In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number
It is closely related to the thermodynamic equation of state and ideal gas law.
The perfect gas equation of state may be written as
is a characteristic thermal speed of the molecules.
The equation of state may be used in Friedmann–Lemaître–Robertson–Walker (FLRW) equations to describe the evolution of an isotropic universe filled with a perfect fluid.
If the fluid is the dominant form of matter in a flat universe, then
In general the Friedmann acceleration equation is
is the second proper time derivative of the scale factor.
If we define (what might be called "effective") energy density and pressure as
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is
, which means that its energy density decreases as
In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
The equation of state for ultra-relativistic 'radiation' (including neutrinos, and in the very early universe other particles that later became non-relativistic) is
which means that its energy density decreases as
In an expanding universe, the energy density of radiation decreases more quickly than the volume expansion, because its wavelength is red-shifted.
Cosmic inflation and the accelerated expansion of the universe can be characterized by the equation of state of dark energy.
In the simplest case, the equation of state of the cosmological constant is
In this case, the above expression for the scale factor is not valid and
More generally, the expansion of the universe is accelerating for any equation of state
[1] According to observations, the value of equation of state of cosmological constant is near -1.
Hypothetical phantom energy would have an equation of state
Using the existing data, it is still impossible to distinguish between phantom
In an expanding universe, fluids with larger equations of state disappear more quickly than those with smaller equations of state.
This is the origin of the flatness and monopole problems of the Big Bang: curvature has
, so if they were around at the time of the early Big Bang, they should still be visible today.
Measuring the equation of state of dark energy is one of the largest efforts of observational cosmology.
, it is hoped that the cosmological constant could be distinguished from quintessence which has
can be viewed as a sort of perfect fluid with equation of state
, and one with vanishing kinetic energy is equivalent to a cosmological constant:
barrier known as the Phantom Divide Line (PDL),[2] is achievable, which makes scalar fields useful models for many phenomena in cosmology.