quantity

equation of state parameter

A number, denoted w, describing the pressure-to-density ratio of dark energy; w=-1 indicates a cosmological constant.
35 related articles · 6 formulas

Description

The equation of state parameter, denoted w, is a dimensionless number that relates the pressure of a substance to its energy density. In cosmology, it is most famously used to characterize dark energy, the mysterious force driving the accelerated expansion of the universe. A value of w = -1 corresponds to a cosmological constant, where the energy density remains constant as space expands, leading to exponential growth. Other values, such as w > -1 (quintessence) or w < -1 (phantom energy), imply that the dark energy density changes over time, with profound implications for the universe's fate.

History

The concept of the equation of state parameter was introduced in the context of cosmology in the 1980s, particularly through work on inflation and dark energy models. The term 'quintessence' was coined by Robert Caldwell, Rahul Dave, and Paul Steinhardt in 1998, shortly after the discovery of cosmic acceleration.

How it works

The parameter is defined by the equation p = wρc², where p is pressure, ρ is energy density, and c is the speed of light. For ordinary matter, w = 0 (pressureless dust); for radiation, w = 1/3. Dark energy has a negative pressure, so w is negative. The value of w is inferred from observations of supernovae, cosmic microwave background, and large-scale structure, which probe how the expansion rate changes over cosmic time. If w is not exactly -1, it suggests dark energy is a dynamic field rather than a constant.

In practice

It is the primary target of next-generation dark energy surveys like DESI and Euclid, which aim to measure w with high precision to determine whether dark energy is truly constant or evolving.

Fun fact

If w is less than -1, the universe would end in a 'Big Rip,' where all matter is torn apart in a finite time, a scenario that some observations have not yet ruled out.

Concept graph →

Formulas

$$w = \frac{P}{\rho}$$
Relates pressure to energy density in cosmology.
What is in the formula
wvariableequation of state parameter — equation of state parameter
Pvariablepressure — pressure pascal
ρvariableenergy density — energy density joule per cubic metre
$$t_{\text{rip}} - t_0 = \frac{1}{|1+w|\sqrt{6\pi G \rho_0}}$$
Time until Big Rip singularity inversely proportional to |1+w| and sqrt(density).
What is in the formula
t_{\text{rip}} - t_0variableTime remaining until Big Rip — time interval second
wvariableEquation of state parameter — equation of state parameter
\rho_0variableCurrent dark energy density — energy density joule per cubic metre
GconstantConstant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\piconstantRatio of circle circumference to diameter — pi = 3.14159
$$F = -\frac{GMm}{r^2} - \frac{4\pi}{3} G m r \rho (1+3w)$$
Gravitational force modified by dark energy pressure, vanishes at w=-1/3.
What is in the formula
FvariableGravitational force magnitude — force newton
MvariableMass of the central object — mass kilogram
mvariableMass of the test particle — mass kilogram
rvariableDistance between masses — distance metre
ρvariableEnergy density of the cosmic fluid — energy density joule per cubic metre
wvariableEquation-of-state parameter of the fluid — equation of state parameter
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$w(a) = w_0 + w_a (1 - a)$$
Dark energy equation of state evolves with scale factor.
What is in the formula
wvariableDark energy equation of state parameter — equation of state parameter
avariableScale factor of the universe — scale factor
w_0variableEquation of state parameter at present epoch — equation of state parameter
w_avariableCoefficient of the evolution term — equation of state parameter
$$w < -\frac{1}{3\Omega_{DE}}$$
Condition for dark energy to cause cosmic acceleration.
What is in the formula
wvariableEquation of state parameter of dark energy — equation of state parameter
Ω_DEvariableDensity parameter of dark energy — density parameter
$$w_{\rm eff} = -1 - \frac{1}{3} \frac{d \ln \rho}{d \ln a}$$
Parameter describing the effective pressure-to-density ratio in cosmology.
What is in the formula
w_effvariableEffective equation of state parameter — equation of state parameter
rhovariableEnergy density of the cosmic fluid — energy density joule per cubic metre
avariableScale factor of the universe — scale factor
d/d ln aoperatorDerivative with respect to the logarithm of the scale factor — logarithmic derivative

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