I'll have to edit and add to this later today, have to go out in few minutes. The standard cosmic model depends strongly on two distance growth rates, the present and the longterm future ones. The easiest most intuitive handle on these growth rates are the two Hubble times = the two percentage growth rates flipped over. The present value of the Hubble time is about 13.9 billion years and this can be thought of as a linear doubling time. I.e. how long it would take any cosmological distance to grow an amount equal to its own length, if it continued at constant speed: its current instantaneous linear rate (without "compounding") A simpler way to think of it is that 1% of the Hubble time is how long it would take distances to grow by 1% at their present rate. So what I want to do in this thread is show in a couple of TOY MODEL FORMULAS how the two Hubbletimes play a role in the model and influence the expansion history distance growth curve. We can and I think will do a lot better than these toy (hand calculator) formulas. They lose accuracy when used back before about redshift 9 or 10 (the earliest galaxies). But nice thing about explicit formulas is that you see the two Hubbletimes, the main parameters, revealed in a transparent way. This can serve as a kind of introduction to the more complete and accurate online cosmology calculators. A nice feature here is the use of a new online calculator which (unlike the google calculator) automatically displays formulas in neat LaTex-like form. When you type in a formula all on the same line, with fractions, for instance written (1/a + 1)/b, the calculator keeps your one-line version in the window so you can edit it but also shows a more immediately readable version in the space right above the window. I'll give an example in the next post.