why did my record player slow down, speed up, then go back to normal?

Too little info, so all would be a guess. On start up, while playing, how often, type of drive....

First, is it idler drive, belt drive or direct drive? If idler, perhaps the idler wheel needs resurfacing, if belt the belt could be slipping. You can put the belt in a bag with talcum powder and shake it up and reuse the belt. If it still slips, get a new belt from the manufacturer.  If it’s direct drive, the speed controller circuitry could be defective.

Brief power outage or surge, bad capacitor, belt slippage, bad bearing, severe stylus drag, finger on the platter, platter rubbing on plinth, Schoenberg, bad karma for having been a troll.

@lewm 

Schoenberg

:D

If this is an older turntable with variable speed, one explanation might be that the speed controls or the speed selector switch are developing corrosion. If this is so, you can expect future events and more often.

Another explanation is a brief power outage.