proportional to the metric

The constant is the cosmological constant. Since is constant, the energy conservation law is unaffected.

The cosmological constant term was originally introduced by Einstein to allow for a static universe (i.e., one that is not expanding or contracting). This effort was unsuccessful for two reasons: the static universe described by this theory was unstable, and observations of distant galaxies by Hubble a decade later confirmed that our universe is, in fact, not static but expanding. So was abandoned, with Einstein calling it the "biggest blunder ever made". For many years the cosmological constant was almost universally considered to be 0.

Despite Einstein's misguided motivation for introducing the cosmological constant term, there is nothing inconsistent with the presence of such a term in the equations. Indeed, recent improved astronomical techniques have found that a positive value of is needed to explain the accelerating universe.

Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side, written as part of the stress–energy tensor:

The resulting vacuum energy is constant and given by

The existence of a cosmological constant is thus equivalent to the existence of a non-zero vacuum energy. The terms are now used interchangeably in general relativity.