What physical side-effects this might have are difficult to predict. It could induce a comet to crash into the Earth for example. Roger Penrose believes human consciousness is due to mysterious properties of gravitation (curvature in space-time and all that) thus an altered colective consciousness could trigger gravitational waves.
Or if it is due to an overlap of alternative universes in the helical structures of DNA we could all have visions of Eternity or float into space as the gravity of Earth fails.

Of course, we know the world will end sometime within the next 5 billion years, when the sun is expected to puff up into a massive red giant star and swallow the Earth whole.

Do we know that for sure? I mean of course the world will, so to say, end when the sun becomes a red giant but will it be by swallowing of the earth? Wont the loss of mass increase earth’s orbit? I remember reading somewhere that earth might just escape being engulfed by the sun due to its increased orbit.