Friedmann Equation with imaginary values Consider the Friedmann equation with no radiation:
$$
\frac{H(t)^2}{H_0^2} = \Omega_{m,0} a^{-3} + \Omega_{k,0} a^{-2} + \Omega_{\Lambda,0}
$$
We can have values for $a(t)$ and the density parameters such as the right hand side of the equation is negative. That would imply an imaginary Hubble constant. Is there any physical interpretation for that?
 A: One way to interpret Friedmann equation with an imaginary Hubble parameter is as arising from some  solution with Euclidean metric signature. One class of such solution, termed “Euclidean wormholes” consists of two large asymptotic regions connected by a “throat”. Many FLRW cosmologies analytically continued into an imaginary time become such Euclidean wormholes.

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*Zhuk, A. (1993). Perfect fluid wormholes. Physics Letters A, 176(3-4), 176-178, doi:10.1016/0375-9601(93)91030-9, free pdf.

Abstract:

It  is shown that most important closed Robertson–Walker–Friedmann universe models with a perfect fluid have ananalytic continuation into the Euclidean region with a wormhole-type topology.

A: There is a close analogy:
If you jump say 3 feet high, you can calculate your speed as a function of you position between 0 to 3 feet high.
Then you wonder what is your speed at 6 feet high during your jump. The good old high school Newtonian mechanics offers an answer: your speed was imaginary at 6 feet high according to the total energy conservation equation.
Now it is your turn to tell me what is the epistemologically transcendent metaphysical interpretation of that.
