The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by:
The Friedmann acceleration equation can be written as
Defining the critical density as
The time derivative of the Hubble parameter can be written in terms of the deceleration parameter:
Except in the speculative case of phantom energy (which violates all the energy conditions), all postulated forms of mass-energy yield a deceleration parameter Thus, any non-phantom universe should have a decreasing Hubble parameter, except in the case of the distant future of a Lambda-CDM model, where will tend to −1 from above and the Hubble parameter will asymptote to a constant value of .
The above results imply that the universe would be decelerating for any cosmic fluid with equation of state greater than (any fluid satisfying the strong energy condition does so, as does any form of matter present in the Standard Model, but excluding inflation). However observations of distant type Ia supernovae indicate that is negative; the expansion of the universe is accelerating. This is an indication that the gravitational attraction of matter, on the cosmological scale, is more than counteracted by the negative pressure of dark energy, in the form of either quintessence or a positive cosmological constant.
Before the first indications of an accelerating universe, in 1998, it was thought that the universe was dominated by matter with negligible pressure, This implied that the deceleration parameter would be equal to , e.g. for a universe with or for a low-density zero-Lambda model. The experimental effort to discriminate these cases with supernovae actually revealed negative , evidence for cosmic acceleration, which has subsequently grown stronger.