Firstly, thank you phys.org for including a link to the arXiv preprint. :-)

Secondly, this comment grew a lot while I was composing it, and it turns into two comments: a crash-speed overview of some aspects of linearized gravity and a few paragraphs describing what's in this paper, forming a quick personal reaction from a pseudonymous nobody.

Thirdly, massive gravity theory is not really new, and the 2010 date in the phys.org writeup refers to a solution for massive gravity in 4-dimensional spacetime by de Rham, Gabadadze and Tolley ( https://arxiv.org/abs/1011.1232 ). Previously, stable solutions were only known in lower dimensioned spacetimes. However, there have been fits and starts of work on this broad family of gravity theories dating to Pauli & Fierz, who proposed a massive spin-two field on a flat spacetime in the 1960s (Blasi & Maggiore give some details at https://arxiv.org/abs/1706.08140 ).

In order to talk about this (dense, technical!) paper, I think one needs to know a little about about perturbatively quantized gravity, which I'll describe over a few paragraphs. You can skip ahead a bit by just accepting that gravitons exchanged by everything (including each other) and that in standard General Relativity gravitons are massless.

When you take a perturbation theory approach to the metric of General Relativity, you fix a background spacetime (which is almost always flat, i.e. described with the Minkowski metric), which gets the label \eta (the solvable), with deviations from \eta held in h (the perturbation). The metric becomes g = \eta + h. Some configurations of moving mass-energy can produce waves in h that propagate according to the (classical) massless wave equation on flat spacetime, analogously to (classical) electromagnetic waves on flat spacetime.

One can proceed to quantize h. Well, really first one expands g = \eta + h + h^2 + h^3 + ... where h^2 etc are quadratic, cubic, and higher-order terms in the perturbation. Next one omits as many of the higher-order terms as one can get away with. In linearized gravity, that means h^2 and up are ignored.

Essentially we turn classical waves in h into large numbers of particles we call gravitons, much as one turns classical electromagnetic waves into large numbers of photons. I omitted indices and a couple of other details (most notably gauge fixing) nevertheless g, \eta and h are all symmetric rank-two tensors. The result of the quantization of (symmetric rank-2 tensor) h is therefore a massless spin-2 gauge boson, which compares with the quantization of electromagnetic waves (as antisymmetric rank-2 tensors [4]) resulting in a massless spin-1 gauge boson.

This is perturbative quantum gravity, a real working quantum theory of gravity, but not a candidate for a more fundamental theory than General Relativity because higher order terms in h are important in a universe with compact massive objects, and we don't know how to include such higher-order terms into this type of quantization.

There is a key pattern between the spin-1 and spin-2 particles: each mediates an interaction between particles that carry a + or - charge.

spin like-charges opposite-charges
---- ------------ ----------------
1 repel attract
2 attract repel

The electromagnetic interaction is an example of one mediated a spin-1 particle, and matter may have an electromagnetic charge + or -. With a suitable choice of gauge, matter may also have a gravitational charge, + or -.

In our universe, the electromagnetic interaction is much stronger than the gravitational interaction, but not everything has an electromagnetic charge. Most importantly, photons themselves do not have an electromagnetic charge. In perturbatively quantized gravity though, everything has a gravitational charge, including gravitons.

If we take perturbatively quantized gravity seriously, in our patch of the universe there is effectively nothing with the opposite gravitational charge of stuff here on earth, probably for reasons similar to why there is approximately no antimatter around us: segregation in the early universe. Essentially why we see no anti-gravity is that even our positrons and antiquarks have the same gravitational charge as everything else around us, so they interact with only one of the possible graviton charges.

That gravitons of the same charge attract one another leads to the higher order terms in h: their self-interaction is the source of non-linearity.

Finally, perturbatively quantized gravity allows us to define an energy scale for the gravitational interaction: it is "low energy" when the quadratic and higher-order terms in h simply do not matter; it is "high energy" or "strong gravity" when they do. The non-linearities higher-order terms in expanded h can be represented by one or more loops of gravitons in Feynman diagrams.

From this we have learned that "strong gravity" appears when the dilating effects of curvature are apparent even at Planck lengths or Planck time, or equivalently "high energy" appears around a tiny object with at least Planck energy. In practice this only appears very close to whatever quantum state there is in the place of classical gravitational singularities. Crucially this is well inside the event horizons of black holes, or in the very early universe. Consequently, perturbatively quantized gravity, and General Relativity, are both reliable "low energy" effective field theories practically everywhere we presently have the technology to study.

Next, on to bigravity.