Alberto Nicolis

Causality, analyticity and an IR obstruction to UV completion

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

The string landscape, black holes and gravity as the weakest force

We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Λ = gMPl, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Λ. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light ``elementary electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.

Starting the Universe: stable violation of the null energy condition and non-standard cosmologies

We present a consistent effective theory that violates the null energy condition (NEC) without developing any instabilities or other pathological features. The model is the ghost condensate with the global shift symmetry softly broken by a potential. We show that this system can drive a cosmological expansion with > 0. Demanding the absence of instabilities in this model requires H2. We then construct a general low-energy effective theory that describes scalar fluctuations about an arbitrary FRW background, and argue that the qualitative features found in our model are very general for stable systems that violate the NEC. Violating the NEC allows dramatically non-standard cosmological histories. To illustrate this, we construct an explicit model in which the expansion of our universe originates from an asymptotically flat state in the past, smoothing out the big-bang singularity within control of a low-energy effective theory. This gives an interesting alternative to standard inflation for solving the horizon problem. We also construct models in which the present acceleration has w<−1; a periodic ever-expanding universe; and a model with a smooth ``bounce connecting a contracting and expanding phase.

Limits on non-Gaussianities from WMAP data

We develop a method for constraining the level of non-Gaussianity of density perturbations when the three-point function is of the equilateral type. Departures from Gaussianity of this form are produced by single field models such as ghost or Dirac–Born–Infeld inflation and in general by the presence of higher order derivative operators in the effective Lagrangian of the inflaton. We show that the induced shape of the three-point function can be very well approximated by a factorizable form, making the analysis practical. We also show that, unless one has a full sky map with uniform noise, in order to saturate the Cramer–Rao bound for the error on the amplitude of the three-point function, the estimator must contain a piece that is linear in the data. We apply our technique to the WMAP data obtaining a constraint on the amplitude fNLequil of equilateral non-Gaussianity: −366xa0<xa0fNLequilxa0<xa0238 at 95%xa0C.L. We also apply our technique to constrain the so-called local shape, which is predicted for example by the curvaton and variable decay width models. We show that the inclusion of the linear piece in the estimator improves the constraint over those obtained by the WMAP team, to −27xa0<xa0fNLlocalxa0<xa0121 at 95% C.L.

Null energy condition and superluminal propagation

We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking u H > 0 in scalar tensor theories of gravity.

Ghosts in massive gravity

In the context of Lorentz-invariant massive gravity we show that classical solutions around heavy sources are plagued by ghost instabilities. The ghost shows up in the effective field theory at huge distances from the source, much bigger than the Vainshtein radius. Its presence is independent of the choice of the non-linear terms added to the Fierz-Pauli lagrangian. At the Vainshtein radius the mass of the ghost is of order of the inverse radius, so that the theory cannot be trusted inside this region, not even at the classical level.

A measure of de Sitter entropy and eternal inflation

We show that in any model of non-eternal inflation satisfying the null energy condition, the area of the de Sitter horizon increases by at least one Planck unit in each inflationary e-folding. This observation gives an operational meaning to the finiteness of the entropy S_dS of an inflationary de Sitter space eventually exiting into an asymptotically flat region: the asymptotic observer is never able to measure more than e^(S_dS) independent inflationary modes. This suggests a limitation on the amount of de Sitter space outside the horizon that can be consistently described at the semiclassical level, fitting well with other examples of the breakdown of locality in quantum gravity, such as in black hole evaporation. The bound does not hold in models of inflation that violate the null energy condition, such as ghost inflation. This strengthens the case for the thermodynamical interpretation of the bound as conventional black hole thermodynamics also fails in these models, strongly suggesting that these theories are incompatible with basic gravitational principles.

Perturbations in bouncing cosmologies: Dynamical attractor versus scale invariance

For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary cosmology, thanks to the existence of a dynamical attractor, which makes local observables equal to the unperturbed solution up to exponentially small terms. Assuming that the physics of the bounce is not extremely sensitive to these corrections, perturbations can be evolved even at the nonlinear level. The resulting spectrum is not scale invariant and thus incompatible with experimental data. This can be explicitly shown in synchronous gauge where, contrary to what happens in the commonly used Newtonian gauge, all perturbations remain small going towards the bounce and the existence of the attractor is manifest.

Quantum Horizons of the Standard Model Landscape

The long-distance effective field theory of our Universe—the Standard Model coupled to gravity—has a unique 4D vacuum, but we show that it also has a landscape of lower-dimensional vacua, with the potential for moduli arising from vacuum and Casimir energies. For minimal Majorana neutrino masses, we find a near-continuous infinity of AdS3 × S1 vacua, with circumference ~ 20 microns and AdS3 length 4 × 1025 m. By AdS/CFT, there is a CFT2 of central charge c ~ 1090 which contains the Standard Model (and beyond) coupled to quantum gravity in this vacuum. Physics in these vacua is the same as in ours for energies between 10−1 eV and 1048 GeV, so this CFT2 also describes all the physics of our vacuum in this energy range. We show that it is possible to realize quantum-stabilized AdS vacua as near-horizon regions of new kinds of quantum extremal black objects in the higher-dimensional space—near critical black strings in 4D, near-critical black holes in 3D. The violation of the null-energy condition by the Casimir energy is crucial for these horizons to exist, as has already been realized for analogous non-extremal 3D black holes by Emparan, Fabbri and Kaloper. The new extremal 3D black holes are particularly interesting—they are (meta)stable with an entropy independent of and GN, so a microscopic counting of the entropy may be possible in the GN → 0 limit. Our results suggest that it should be possible to realize the larger landscape of AdS vacua in string theory as near-horizon geometries of new extremal black brane solutions.

Microcausality in curved space-time

It is well known that in Lorentz-invariant quantum field theories in flat space the commutator of spacelike separated local operators vanishes (microcausality). We provide two different arguments showing that this is a consequence of the causal structure of the classical theory, rather than of Lorentz invariance. In particular, microcausality holds in arbitrary curved space-times, where Lorentz invariance is explicitly broken by the background metric. As illustrated by an explicit calculation on a cylinder this property is rather nontrivial at the level of Feynman diagrams.