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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 numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.) The Hubble distance would be the distance between the Earth and the galaxies which are currently receding from us at the speed of light, as can be seen by substituting D = cH −1 into the equation for Hubble's law, v = H 0 D.
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 ...
This spacetime diagram shows how the light cones for two light particles spaced some distance apart at the time of last scattering (ls) do not intersect (i.e. they are causally disconnected). The horizontal axis is comoving distance, the vertical axis is conformal time, and the units have the speed of light as 1. For reference.
Much like the concept of a terrestrial horizon, it represents the boundary between the observable and the unobservable regions of the universe, [1] so its distance at the present epoch defines the size of the observable universe. [2] Due to the expansion of the universe, it is not simply the age of the universe times the speed of light ...
This distance is the time that it took light to reach the observer from the object multiplied by the speed of light. For instance, the radius of the observable universe in this distance measure becomes the age of the universe multiplied by the speed of light (1 light year/year), which turns out to be approximately 13.8 billion light years.