At the time, the expansion of the universe was a decelerating expansion. The acceleration phase didn't start until later.
What this is saying is that according to their model, the density of dark energy seems to have increased at early times and then leveled out.
My guess is that there's something wrong with their model. My reasoning is as follows:
1) The dark energy density was much smaller before ##z=1.5## as a fraction of the total density compared to its value today. By my estimate, the dark energy density at ##z=1.5## would have been approximately 15% of the total energy density. At the start of the range, ##z=7.5##, the dark energy density would have been around 0.5% of the total.
2) Because the density of dark energy was much smaller as a percent of the total, a small misunderstanding of matter, which has by far the largest contribution to the expansion, would show up as a variation of dark energy instead.
There might be something interesting going on here, such as an interaction between matter and dark energy. But it might also just be a small systematic effect for early quasars. Or non-zero spatial curvature.
Whatever is going on here, though, it's probably related to the discrepancy in measurements of ##H_0## between the CMB and nearby observations.
