The private equity industry -- excluding VC, which represents a small fraction of total capital raised -- relies extensively on debt (LBOs, debt-financed infrastructure deals, debt-financed real estate deals, etc.), i.e., borrowing to juice returns. It's not a coincidence that the industry was born in the 1980's, when interest rates in the US began declining, after the Fed had increased them to combat high inflation in the 1970's. Ever since, for four decades now, interest rates have only declined and declined, in fits and starts, making life easier and easier for borrowers of all kinds:

https://fred.stlouisfed.org/graph/?g=RveY

Many private equity deals that arguably were economically viable when the 10-year treasury's annual yield was ~0.6%, less than a year ago, may not be viable now that the 10-year treasury's annual yield is ~3%, and are likely to suffer financial distress if interest rates rise further -- say, 10-year treasury yields of ~5%, ~6%, or more. If that sounds high, keep in mind that the last time the Fed had to deal with high inflation, in the 1970's, the 10-year treasury yield rose to a peak of ~16%!

Over the same past four decades, valuation multiples have only risen and risen, in fits and starts, making life easier and easier for those who make money by buying businesses, holding them for a while, and selling them down the road. For example, here's the ratio of US stock market capitalization to the size of the US economy (GDP):

https://fred.stlouisfed.org/series/DDDM01USA156NWDB

The rise in valuation multiples over the past four decades makes sense, given that the net present value of any business is inversely proportional to the discount rate used to value its future profits, and discount rates are equal to prevailing long-term treasury rates plus a premium. If interest rates continue to rise, valuation multiples are bound to decline too.

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EDITS: Changed language in response to comments below so it better reflects what I meant to write in the first place.