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recognized the expansion of the universe by late 1920s. He can be excused for making this mistake because astronomical observation in earlier time indicated a homogeneous distribution of objects in the sky and the view did not seem to change over "long" time. It induced him to assume a constant density in Eq.(18a). Simple mathematics as well as from solution of the equation^{§} shows that such model describes an expanding universe. In order to avoid this "unwanted" predicament, he introduced a repulsive term (/3) = 4G/3c^{2} in Eq.(20c) to make d^{2}R/dt^{2} = 0. The additional term would make dR/dt = 0 as well if k = 4GR^{2}/c^{2} in Eq.(20a). Thus, R = R_{0} = constant. However, this universe is unstable. A small perturbation would induce collapse or expansion forever. With the discovery of cosmic acceleration, it is fashionable again to | |

## Figure 10l Einstein and His Cosmic Blunder |
re-introduce the cosmological constant back into the model universe. The crucial difference is that we now know the density is not a constant; it varies with time as the universe expands. The two terms on the right-hand side of Eq.(20f) equal to each other only momentarily about 8 billion years after the Big Bang. |

for k > 0, R = (R

for k < 0, R = (R

for k = 0, R = R

where H = (8G/3)

The formula for k = 0 also describe the cosmic expansion in the steady state universe. The Hubble Law can be readily derived as :

dR/dt = HR,

where H can be considered as the "Hubble constant" for the steady state universe.

The deceleration parameter is defined by:

q = - [R(d

which becomes q = -1 for the steady state universe, i.e., it just reiterates the accelerating characteristic of this model universe. The steady state theory states that not only are there no privileged locations in space, there are no privileged moments in time as well. Thus, the global properties of the universe, such as density and Hubble constant remain constant with time. The theory fell out of favor when observational evidence strongly suggested that the global properties do change with time as indicated by the discoveries of the Cosmic Microwave Background and the quasi-stellar objects.

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