One of the big questions about carbon taxes are what to do with the revenue. The two main suggestions are to a) use it to pay for mitigation projects or b) refund it to taxpayers in equal lump-sum payments (which is called "fee and dividend").
There's also a third approach, which says that the proceeds from a carbon tax should be used to reduce capital gains and income taxes. The idea here is that reducing those taxes will lead to more long-term economic growth, which effectively reduces the cost per ton of CO2 that gets mitigated. This approach is called "double dividend".
There are a few problems with this. One is that the benefits of that future economic growth won't be shared equally by everyone who pays the carbon tax. If I have to pay more for gas, it doesn't help my bottom line to know that some future billionaire will pay lower capital gains taxes. Equal lump-sum payments turn normally regressive carbon taxes into progressive tax schemes, since the lump-sum payments represent a higher percentage of income for lower-income people than for higher-income people. Double dividend makes the carbon tax even more regressive, by disproportionately benefiting high-income earners and people who draw a significant portion of their income from capital gains.
Another issue is that the economic growth from double dividend would primarily benefit future generations, and would end up being more expensive for current generations. The reasons for this are complicated, but the short version is that double dividend only benefits people during certain periods of their lives (mostly while they're young), whereas equal lump-sum payments apply to all age cohorts. Slashing the capital gains tax would result in a moderate lifetime income boost to very young people (who have a whole lifetime ahead of them to take advantage of the reduced tax), but a negative overall impact on anyone over the age of about 40. Slashing labor tax rates has a negative welfare impact on everyone, regardless of age, though older people end up doing worse than younger people. This is especially important because current generations are the ones who will have to do most of the work of fighting against climate change, and it's even more important because the older generations that would be harmed by double dividend wouldn't even see any benefit to climate change mitigation during their lifetimes.
The Federal Reserve Board of Governors in Washington DC.
https://www.federalreserve.gov/econres/notes/feds-notes/green-dividend-d...