Luca Amendola

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Aller guten Dinge sind drei


The two different ways in which the three metrics and matter can couple in trigravity.

I don’t know whether this is true (nor why it should), but the curious German saying giving the title of this post was also the right title for one of our most recent papers. Fact is, there is one case in which two is not enough: bimetric gravity. This theory of gravity assumes there are two metrics (that is, two gravitational fields) in our Universe. One is the ordinary gravity that makes apples fall and planets go round their Sun; the other is there only to give gravity a tiny mass. Why should we assign a mass to gravity particles, also known as gravitons or gravitational waves? In fact, there is no reason, but since there is no reason also to assume they are massless, it is very interesting to explore what happens if there is a non-zero mass. Amazingly, this apparently innocuous problem has remained unsolved for seventy years, until recently some clever theorists found a way to invent a theory with a massive graviton. A bit like superstrings require extra-dimensions to work, so massive gravity requires an extra metric to work.

Sadly, however, it doesn’t really work! That is, even after adding a metric, things do not march as hoped for. Either there is no nice solution at all (e.g., a cosmology in which the Universe does not expand), or the solutions exist but are unstable, or if they are stable they are identical to ordinary spacetimes and therefore the new physics remains virtually undetectable.

That’s where the German saying proved useful. If two is not enough, try with three. So we added a third metric and let the wheels roll. We found a large number of viable cosmologies that might provide an alternative to the venerable  standard Einsteinian gravity. However, this is just the beginning. In fact, we don’t know yet if our solutions are stable at all. If not, since there is no saying extolling the virtues of four,  I would begin to suspect that, after all, one is better than anything.