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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.
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 ...
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 ...
where is the Hubble constant, is the proper distance, is the object's recessional velocity, and is the object's peculiar velocity. The recessional velocity of a galaxy can be calculated from the redshift observed in its emitted spectrum. One application of Hubble's law is to estimate distances to galaxies based on measurements of their ...
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.
The speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour).
Because the speed of light is finite, the light reaching us from this pair of objects must have left them long ago when they were nearer to one another and spanned a larger angle on the sky. The turnover point can therefore tell us about the rate of expansion of the universe (or the relationship between the expansion rate and the speed of light ...