in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe.
is the scale factor of the universe and the dots indicate derivatives by proper time.
(recent measurements suggest it is), and in this case the deceleration parameter will be negative.
[1] The minus sign and name "deceleration parameter" are historical; at the time of definition
was expected to be negative, so a minus sign was inserted in the definition to make
Since the evidence for the accelerating universe in the 1998–2003 era, it is now believed that
was positive in the past before dark energy became dominant).
varies with cosmic time, except in a few special cosmological models; the present-day value is denoted
The Friedmann acceleration equation can be written as
extends over the different components, matter, radiation and dark energy,
is the equivalent mass density of each component,
is 0 for non-relativistic matter (baryons and dark matter), 1/3 for radiation, and −1 for a cosmological constant; for more general dark energy it may differ from −1, in which case it is denoted
Defining the critical density as
where the density parameters are at the relevant cosmic epoch.
where the density parameters are present-day values; with ΩΛ + Ωm ≈ 1, and ΩΛ = 0.7 and then Ωm = 0.3, this evaluates to
for the parameters estimated from the Planck spacecraft data.
; but its value can be inferred by fitting cosmological models to the CMB data, then calculating
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
(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
The experimental effort to discriminate these cases with supernovae actually revealed negative
, evidence for cosmic acceleration, which has subsequently grown stronger.