Two basic kinds of astronomy observations, the first being discrepancies on the order of 9% in different kinds of measurements of Hubble's constant which measures the rate at which the expansion of the universe seems to be accelerating, and the other involving discrepancies in the apparent rate of expansion over time from a constant value based upon myriad observations of very old quasars.
Both of these results could be due to systemic errors in astronomy measurements which are hard to quantify, or could be solved by new physics such as quintessence or phantom energy theories in which the amount of dark energy is not constant (as it is if the cosmological constant is merely added to the equations of general relativity, the leading and most simple explanation for what is observed).
The problem with the new physics approaches discussed in the article, is that the kinds of new physics that would be necessary to reproduce what the observational evidence seems to show is very weird and ill motivated. Even the proponents of these new physics explanations justify them more as a proof of concept, showing that it is possible to come up with some sort of new physics that could explain the data, rather than strongly arguing that their crazy mechanism are actually what is causing the observational discrepancies that we see.
I don't rule out the possibility of new physics in this area that will help explain the data either, although at least some of the discrepancies are almost surely due to systemic errors in astronomy observations that aren't well quantified. But, if there is a new physics solution, it seems very unlikely that the ones proposed (such as a 100,000 year period in the early universe where extra dark energy appears for a while and then vanishes, or a theory in which energy is not conserved when things go fast enough) are actually the right ones.
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