## Federico Piazza

### Years:

My research mainly focuses on the two periods of accelerated expansion that our cosmological observations strongly indicate: Inflation and Dark Energy. Despite the amazing quality of present and forthcoming observations, our knowledge of the Universe is inevitably indirect and the details of the `real theories' of Inflation and Dark Energy (btw, have you ever suspected that they might be the same thing? Don't be ashamed, **it happens)** may remain elusive for a long time. For these reasons, I intend to follow two main ``strategies":

• **Bet on nature being fair, and simple**. Among competing theories, there could be an overwhelmingly simple one out there, able to fit all data with just one or two, or even none, adjustable parameters. In parallel with a healthy ‘model building’ activity, we should not give up looking for major conceptual breakthroughs.

• **Look for effective descriptions**. Nature is not necessarily fair, nor simple. If the ‘real theory’ – of inflation or dark energy – has as many parameters as the Standard Model, we might never be able to discover it nor fit all its parameters. We should therefore develop effective models that are insensitive to the microphysical details.

### Current research activities:

**Effective field theory of Dark Energy**

My most recent achievement is the “Effective field theory of Dark Energy” (EFT of DE): a single unifying framework in which the specific features of DE (both at the level of the expansion history and of the growth rate) can be studied and tested against data. With my collaborators I have developed a formalism to parameterize and study the effects of dark energy beyond the background evolution. By extending to late time cosmology the “unitary gauge” formalism developed for inflation by Creminelli et al., we write down the most generic DE action containing only one scalar degree of freedom more than GR. The advantages of the EFT of DE are similar to those that traditional effective field theory has in particle physics. I think this formalism will soon become the *standard* for describing features and properties of DE models, and used to fit data in future galaxy surveys such as EUCLID.

**Goldstone theorems, Spontaneous breaking of Lorentz symmetry and breaking condensed matter.**

Recently, Alberto Nicolis and I have formulated a non-relativistic Goldstone theorem of a novel type. In cases of systems at finite charge density, we proved that if such a charge is part of a non-Abelian group of symmetries, the remaining Nambu-Goldstone particles associated with the other broken generators become *massive*, and their masses can be calculated *exactly* in terms of the chemical potential and of the structure constants of the symmetry group. This is one of the very few *exact results in field theory* that involves a finite mass gap (as opposed to be valid in the lowest energy limit, as the usual Goldstone theorem). More recently, in collaboration with Nicolis, Riccardo Penco and Rachel Rosen, I have studied systematically the low energy theory of systems at finite charge density by means of a *coset construction*, which is useful to approach the low-energy behavior of theories in which some of the symmetries are spontaneously broken. Such a construction confirms the existence of the gapped excitations predicted by Nicolis and me, and finds, in some cases, *additional* gapped excitations, whose mass, still of the order of the chemical potential, is not univocally fixed by the symmetry algebra. In an extended collaboration which includes Riccardo Rattazzi, we are now “classifying” condensed matter system on the basis of the possible spontaneous Lorentz-symmetry breaking patterns, in the presence of additional internal symmetries.

### Recent articles:

1. Zoology of condensed matter: framids, ordinary stuff, and galileids" A. Nicolis, R. Penco, F. Piazza, R. Rattazzi and R. A. Rosen, to appear [hep-th].

2. Healthy theories beyond Horndeski" J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi. arXiv:1404.6495 [hep-th] HEP entry

3. Phenomenology of dark energy: exploring the space of theories with future redshift surveys" F. Piazza, H. Steigerwald and C. Marinoni. arXiv:1312.6111 [astro-ph.CO] HEP entry JCAP, in press.

4. Effective Field Theory of Cosmological Perturbations" F. Piazza and F. Vernizzi, Class. Quant. Grav. 30, 214007 (2013) [arXiv:1307.4350 [hep-th]]HEP entry

5. More on gapped Goldstones at finite density: More gapped Goldstones" A. Nicolis, R. Penco, F. Piazza and R. A. Rosen, JHEP 1311, 055 (2013) [arXiv:1306.1240 [hep-th]] HEP entry

6. Essential Building Blocks of Dark Energy" J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, JCAP 1308, 025 (2013) [arXiv:1304.4840 [hep-th]]HEP entry

7. The Effective Field Theory of Dark Energy" G. Gubitosi, F. Piazza and F. Vernizzi, JCAP 1302, 032 (2013), [arXiv:1210.0201 [hep-th]] HEP entry

8. Infrared-modified Universe" F. Piazza, arXiv:1204.4099 [gr-qc] HEP entry

9. Relativistic non-relativistic Goldstone theorem: gapped Goldstones at Finite Charge Density" A. Nicolis and F. Piazza, Phys. Rev. Lett. 110, 011602 (2013) [arXiv:1204.1570 [hep-th]] HEP entry

10. Scalar-tensor theories, trace anomalies and the QCD-frame" F. Nitti and F. Piazza, Phys. Rev. D 86, 122002 (2012) [arXiv:1202.2105 [hep-th]], HEP entry