general relativity - What is the equation for the scale factor of the universe, a(t), for the best fit of data to the $Lambda CDM$ Model of Cosmology?

Ideally I like a single formula or multiple formulas for different time ranges that would cover the time from the end of inflation through 100+ billion years after the big bang using the $\Lambda CDM$ Model. I know that from the end of inflation back to the time of the big bang would be much more speculative, but some wild estimate would be appreciated for that time range also!

The Friedmann–Lemaître–Robertson–Walker metric defines the scale factor, a(t), from the metric: $$-c^2d\tau^2 = -c^2dt^2+a(t)^2d\Sigma^2$$ where $d\Sigma^2$ ranges over the 3 dimensional space of the universe and does not depend on time. Usually the scale of the scale factor is set by defining $a(t_{now}) = a(13.78 B yr) \equiv 1$