[analog31]

A rapid change in CO2 concentration could be a clue that something such as life is rearranging the molecules on a planet. In fact, I think the aliens have been monitoring us with a spectrometer for a few million years, and have guessed that we're here.

[TeMPOraL]

Indeed, and looking at exoplanets through a spectrometer is a possible way for us to discover life in our stellar neighborhood, should it exist. But as I mentioned in my parallel reply, oxygen is better than CO2 for initial screening, because its very presence on a randomly observed planet indicates something wonky is going on - there shouldn't be any, unless it's being actively replenished by some process, as otherwise it would've oxidized other matter both on the surface and in the atmosphere, and be long gone by the time we pointed our telescopes at that world.