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Here, is the gravitational constant, is the energy density within the universe, is the pressure, is the speed of light, and is the cosmological constant. A positive energy density leads to deceleration of the expansion, a ¨ < 0 {\displaystyle {\ddot {a}}<0} , and a positive pressure further decelerates expansion.
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 Friedmann equations showed the universe might be expanding, and presented the expansion speed if that were the case. [5] Before Hubble, astronomer Carl Wilhelm Wirtz had, in 1922 [ 6 ] and 1924, [ 7 ] deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede ...
Even light itself does not have a "velocity" of c in this sense; the total velocity of any object can be expressed as the sum = + where is the recession velocity due to the expansion of the universe (the velocity given by Hubble's law) and is the "peculiar velocity" measured by local observers (with = ˙ () and = ˙ (), the dots indicating a ...
It represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe. Due to the expansion of the universe, it is not simply the age of the universe times the speed of light, as in the Hubble horizon, but rather the speed of light ...
Also, since it originates from ordinary general relativity, it, like general relativity, allows for distant galaxies to recede from each other at speeds greater than the speed of light; local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light. [7]
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...
The accelerated expansion of the Universe was indeed observed. [1] According to observations, the value of equation of state of cosmological constant is near -1. Hypothetical phantom energy would have an equation of state w < − 1 {\displaystyle w<-1} , and would cause a Big Rip .