Editing Cosmic inflation (section)

===Space expands===
In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out [[Schwarzschild metric|Schwarzschild black hole]]—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially).

In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following [[metric tensor|metric]]:<ref>{{cite journal |last1=Melia |first1=Fulvio |year=2008 |title=The Cosmic Horizon |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=382 |issue=4 |pages=1917–1921 |doi=10.1111/j.1365-2966.2007.12499.x |doi-access=free |bibcode=2007MNRAS.382.1917M |arxiv=0711.4181 |s2cid=17372406 }}</ref><ref>{{cite journal |last1=Melia |first1=Fulvio |date=2009 |title=The Cosmological Spacetime |journal=[[International Journal of Modern Physics D]] |volume=18 |issue=12 |pages=1889–1901 |doi=10.1142/s0218271809015746 |display-authors=etal |bibcode=2009IJMPD..18.1889M |arxiv=0907.5394 |s2cid=6565101 }}</ref>

:<math>
ds^2=- (1- \Lambda r^2) \, c^2dt^2 + {1\over 1-\Lambda r^2} \, dr^2 + r^2 \, d\Omega^2.
</math>

This exponentially expanding spacetime is called a [[de Sitter space]], and to sustain it there must be a [[cosmological constant]], a [[dark energy|vacuum energy]] density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure ''p'' equal in magnitude to its energy density ''ρ''; the [[Equation of state (cosmology)|equation of state]] is {{nowrap begin}}''p=−ρ''{{nowrap end}}.

Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.