Seeking a plot of the energy history of the Universe How can we plot the energy density $\rho$ as a function of the age $t$ of the universe (or temperature $T$) from the time of radiation domination to the time of cosmological constant domination with intermediate matter domination phase? I know that $$a\propto t^{1/2}, t^{2/3}, e^{\Lambda t}$$ in the radiation, matter, and CC dominated phases respectively. Therefore, $$\rho\propto t^{-2}, {\rm constant}$$ for radiation/matter domination and CC domination respectively. In short, I am looking for a continuous curve $\rho(t)$ vs $t$. Can we identify the crossover from radiation to matter domination in this curve?
 A: 
Solidification asked: "How can we plot the energy density ρ as a function of the age t of the universe (or temperature T) from the time of radiation domination to the time of cosmological constant domination with intermediate matter domination phase?"

For the Ω I recommend a log/linear plot where the time (on the x-axis) is logartihmic and the Ω (on the y-axis) are linear. Red is for radiation, blue for matter and green for dark energy:

We have radiation to matter parity at 50000 years after the big bang, radiation to dark energy parity at 600 million years, and matter to dark energy parity at 10¹⁰ years. ρ (in GeV/c²/m³):

The accelerated expansion however does not start when Ω or ρ for dark energy becomes the largest, but when ä=0, which is at around 7.7 billion years (this plot is linear on both axes):

If you click on the images you get different combinations of logarithmic and linear axes and plot ranges, where different features are highlighted. The equations are also linked in the description on the bottom of the first two links, where you can also find the initial values for the cosmological parameters.
