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The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. [1] It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it.
Thus, an accelerating universe took a longer time to expand from 2/3 to 1 times its present size, compared to a non-accelerating universe with constant ˙ and the same present-day value of the Hubble constant. This results in a larger light-travel time, larger distance and fainter supernovae, which corresponds to the actual observations.
The expansion of the universe is parameterized by a dimensionless scale factor = (with time counted from the birth of the universe), defined relative to the present time, so = =; the usual convention in cosmology is that subscript 0 denotes present-day values, so denotes the age of the universe.
English: Expansion of the universe, comoving coordinate grid Horizontal axis: Comoving distance in billion light years. Vertical axes: time since Big Bang in billions of years Shown are the Particle Horizon RP (green), Event Horizon RE (magenta), Hubble Radius RH (blue). Past and future light cones RL (orange) are animated.
It relates the proper distance (which can change over time, unlike the comoving distance which is constant and set to today's distance) between a pair of objects, e.g. two galaxy clusters, moving with the Hubble flow in an expanding or contracting FLRW universe at any arbitrary time to their distance at some reference time . The formula for ...
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated, the theorem ...
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In physical cosmology, the Big Rip is a hypothetical cosmological model concerning the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, and even spacetime itself, is progressively torn apart by the expansion of the universe at a certain time in the future, until distances between particles will infinitely increase.