The Einstein–de Sitter universe is a model of the universe proposed by

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

and Willem de Sitter in 1932. On first learning of

Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects ...

's discovery of a linear relation between the redshift of the galaxies and their distance, Einstein set the

cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...

to zero in the

Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedman ...

, resulting in a model of the expanding universe known as the

Friedmann–Einstein universe The Friedmann–Einstein universe is a model of the universe published by Albert Einstein in 1931. The model is of historic significance as the first scientific publication in which Einstein embraced the possibility of a cosmos of time-varying radiu ...

. In 1932, Einstein and De Sitter proposed an even simpler cosmic model by assuming a vanishing

spatial curvature General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

as well as a vanishing cosmological constant. In modern parlance, the Einstein–de Sitter universe can be described as a

cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...

model for a flat matter-only

Friedmann–Lemaître–Robertson–Walker metric The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...

(FLRW) universe. Lars Bergström & Ariel Goobar: "''Cosmology and Particle Astrophysics''", 2nd ed.

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

(2004), p. 70+77. . In the model, Einstein and de Sitter derived a simple relation between the average density of matter in the universe and its expansion according to ''H''₀² = ''кρ''/3, where ''H''₀ is the

Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...

, ''ρ'' is the average density of matter and ''к'' is the

Einstein gravitational constant In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

. The size of the Einstein–de Sitter universe evolves with time as

a\propto t^

, making its current age 2/3 times the

Hubble time Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...

. The Einstein–de Sitter universe became a standard model of the universe for many years because of its simplicity and because of a lack of empirical evidence for either spatial curvature or a cosmological constant. It also represented an important theoretical case of a universe of critical matter density poised just at the limit of eventually contracting. However, Einstein's later reviews of cosmology make it clear that he saw the model as only one of several possibilities for the expanding universe. The Einstein–de Sitter universe was particularly popular in the 1980s, after the theory of

cosmic inflation In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...

predicted that the curvature of the universe should be very close to zero. This case with zero

implies the Einstein–de Sitter model, and the theory of

cold dark matter In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...

was developed, initially with a cosmic matter budget around 95% cold dark matter and 5% baryons. However, in the 1990s various observations including galaxy clustering and measurements of the

led to increasingly serious problems for this model. Following the discovery of the

accelerating universe Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered during ...

in 1998, and observations of the

cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...

and galaxy

redshift survey In astronomy, a redshift survey is a survey of a section of the sky to measure the redshift of astronomical objects: usually galaxies, but sometimes other objects such as galaxy clusters or quasars. Using Hubble's law, the redshift can be used ...

s in 2000–2003, it is now generally accepted that

dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...

makes up around 70 percent of the present energy density while

contributes around 25 percent, as in the modern

Lambda-CDM model The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) associated with d ...

. The Einstein–de Sitter model remains a good approximation to our universe in the past at redshifts between around 300 and 2, i.e. well after the radiation-dominated era but before dark energy became important.

Notes and references

{{DEFAULTSORT:Einstein-de Sitter universe General relativity Albert Einstein

See also

Notes and references