It has been well-established by now that the expansion of the Universe is and has been for some time accelerating. This stunning fact can not be straightforwardly accommodated within the standard cosmological model if both the general relativity as the theory of gravity and only standard, matter- or radiation-like, cosmological components are allowed for. One, or both, of these assumptions have to give up.

In the current standard cosmological model this acceleration of the expansion is accounted for by an effective component with positive energy density and negative pressure, which is commonly referred to as dark energy. The recent measurements, combining constraints from the supernovae, galaxy surveys, and cosmic microwave anisotropy determine the energy density of dark energy to be: Ω(DE) = 0.7 with a few percent precision. They also set an upper limit for the ratio of its pressure to its density to be: w = -1.03 +- 0.03 (Planck 2018).

What’s the nature of dark energy, whether it is a true extra component or merely an effective description of an action of modified gravity model or something else, remains a mystery. And not just any mystery … but truly one of the most profound mysteries of modern cosmology and indeed physics at this time given that any conceivable resolution seems to be calling for a significant rewrite of our understanding of fundamental physical laws.

As things stand all the observations so far tend to allow for a specific case of dark energy with absolute value of its (negative) pressure equal exactly to its energy density, i.e., w = -1. This, lo and behold, is mathematically equivalent to introducing an extra term in Einstein’s equations, called the cosmological constant and known in popular literature as Einstein’s ‘biggest blunder’, following Einstein’s very own admission. This is because the rationale behind introducing it and thus extending the original general relativity, was quickly shown to be ill-conceived and in fact unsuccessful as it did not achieve the intended goals anyway. Indeed, while the extra, cosmological constant term had been devised to allow for a static, non-expanding Universe, our own Universe was shown contemporaneously by Hubble to be happily expending.

While having it back on the agenda may then look as Einstein’s last laugh after all, such a solution is still discouraged from theoretical and (scientific) esthetics points of view … So, while we may be forced to accept it at some point, we stick with the blunder interpretation for time being …

Well, if not the cosmological constant then what ?!

In some sense, its profound fundamental consequences notwithstanding a modification of the laws of gravity may seem as the most likely resolution of the conundrum. What do we really know about the gravity on the scales as large as the observable Universe after all ?!

However, by all means the general relativity is one of the biggest success stories in physics. And for good reasons !

It has passed numerous observational tests over the centenary since it was introduced and describes qualitatively and quantitatively phenomena very diverse in their nature and context, including,

- the expansion of the Universe at least up to the onset of the acceleration;
- the growth of structures in the Universe, from filaments to clusters of galaxies, to galaxies, the normal and dwarf ones,
- the bending of light – the strong one, strong lensing, and the weak one, weak lensing;
- the binary systems including those composed of the very dense bodies, pulsars, regular neutron stars or black holes;
- the properties of those dense stellar size bodies themselves;
- the seismology of our Sun;
- the dynamics of our planetary systems,

and many others.

If this was not impressive enough the general relativity has also made some stunning, unexpected predictions, say, of black holes and gravitational waves for one, which have been all dully confirmed. It even predicted that the speed of the gravitational waves should be the same as the speed of light, what indeed has been recently confirmed, adding yet another spectacular success to the theory portfolio.

Nevertheless, at some time it has been shown that with a stretch of imagination some extensions of the general relativity are possible. Those can retain all the good, while potentially resolving the issue of dark energy … Sounds like a win-win situation !

Being possible is however one thing. Another thing is how easy this is. And this is not, as some of the models, which gained some prominence a few years ago and which are called DHOST (for degenerate high-order scalar-tensor theories), and their proponents, have recently learned. Those models got rejected in bulk on the hands of a high precision confirmation of the fact that the speed of the gravitation waves is consistent with that of the speed of light (well at low redshift strictly speaking …) up to quite impressive precision. Such a ‘massive model extinction’ is a good sign overall … (well, once the ‘mourning period’ is over for those involved). It just means that there is a lot of pertinent data to guide the search for the successful model … This is what makes life tough for the model builders …

So the scientists are essentially still clueless as far as the nature of dark energy is concerned.

But great data sets are already available, which will allow to probe this question observationally further than ever before. And more equally pertinent data is coming … From high redshift supernovae and quasar observations, and capitalizing on their strong lensing, to galaxy surveys pinning down characteristic features of galaxy correlations, so called Baryonic Acoustic Oscillations, to Sunyaev-Zel’dovich cluster surveys, to the weak lensing of the distant objects as well as of the cosmic microwave background anisotropies, the efforts are under way to characterize the properties of dark energy with precision and redshift range going far and beyond what’s known today …

And yes one should not forget about ‘the new kid in the town’, who already made herself heard … gravitational wave astronomy …