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Yes, in principle, under a gold standard, the central bank buys more gold, which increases money supply, and potentially lowers interest rates.

This is very different than fiat currency. With fiat currency, the central bank can buy bonds, but it can even just print money and give it away. ( that's called a helicopter drop, which is one way to actually do it..)

Even though in a gold standard, the central bank can increase money supply, this is different than buying bonds. This is because since money is backed by gold, it can't loose value relative to gold. In this case, it's really hard for the central bank to lower the value of money if it wants to, for example to stop a deflation.