How to fill colors between GridLines, or to color between different regions on the x-axis, like this graph. Also to add the descriptions inside the plot, and to make the AxesLabels beside and below the plot as ln H and ln (a/a0), respectively. 
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3 Here is an example using several Plot options. Not sure if this will be enough--maybe you need dynamic computation of some options, but hopefully this will get you started:
Plot[ {Sin[x], Cos[x]}, {x, 0, 10}, AxesOrigin -> {0, -1}, Frame -> True, FrameTicks -> All, Prolog -> {LightBrown, Rectangle[{-1, -2}, {3, 2}], LightGreen, Rectangle[{8, -2}, {11, 2}]}, FrameLabel -> {Log[a/Subscript[a, 0]], Log[H]}, PlotLegends -> Placed["Expressions", {.6, .15}]] 
- 3$\begingroup$ I usually use a device similar to the one here for background rectangles, whenever I can't be bothered to reckon out vertical ranges:
Plot[{Sin[x], Cos[x]}, {x, 0, 10}, AxesOrigin -> {0, -1}, Frame -> True, FrameTicks -> All, Prolog -> {{LightBrown, Rectangle[Scaled[{0, -1}, {0, 0}], Scaled[{0, 1}, {3, 0}]]}, {LightGreen, Rectangle[Scaled[{0, -1}, {8, 0}], Scaled[{0, 1}, {10, 0}]]}}, FrameLabel -> {Log["a"/Subscript["a", 0]], Log["H"]}, PlotLegends -> Placed["Expressions", {.6, .15}]]$\endgroup$J. M.'s missing motivation– J. M.'s missing motivation2022-06-08 17:30:51 +00:00Commented Jun 8, 2022 at 17:30 - 1$\begingroup$ Nice improvement! $\endgroup$lericr– lericr2022-06-08 17:32:57 +00:00Commented Jun 8, 2022 at 17:32
- $\begingroup$ Many thanks for the answers. $\endgroup$Dr. phy– Dr. phy2022-06-08 17:55:38 +00:00Commented Jun 8, 2022 at 17:55