I think the cause and the effect is reversed. There is more money for investment now than ever before (due to an aging population, and increased inequality) which leads to both a low/zero interest rate, and lots of money for PE.
If it was an artificially low interest rate we'd see wage inflation, as opposed to just asset inflation.
Interest rates are artificial. IMHO they are currently way too low. I dont even think the absolute rate is what affects the economy, its rate of change in interest rates that causes change. Declining rates stimulate the economy while rising ones act as a brake. The absolute level of the rates determine where money flows and inversely affects the price of big things like housing and cars. Low rates lead to inequality and hardship. These are just thoughts and observations, I would love to build a good mathematical model.
Nominal interest rates are artificial. Real interest rates (nominal rates - inflation) are not. If central banks set nominal interest rates too low you get inflation which negates the purchasing power of the borrowed money. That's what the grandparent poster was alluding to.
(The mathematical model - and the proof - for this is taught in most introductory macroeconomics courses. So is monetarism, which is the "declining rates = stimulus" that you mention.)
It's been a persistent question why the super-low nominal interest rates that central banks have set for the last decade haven't resulted in consumer inflation, and there's no consensus among experts for it. My personal theory is that it comes from the entry of China and other large developing nations into the world economy, which a.) has dramatically lowered the price of labor-intensive consumer manufacturing, offsetting much of the inflation caused by the large money supply and b.) changed the mix of savers in the world economy; Chinese people are much more in the habit of saving large fractions of their income than Americans are, which leads to a glut of savings, which lowers the real interest rate.
I think you're right that low interest rates boost wealth inequality due to rising asset prices, but they also reduce income equality because of the tight labor market.
And by artificially low I meant below the natural interest rate or NAIRU.
It's just a natural product of capitalism[1]. When you can buy a chunk of a business and own that chunk of its profits, you can use those profits to buy a larger chunk of the business, repeat ad nauseum, until you have so much money that your needs for more profit aren't satisfied by any one business, but you have enough money to perform multi-business maneuvers. Higher interest rates might make some of these maneuvers less possible in the short term, but that would just delay the problem until the wealthiest capital-owners accumulate enough money that they can put forth more collateral to get better loans.
[1] By capitalism I mean private ownership specifically, not the usual HN definition of something something markets something something competition.