A
de Sitter universe is a solution to
EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
's field equations of
General RelativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
which is named after
Willem de SitterWillem de Sitter was a Dutch mathematician, physicist and astronomer.Born in Sneek, De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa . Then, in 1908, de Sitter was appointed to the...
. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the
cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
, thought to correspond to
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be...
.
A de Sitter universe has no ordinary matter content but with a positive
cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
which sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate:
- ,
where the constants of proportionality depend on conventions.
A
de Sitter universe is a solution to
EinsteinAlbert Einstein was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of...
's field equations of
General RelativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
which is named after
Willem de SitterWillem de Sitter was a Dutch mathematician, physicist and astronomer.Born in Sneek, De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa . Then, in 1908, de Sitter was appointed to the...
. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the
cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
, thought to correspond to
dark energyIn physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be...
.
Mathematical Expression
A de Sitter universe has no ordinary matter content but with a positive
cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
which sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate:
- ,
where the constants of proportionality depend on conventions. The cosmological constant is and is the
Planck massIn physics, the Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined so that...
.
It is common to describe a patch of this solution as an expanding universe of the
FLRWThe Friedmann–Lemaître–Robertson–Walker metric is an exact solution of Einstein's field equations of general relativity; it describes a simply connected, homogeneous, isotropic expanding or contracting universe...
form where the scale factor is given by:
- ,
where the constant
H is the Hubble expansion rate and
t is time. As in all FLRW spaces, , the
scale factorThe scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...
, describes the
expansion of physical spatial distancesThe metric expansion of space is the averaged increase of metric distance between distant objects in the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...
.
Our universe is becoming like de Sitter universe
Because our Universe has entered the
Dark Energy Dominated EraThe Dark-Energy-Dominated Era refers to one of the three phases of the known universe, the other two being the Matter-Dominated Era and the Radiation-Dominated Era. The Dark-Energy-Dominated Era began after the Matter-Dominated Era, i.e. when the Universe was about 5 billion years old...
a few billion years ago, our universe is probably approaching a de Sitter universe in the infinite future. If the current acceleration of our universe is due to a cosmological constant then as the universe continues to expand all of the matter and radiation will be diluted. Eventually there will be almost nothing left but the cosmological constant, and our universe will have become a de Sitter universe.
Relative Expansion becomes faster than light
The exponential expansion of the scale factor means that the physical distance between any two non-accelerating observers will eventually be growing faster than the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
. At this point those two observers will no longer be able to make contact. Therefore any observer in a de Sitter universe would see
event horizonIn general relativity, an event horizon is a boundary in spacetime, most often an area surrounding a black hole, beyond which events cannot affect an outside observer...
s beyond which that observer can never see nor learn any information. If our universe is approaching a de Sitter universe then eventually we will not be able to observe any
galaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The name is from the Greek root galaxias [γαλαξίας], meaning "milky," a reference...
other than our own
Milky WayThe Milky Way, or simply the Galaxy, is the galaxy in which the Solar System is located. It is a barred spiral galaxy that is part of the Local Group of galaxies...
and a few others in the gravitationally bound
Local GroupThe Local Group is the group of galaxies that includes our galaxy, the Milky Way. The group comprises about 30 galaxies , with its gravitational center located somewhere between the Milky Way and the Andromeda Galaxy...
.
Modelling cosmic inflation
Another application of de Sitter space is in the early universe during
cosmic inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
. Many inflationary models are approximately de Sitter space and can be modeled by giving the Hubble parameter a mild time dependence. For simplicity, some calculations involving inflation in the early universe can be performed in de Sitter space rather than a more realistic inflationary universe. By using the de Sitter universe instead, where the expansion is truly exponential, there are many simplifications.
See also
- Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential expansion of the universe at the end of the grand unification epoch, 10
−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density...
- De Sitter space
In mathematics and physics, n-dimensional de Sitter space, denoted , is the Lorentzian analog of an n-sphere...
for more mathematical properties
- Deceleration parameter
The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of the universe. It is defined by:where is the scale factor of the universe and the dots indicate derivatives by proper time...