I work on different angles to understand the role of scale symmetry in the Early and Late Universe, trying to provide answers to the following questions:
- Which are the essential building blocks of a successful scale-invariant theory?
- If happening in Nature, is the realisation of this symmetry global or local?
- Is it explicitly or spontaneously broken?
- Can these two symmetry-breaking patterns coexist? Which is the role of gravity?
- Can we distinguish different realisations of scale symmetry with observations?
- Which are the generic predictions of the paradigm?
- Are inflation and dark energy just to sides of it?
SCALE INVARIANCE IN PARTICLE PHYSICS AND COSMOLOGY
The seminal discovery of a light Higgs field in the LHC has left us with a perfect Standard Model of particle physics potentially valid up to arbitrarily high energies. At the same time, and with the current experimental status, the vast difference between the Higgs mass and the gravitational energy scale leads to some of the most mysterious puzzles in particle physics: the extreme sensitivity of the electroweak scale to Planckian effects and the infamous cosmological constant problem, whose standard theoretical expectation is off by more than 120 orders of magnitude.
The absence of new physics beyond the Standard Model has rejuvenated scale invariance as an interesting solution to the above hierarchy problems, being able to forbid the inclusion of a Higgs mass term and a cosmological constant in the Standard Model action. In simple words, scale invariance is a universal feature of objects or laws that remains intact when the scales of length, energy or any dimensionful variable are multiplied by a common factor. A viable scale-invariant theory should exhibit, however, dilatation symmetry breaking in one way or another in order to describe the appearance of physical scales. According to the form this symmetry breaking is implemented, one can consider two different scenarios:
1. Spontaneously-broken scale symmetry: Scale symmetry is assumed to be exact but spontaneously broken by the non-zero expectation value of a given field or operator. In this type of setting, scale invariance is preserved at the quantum level by means of a scale-invariant regularisation prescription. Maintaining dilatation symmetry intact makes the theory non-renormalizable.
2. Emergent scale symmetry: Scale symmetry is taken to be anomalous and realised only in the vicinity of non-trivial fixed points. The transition among these fixed points happens through a crossover regime where physical scales emerge through dimensional transmutation, as happens for instance in QCD.
The synergy of gravity and scale invariance has far-reaching consequences. On the one hand, the breaking of dilation 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 therefore the solution of the hierarchy problem, could be a natural consequence of emergent scale symmetry, as already suggested by several functional renormalisation group studies within the asymptotic safety paradigm. In the following, we discuss some of these issues for the two scenarios described above.
SPONTANEOUSLY-BROKEN SCALE SYMMETRY
Higgs-based inflationary models based on spontaneously-broken scale symmetry are extremely appealing. Indeed, although the Higgs field alone is not able to produce an early exponential expansion of the Universe, it can do it in the presence of the non-minimal couplings to gravity needed to fulfil scale invariance in the gravitational sector. These so-called Higgs-Dilaton scenarios turn out to be highly predictive. On the one hand, the existence of an effectively conserved current related to dilatations makes these models essentially indistinguishable from single–field inflationary scenarios, from which they “inherit” all their virtues. On the other hand, the symmetries of the Einstein-frame kinetic sector lead to universal predictions almost insensitive to the details of the inflationary potential. At low energies, the invariance under volume–preserving diffeomorphisms gives rise to a unique run–away potential for the dilaton field, which can play the role of dynamical dark energy.
Interestingly, the early and late Universe dynamics described above may become intertwined, leading to non-trivial consistency relations among the inflationary observables and the present dark-energy equation of state parameter. In some cases, this makes Higgs-Dilaton scenarios comparable with—or even superior to— the concordance ΛCDM model given the present data sets. Interestingly, the measurements of future galaxy redshift surveys such as Euclid or SKA2 or CMB polarisation experiments such as LiteBIRD could translate into a more than 3σ separation among the simplest Higgs-Dilaton model and ΛCDM.
The relation between the inflationary masses and the low-energy masses of the Higgs and the top quark is, however, subject to ambiguities associated to the non-renormalizability of the Standard Model non-minimally coupled to gravity. The remnants of the different ultraviolet completions modify the running of the Higgs self-coupling and can give rise to an effective potential containing one extra minimum at energies between the electroweak and the Planck scale. The fate of the Universe after inflation (i.e. whether the Universe ends in the true or the false vacuum) depends on the maximal temperature of the Standard Model plasma produced during (p)reheating.
EMERGENT SCALE SYMMETRY
The resurgence of scale symmetry around ultraviolet and infrared fixed points in the renormalisation group flow may lead to the generation of an approximately scale-invariant spectrum of primordial density fluctuations and to the appearance of a dynamical dark energy component. The crossover to the infrared fixed point happens generically through a kinetic domination regime, which can have far reaching consequences in the presence of spectator fields non-minimally coupled to gravity. These include among others the generation of the matter-antimatter asymmetry of the Universe, the creation of short-lived topological defects leading to a detectable gravitational wave emission or a boosted production of dark matter after inflation.
On top of the kinetic dominated regime, the crossover from the ultraviolet to the infrared fixed point leads to the appearance of long-range attractive dilaton-mediated forces stronger than gravity. This opens the possibility of having significant clumping of matter prior to matter-radiation equality. Dark-matter candidates such as primordial black holes or similar screened objects could be then produced without the need of any particular feature in the spectrum of primordial density fluctuations generated during inflation.