IANACosmologist, but in for a penny, in for a pound. If one accepts weirdness along the lines of extra spatial dimensions and mathematical singularities made physical, why not throw in a few extra dimensions for time or why not have imaginary time (in Hawking's sense)?

> One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. [1]

[1] https://en.wikipedia.org/wiki/Imaginary_time