De Sitter universe

A de Sitter universe is a

concordance models of physical cosmology

are converging on a consistent model where our universe was best described as a de Sitter universe at about a time

t=10^{-33}

seconds after the fiducial Big Bang singularity, and far into the future.

Mathematical expression

A de Sitter universe has no ordinary matter content but with a positive cosmological constant ( $\Lambda$ ) that sets the expansion rate, $H$ . A larger cosmological constant leads to a larger expansion rate:

H\propto {\sqrt {\Lambda }},

where the constants of proportionality depend on conventions.

It is common to describe a patch of this solution as an expanding universe of the

FLRW form where the scale factor is given by^[1]

a(t)=e^{Ht},

where the constant $H$ is the Hubble expansion rate and $t$ is time. As in all FLRW spaces, $a(t)$ , the

expansion of physical spatial distances

.

Unique to universes described by the FLRW metric, a de Sitter universe has a

Hubble Law that is not only consistent through all space, but also through all time (since the deceleration parameter

is

q=-1

), thus satisfying the

inflation and dark energy were developed. Before then, it was assumed that the Big Bang implied only an acceptance of the weaker cosmological principle, which holds that isotropy and homogeneity apply spatially but not temporally.^[2]

Relative expansion

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 light. At this point those two observers will no longer be able to make contact. Therefore, any observer in a de Sitter universe would have cosmological horizons 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 galaxies other than our own Milky Way (and any others in the gravitationally bound Local Group, assuming they were to somehow survive to that time without merging).^[3]

Role in the Benchmark Model

The

Benchmark Model

is a model consisting of a universe made of three components – radiation, ordinary matter, and dark energy – that fit current data about the history of the universe. These components make different contributions to the expansion of the universe as time elapses. Specifically, when the universe is radiation dominated, the expansion factor scales as

a\propto t^{\frac {1}{2}}

, and when the universe is matter dominated

a\propto t^{\frac {2}{3}}

. Since both of these grow slower than the exponential, in the future the scale factor will be dominated by the exponential factor

a\propto e^{H_{0}t}

representing the pure de Sitter universe. The point at which this starts to occur is known as the matter-lambda equivalence point and the modern-day universe is believed to be relatively close to this point.^[4]

References

McGraw-Hill
. p. 468.

ISBN 978-0-12-219141-1
.

ISBN 978-3-662-48077-9
.

ISBN 978-1-107-15483-4
.

Retrieved from "https://en.wikipedia.org/w/index.php?title=De_Sitter_universe&oldid=1214146932"

[1] McGraw-Hill
. p. 468.

[2] ISBN 978-0-12-219141-1
.

[3] ISBN 978-3-662-48077-9
.

[4] ISBN 978-1-107-15483-4
.

[1]

[2]

[3]

[4]

Mathematical expression

Relative expansion

Role in the Benchmark Model

See also

References