Variation of Hubble constant in model universe

[tomwilliam2]

Homework Statement

For a problem I'm doing, I am considering a universe in which k=0, and I'm told that I can consider most of the expansion to have happened during a phase when only one of the density parameters was dominant (I know which one, as well), but I don't know the scale factor or the critical density.
The density is dominated for most of the expansion by one component only, so I know how the scale factor varies with time (to a good approximation). I've completed what is required of me in the question but I can only get the answer in terms of H_0.

Now, my question is: do you think it is appropriate to use the consensus value for H_0 in our universe? It worries me because our universe is not k=0 (but only approximately spatially flat) and also the approximation of radiation leading to most of the expansion is also an approximation. Or am I worrying about nothing as the answer isn't required to a great level of precision?
Thanks in advance

Homework Equations

The Attempt at a Solution

 

[clamtrox]

It's very appropriate to use the "direct" measurement value, for example http://arxiv.org/abs/1103.2976. This is based on distance laddering up to supernovae, and is fairly independent of any cosmological assumptions.

I wouldn't use the Planck value though, as that has much more modelling baggage hidden behind it.

 

[tomwilliam2]

Thanks, that might be the way to go. What I'm asked for in the question is a ratio of scale factors, between now and a given time in the past t_1 (for which I don't know the redshift). I can use the given value of t_1 but then I need to make an estimate of t_0, or I can get the answer in terms of H_0, as I mentioned. If I compare the answers using these two approaches, they are wildly different. I think perhaps using the value of t_0 in our universe is inappropriate, but if only I could work out how to get a numerical answer not involving H_0 or t_0...