Francesc Cunillera - Dark Energy: From EFTs to Supergravity

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There is an enduring debate as to whether the study of string theory, or indeed any theory of quantum gravity, represents science in the traditional sense of making conjectures, deriving predictions and carrying out experiments to test those predictions. The key obstacle is the scale at which quantum gravity effects are likely to manifest themselves, being far in excess of any foreseeable experiment. Nevertheless, such criticisms, at least in the context of string theory, are a little overstated.

String theory is built on two pillars of twentieth-century physicsquantum mechanics and relativity. Indeed, if we consider the two to two scattering of gravitons in General Relativity, the amplitude describing the process violates unitaritya key ingredient of quantum mechanicswhenever the incident energy exceeds the Planck scale. The only known completion of this amplitude that preserves unitarity, remains weakly coupled and preserves Lorentz invariance to arbitrarily high energies, is the Virasoro-Shapiro (VS) amplitude. This is precisely the amplitude describing the scattering of closed strings in string theory. Thus, the foundation of string theory relies heavily on those two fundamental pillars of quantum mechanics and relativity. If either pillar should fall in experiment, then so will string theory.

In the last decade and a half, the so-called swampland programme has sought to provide another key test of string theory and its underlying principles. What the swampland programme seeks to do is to consider the space of consistent low-energy effective theories and to split them into those that are in the landscape and those that are in the swamp. If a theory is in the swamp, this is because it cannot be derived as the low-energy limit of a consistent compactification of string theory. If it is in the landscape, then the converse is truewe should be able to derive it from string theory. As an example, consider a theory of particles charged under a gauged U(1), minimally coupled to General Relativity. In principle, this theory is a consistent quantum field theory at low energies regardless of the strength of the corresponding electromagnetic and gravitational forces. However, a study of the decay of extremal black holes suggests that only those theories for which gravity is the weakest force can emerge from a consistent theory of quantum gravity like string theory. If the gravitational force is stronger than the electromagnetic force, the theory is expected to be in the swamp. In this sense, we can test quantum gravity simply by comparing the relative strength of gravity compared with the other fundamental forces in nature.

There are many swampland conjectures including the weak gravity conjecture described above, the distance conjecture and the controversial de Sitter conjecture. The latter is the claim that stable de Sitter vacua are in the swamp. The evidence for this is circumstantial, loosely based on the difficulty in deriving consistent solutions from perturbative string compactifications. The underlying reason for this is in the need to break supersymmetry in de Sitter, which can place considerable restrictions on calculational control. However, if true, the de Sitter swampland conjecture has far-reaching implications for both the early and late universe. At early times, the conjecture is in tension with inflation. At late times, it is in tension with dark energythe observation that the universe is undergoing a period of quasi de Sitter accelerated expansion. To release the tension with late universe physics, it is often assumed that dark energy should not be associated with a de Sitter vacuum, but with a dynamically evolving field dubbed quintessence. This is usually taken to be a scalar in slow roll along a moderately flat (effective) potential.