Metric with 5D signature: +---+

From a paper that a friend sent to me (on inflation theory which I am still in learner mode) a 5D signature +---+ was specified with the 5th dimension being a velocity dimension. I didn't know that you could have a metric that mixed space-time with a velocity dimension. Can someone explain basically what this means and possibly point to sources for more information.

• Could you provide a link to the paper for reference? – Kyle Kanos Oct 22 '14 at 16:25
• Referenced paper: arxiv.org/abs/astro-ph/0501526 – K7PEH Oct 22 '14 at 16:32
• Note: the paper's topic is on Hubble's parameter and expansion but the "inflation" aspect I mentioned above is that my friend sent the paper to me in response to some things we were discussing on inflationary big bang models. – K7PEH Oct 22 '14 at 16:33
• one can have a metric with multiple "time-like" signatures, implying multipel times. An intepretation i give to this, is these time-like coordinates represent durations (or eigen-times) of system processes, rather than event-times (as usualy implied). So velocity can also be used (think frequency). i'll try to find clear examples and references of this, although i'm not aware of similar approaches as the one i explained above. – Nikos M. Oct 22 '14 at 17:14
• If I think frequency (inverse time) given velocity, it seems I can just as easily think space (like distance) since velocity is $[L][T]^{-1}$. And, although multiple time-like signatures mathematically could be included, things I have read suggested that none represent space-time described by GR. Resources to study would be very helpful if you could find them. – K7PEH Oct 22 '14 at 17:23