They absolutely can, by quantitative easing (aka large-scale asset purchases) buying $4 trillion of bonds priced to keep yields in range. This market can remain irrational longer than anyone can remain solvent.

By price-fixing this market they stimulate liquidity. Institutions (such as pensions) that would normally buy safe bonds are forced to invest elsewhere at marginal yields (ie. corporate bonds and MBS). Other, more risky, investors chase growth stocks with marginal yields.

> you should get price inflation or deflation.

Indeed there has been, though currently visible only through asset prices such as bonds, stocks, securities and housing. Who can complain?

The danger comes when the tide goes out and yields go up [1]. All that extra liquidity washes from assets into yields, thereby driving inflation on produce.

[1] And up yields must, to determine how much have been swimming naked.