This thread is meant to give a basic introduction to the equation that governs distance growth, how it changes over time.(adsbygoogle = window.adsbygoogle || []).push({});

If you've worked with Jorrie's calculator ("Lightcone") you may know that the present distance growth rate is about 1/144 of a percent per million years, and thelongtermrate that it is tending towards is 1/173 % per million years.

The calculator makes tables of universe history showing what the growth rate (and other descriptors) have been in the past and what they will be at various times in future. It's running the standard cosmic model and it's based on the Friedmann equation (derived from Einstein GR around 1923).

I'll denote the rate at time t by H(t) and the longterm rate, which is an important constant, by H_{∞}.

Some people like to use metric units consistently. If you're not a metric purist and are more comfortable with familiar quantities like percents and years, then skip the next two lines. On the other hand if you like metric units you can find out the two key rates by pasting the percentage versions into google like this:

(1/144) percent per million years in attohertz

(1/173) percent per million years in attohertz

In this thread I want to be able to use the google calculator easily, with its automatic unit conversions, so I don't want to go against its conventions. It measures a key quantity, energy density, inpascals:a pascal can just as well be read as an energy density of one joule per cubic meter, as it can be as one newton of force per square meter. Algebraically they are the same: N/m^{2}= Nm/m^{3}

Everything about the Friedmann equation, and the standard cosmic model that runs on it, is simpler if we assume large-scale spatial curvature is zero. Spatial curvature has been measured and the observed value is near zero (within less than one percent, with high confidence) so for the sake of a basic introduction we can assume spatial flatness. That doesn't meanspacetimecurvature is zero. the 4D geometry can still have curvature, e.g. related to the the expansion or contraction of distances over time.

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# Kindercosmos--basic Friedmann

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