Every child knows: there is nothing more dangerous than ghosts! Since children never lie, we also have to be extremely careful with theories that predict ghosts. While they are often assumed to be haunting spectres made of bed sheets that float over the floor, ghosts in theories of modified gravity should better be seen as some scalar fields that carry negative kinetic energy. If an apple would interact with such a field, then it could gain an arbitrary amount of energy from this ghostly field. In this case, the apple could jump up from the ground into the treetop! Let’s make it even worse: Imagine an empty box, nothing but vacuum. If there is a ghost then it can decay to arbitrary negative energies. But energy is still conserved, the positive amount of energy must go somewhere. And indeed, this energy will be used to create particles. Dramatically, this will happen instantaneously!
What will you see if you empty a box, close it and open it again? Exactly, it will still be empty and will not be filled with water or even 100 Euro bills. Moreover, nobody has seen any apple jumping up from the ground onto a branch of a tree.
Ghosts seem to be scary, too scary to accept them in any theory of gravity. But in a recent project, we really wanted to explore the limits and find out whether there is any way to live with them, without contradicting any observation. As a toy model, we have invented a new theory in which the graviton, the particle that mediates the gravitational force, is massive and comes along with a ghost. Since no theory of gravity can be valid on all energy scales, we assumed that for tiny scales physics does not necessarily behave identical for two different observers. Such a behaviour is indeed predicted by more fundamental theories like quantum gravity. In doing this, we killed two birds with one stone: We have shown that the ghost in our theory is tame and will not lead to disastrous predictions like an instantaneous decay of the vacuum or balls rolling up a hill spontaneously. Furthermore, we present the first consistent model of a massive graviton that is cosmologically viable and does not need an additional graviton, that is assumed to exist in extensions like bimetric gravity or even 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.
Euclid is a telescope satellite that will be launched by the European Space Agency in 2020. Its scope is to create the largest ever three-dimensional map of galaxies, both in position and in distance. Beside the position, Euclid will also deliver images of billions of galaxies, allowing a study of the minuscule deflections that light suffers when zipping through the gravitational fields that permeate the space.
What can we do with the huge dataset that Euclid will offer to the scientific community? This is the question we tried to answer in the paper Cosmology and Fundamental Physics with the Euclid Satellite, that we recently submitted to the archives and to Living Reviews in Relativity, superseding a previous version.
So, again, what can we do with the Euclid dataset? The short answer is, almost everything. The long answer is contained in our 300-pages-long, 70-authors paper. But just to give a glimpse into it, we can test whether gravity is Einsteinian also “out there” and not just in the solar system, we can measure whether galaxies are distributed differently from light, we can weigh the mass of neutrinos better than on Earth, we can probe the distribution of dark matter, we can measure the expansion rate of the Universe, we can understand how the initial fluctuations have been generated during inflation, we can detect deviations from homogeneity and isotropy, if any, and answer dozen other questions that have been circulating within the astrophysical community in the last decades. All of this with an unprecedented precision.
So, if you wish to prepare yourself for Euclid, read this paper. It’s going to be a long travel, but worth it.