deceleration parameter

In cosmology, the deceleration parameter (often represented by q) is a quantification of the deceleration (slowing) of the expansion of the universe:

      a d²a/dt²
q ≝ - —————————
      (da/dt)²

• q - deceleration parameter.
• a - scale factor.
• t - time.
• da/dt - a's rate of change.
• d²a/dt² - da/dt's rate of change.

Of interest is the q value of 0.5 (called q_c), the value it would maintain if the universe remained flat, i.e., the exact minimum expansion that would not reverse into contraction. Determinations (specifically, comparing counts of Type Ia supernovae at various redshifts) show the universe's expansion rate is increasing, and the deceleration parameter is in the general range of -0.55 or -0.60, its negative value indicating an acceleration in the universe's expansion. Thus there must be a force counteracting the inward pull of the universe's gravity (which would tend to slow expansion), and the term dark energy was coined for whatever is providing it. A parameter for deceleration rather than acceleration was presumably adopted by cosmologists before such a determination was made and it was presumed that the universe's expansion was slowing.