Not a Bang but a Whimper

Throughout the DARKMOD workshop which was held in Orsay and Saclay last month, we had discussions about the rumoured detection of gravitational waves from the merging of neutron stars and an accompanying electromagnetic detection. The discovery has now been well publicised with important and drastic consequences for some dark energy models. Essentially as soon as any scalar-tensor theory induces some type of mixing between the kinetic terms of scalars and gravitons the speed of gravitational waves is modified. This is particularly the case in models of the Horndeski type and beyond as soon as they induce the late time acceleration of the expansion of the Universe via a significant time dependence for the scalar field. The constraints on these theories from binary pulsars and from the Cerenkov effect which would be emitted by cosmic rays, i.e. gravitons emitted by heavy and relativistic particles, were already very tight. Enough to cast doubts on the scenarios. Now the recent measurement of an electromagnetic counterpart to the collision between the neutron stars implies that the speed of gravitons in the late time Universe cannot deviate from the speed of light by more than one part in one million billions... Hence the models are essentially, bar any weird fine tuning, excluded. This removes all the fourth and fifth order Horndeski, e.g, Galileons, from the list of potential candidates for self-induced dark energy. A flurry, well 3-4 papers, jumped on the band wagon and published a compendium of the constraints from the LIGO/VIRGO measurements. Common practice in science... most acknowledged the DARKMOD discussions (in particular Emilio Bellini, Paolo Creminelli, Iggy Sawicki and Filippo Vernizzi). In fact the space of viable theories has been even more reduced by the work of Alexander Barreira and friends who show that third order Horndeski models (apart from some KGB theories as presented in the DARKMOD sessions by Iggy Sawicki and Alex Vikman) give a wrong Integrated Sachs Wolfe (ISW) effect in the Cosmic Microwave Background (CMB). This effect takes into account the entire history of gravitation since light emerged from the primordial fog and appears as large scale fluctuations in the temperature of the sky measured by the CMB. So pretty much out is the cubic Galileon. This is not even the end of the massacre :) as a paper published earlier this year by Papallo and Reall claims that the only Horndeski theory for which the Cauchy problem is well posed excludes all third order Horndeski theories. What are we left with then? As explained by the arch-raconteurs Alex Vikman and Iggy Sawicki during DARKMOD, essentially scalar tensors a la Brans-Dicke, i.e. the ones which are protected by the chameleon or Damour-Polyakov mechanisms, or K-mouflage, with its own screening of scalar fluctuations in dense environments, stand . Now as said to me by Jeremy Sakstein, this just means that none of our models of dark energy, when coupled to matter, can generate the late time acceleration without some kind of vacuum energy. Even if we call the vacuum energy the value of a scalar potential or something like this, there must be an extra vacuum energy density out there as it is well-known that self-acceleration cannot appear in chameleons or -Kmouflage.

Maybe we are going to have to face, unless Euclid or other large scale surveys detect something in the next few years, what my ever so optimistic friend Jerome Martin has been telling me for years: a cosmological constant ! (which by the way and Jerome agrees we do not even now how to calculate in Quantum Field Theory, not because of any cut-off dependence, this is non-sensical in Lorentz invariant theories, or lord knows what but more pragmatically because after renormalisation at low energy there is no understanding of the scale-dependence of the vacuum energy... not like the centre of mass energy of particle physics...). Or maybe what we are all doing is simply to enlarge the scope of gravitational theories, irrespective of cosmology? Next month we have a workshop in Leiden about "Dark Energy in the Laboratory" where a lot of clever people will discuss how weird modifications of gravity could be tested on earth.

There has been some really interesting developments on the massive gravity front too. There has been a claim that massive gravity models are ruled out because of the usual arguments about positivity in Quantum Field Theory (QFT), essentially the optical theorem and stating that cross sections are positive (see the recent paper by my colleague Brando Bellazzini and colleagues). This poses serious issues in models with many derivatives, e.g. K-mouflage, Galileons and massive gravity. The conventional point of view is to say that these theories are sick. As recalled by Claudia de Rham, Andrew Tolley, and Scott Melville, this appears to be more complex. First all these theories are effective field theories which are expected to break down at some short distance scale. The main issue is whether this happens well within the Vainshtein radius, if correct then in this case the model is interesting as gravity is retrieved before the theory becomes kaput or more precisely before higher order corrections must play a role and modify its behaviour at high energy, or not. It turns out that cosmological massive gravity theories have a predictivity range which may not extend to short distances like the ones of table-top experiments. To go beyond one must complete the models... a challenge! There could be another way out, in the sense that the positivity bounds assume the whole arsenal of QFT, in particular the Froissard bound to close contours and the whole S-matrix trickery. It could be that massive gravity etc could be described by much "softer" theories where locality breaks down (hence no Froissard bound...). The theory could classicalise and be described by "lumps" or maybe by some higher dimensions?? Anyway not dead yet ...