Enrico Trincherini

Galilean genesis: an alternative to inflation

We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): >> H2. The model is based on the recently introduced Galileon theories, which allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats. This solution is a dynamical attractor and the Universe is driven to it, even if it is initially contracting. The study of perturbations of the Galileon field reveals some subtleties, related to the gross violation of the NEC and it shows that adiabatic perturbations are cosmologically irrelevant. The model, however, suggests a new way to produce a scale invariant spectrum of isocurvature perturbations, which can later be converted to adiabatic: the Galileon is forced by symmetry to couple to the other fields as a dilaton; the effective metric it yields on the NEC violating solution is that of de Sitter space, so that all light scalars will automatically acquire a nearly scale-invariant spectrum of perturbations.

Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic non-Gaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.

Energy’s and amplitudes’ positivity

In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration’s stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced ‘galileon’, or more precisely its conformally invariant version. We show that the theory’s low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual.

Subluminal galilean genesis

A bstractWe put forward an improved version of the Galilean Genesis model that addresses the problem of superluminality. We demote the full conformal group to Poincaré symmetry and dilations, supplemented with approximate galilean shift invariance in the UV and at small field values. In this way fluctuations around the NEC-violating cosmological background are made substantially subluminal, and superluminality cannot be reached by any small change of the solution, in contrast with the original model. Dilation invariance still protects the scale-invariance of correlation functions of a massless test scalar — which is the source of the observed cosmological fluctuations — but the explicit breaking of the conformal group can be potentially observed in higher-order correlators. We also highlight a subtlety in matching the NEC-violating phase with the standard cosmological evolution, and discuss the possible couplings of the Galileon to gravity.

Heavy Vectors in Higgs-less models

One or more heavy spin-1 fields may replace the Higgs boson in keeping perturbative unitarity up to a few TeV. By means of two prototype chiral models for the heavy spin-1 bosons, a composite model or a gauge model, we discuss if and how the sole exchange of the same fields can also account for the electroweak precision tests. While this proves impossible in the gauge model, the composite model hints to a positive solution, which we exploit to constrain the phenomenological properties of the heavy vectors.

Weakly broken galileon symmetry

Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.

Non-linear representations of the conformal group and mapping of galileons

A bstractThere are two common non-linear realizations of the 4D conformal group: in the first, the dilaton is the conformal factor of the effective metric ημνe−2π ; in the second it describes the fluctuations of a brane in AdS5. The two are related by a complicated field redefinition, found in [1] to all orders in derivatives. We show that this field redefinition can be understood geometrically as a change of coordinates in AdS5. In one gauge the brane is rigid at a fixed radial coordinate with a conformal factor on the AdS5 boundary, while in the other one the brane bends in an unperturbed AdS5. This geometrical picture illuminates some aspects of the mapping between the two representations. We show that the conformal Galileons in the two representations are mapped into each other in a quite non-trivial way: the DBI action, for example, is mapped into a complete linear combination of all the five Galileons in the other representation. We also verify the equivalence of the dilaton S-matrix in the two representations and point out that the aperture of the dilaton light-cone around non-trivial backgrounds is not the same in the two representations.

Inequivalence of coset constructions for spacetime symmetries

A bstractNon-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios.

Inflation from Minkowski Space

A bstractWe propose a class of scalar models that, once coupled to gravity, lead to cosmologies that smoothly and stably connect an inflationary quasi-de Sitter universe to a low, or even zero-curvature, maximally symmetric spacetime in the asymptotic past, strongly violating the null energy condition H⋅≫H2