Scale invariance in particle physics and cosmology

The synergy of the Standard Model of particle physics and General Relativity led to a consistent framework that has been confirmed by numerous experiments and observations. In spite of their undeniable success, these theories cannot be considered as complete theories of Nature. On the one hand, they fail to explain basic observational facts such as the existence of neutrino masses, the presence of a sizable dark matter component or the matter-antimatter asymmetry of the Universe. On the other hand, there is no satisfactory account of tiny dimensionless ratios, such as the Fermi scale over the Planck scale (hierarchy problem), or the dark energy density or cosmological constant in units of the Planck mass.

The discovery of a relatively light Higgs boson at the LHC together with the absence of new physics beyond the Standard Model rejuvenated scale symmetry as an appealing scenario where to address the hierarchy problem. This symmetry consists of a common multiplicative scaling of all fields according to their dimension. No dimensional parameters are allowed to appear in the action. In particular, dilatation symmetry ensures the absence of a Higgs mass term.

In order to describe the appearance of physical scales, a viable scale-invariant theory should exhibit dilatation symmetry breaking in one way or another. This symmetry breaking could be explicit as a consequence of dimensional transmutation, as happens for instance in QCD. In this case, the dilatation symmetry is anomalous and appears only in the vicinity of non-trivial fixed points. In addition, spontaneous scale symmetry breaking driven, for instance, by the vacuum expectation value of a scalar field, could provide particle masses even in the absence of explicit mass terms. In this type of scenarios, scale invariance can be preserved at the quantum level by means of a scale-invariant regularization prescription or as a consequence of a fixed point of running couplings.

The inclusion of gravity in the aforementioned scale-invariant framework might have far-reaching consequences. On the one hand, the breaking of the continuous dilatation symmetry translates into the appearance of a pseudo-Goldstone boson or dilaton which, due to its small mass, could potentially contribute to the early and late time acceleration of the Universe or to the number of relativistic degrees of freedom at big bang nucleosynthesis and recombination. On the other hand, the small value of the Higgs mass at the Planck scale and the associated emergence of scale invariance could be a natural consequence of asymptotic safety, as already suggested by several functional renormalization group studies.