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*a*increases according to a two-thirds power law. In such a universe, the expansion of the universe gradually slows down (but never stops).

In recent years it has been discovered (?) that the rate of expansion of the universe is not slowing down but it is either constant or even increasing slightly. In order to account for this cosmologists have reintroduced the cosmological constant in the guise of dark energy which almost exactly counteracts the retarding effect of gravity.

In other words, the scale parameter is proportional to time. ie [tex]a \propto t[/tex]. But [tex] a = a0 t[/tex] is not a solution to the Friedmann equations.

It follows that if the universe has expanded linearly since the Big Bang, the cosmological constant must have changed during that period. Alternatively, [tex]\Lambda[/tex] is constant but we just happen to live at the time when the total mass-energy density [tex]\Omega = 1[/tex]

I have never liked the introduction of [tex]\Lambda[/tex]. And I find the extraordinary coincidence that we happen to live at the exact time in the history of the universe when [tex]\Omega[/tex] = 1 too much to stomach.

What is going on?