Initial Conditions for Critical Higgs Inflation

It has been pointed out that a large non-minimal coupling $\xi$ between the Higgs and the Ricci scalar can source higher derivative operators, which may change the predictions of Higgs inflation. A variant, called critical Higgs inflation, employs the near-criticality of the top mass to introduce an inflection point in the potential and lower drastically the value of $\xi$. We here study whether critical Higgs inflation can occur even if the pre-inflationary initial conditions do not satisfy the slow-roll behaviour (retaining translation and rotation symmetries). A positive answer is found: inflation turns out to be an attractor and therefore no fine-tuning of the initial conditions is necessary. A very large initial Higgs time-derivative (as compared to the potential energy density) is compensated by a moderate increase in the initial field value. These conclusions are reached by solving the exact Higgs equation without using the slow-roll approximation. This also allows us to treat consistently the inflection point, where the standard slow-roll approximation breaks down. Here we make use of an approach that is independent of the UV completion of gravity, by taking initial conditions that always involve sub-planckian energies.Comment: 8 pages, 5 figures; v2: comments and references added, version accepted for publication in Physics Letters

A Simple Motivated Completion of the Standard Model below the Planck Scale: Axions and Right-Handed Neutrinos

We study a simple Standard Model (SM) extension, which includes three families of right-handed neutrinos with generic non-trivial flavor structure and an economic implementation of the invisible axion idea. We find that in some regions of the parameter space this model accounts for all experimentally confirmed pieces of evidence for physics beyond the SM: it explains neutrino masses (via the type-I see-saw mechanism), dark matter, baryon asymmetry (through leptogenesis), solve the strong CP problem and has a stable electroweak vacuum. The last property may allow us to identify the Higgs field with the inflaton.Comment: 8 pages, 4 figures. Phys. Lett. B version: references and discussion on light right-handed neutrinos adde

Critical Higgs inflation in a Viable Motivated Model

An extension of the Standard Model with three right-handed neutrinos and a simple invisible axion model can account for all experimentally confirmed signals of new physics (neutrino oscillations, dark matter and baryon asymmetry) in addition to solving the strong CP problem, stabilizing the electroweak vacuum and satisfying all current observational bounds. We show that this model can also implement critical Higgs inflation, which corresponds to the frontier between stability and metastability of the electroweak vacuum. This leads to a value of the non-minimal coupling between the Higgs and the Ricci scalar that is much lower than the one usually quoted in Higgs inflation away from criticality. Then, an advantage is that the scale of perturbative unitarity breaking on flat spacetime can be very close to the Planck mass, where anyhow new physics is required. The higher dimensional operators are under control in this inflationary setup. The dependence of the cutoff on the Higgs background is also taken into account as appropriate when the Higgs is identified with the inflaton. Furthermore, critical Higgs inflation enjoys a robust inflationary attractor that makes it an appealing setup for the early universe. In the proposed model, unlike in the Standard Model, critical Higgs inflation can be realized without any tension with the observed quantities, such as the top mass and the strong coupling.Comment: 13 pages, 6 figures; v2: explanations and references added; v3: title changed and more explanations added (version accepted by PRD

Higgs Inflation at NNLO after the Boson Discovery

We obtain the bound on the Higgs and top masses to have Higgs inflation (where the Higgs field is non-minimally coupled to gravity) at full next-to-next-to-leading order (NNLO). Comparing the result obtained with the experimental values of the relevant parameters we find some tension, which we quantify. Higgs inflation, however, is not excluded at the moment as the measured values of the Higgs and top masses are close enough to the bound once experimental and theoretical uncertainties are taken into account.Comment: 7 pages, 3 figures; v2: few comments added to emphasize the importance of the results, published in Phys. Lett.

Quadratic Gravity

Adding terms quadratic in the curvature to the Einstein-Hilbert action renders gravity renormalizable. This property is preserved in the presence of the most general renormalizable couplings with (and of) a generic quantum field theory (QFT). The price to pay is a massive ghost, which is due to the higher derivatives that the terms quadratic in the curvature imply. In this paper the quadratic gravity scenario is reviewed including recent progress on the related stability problem of higher derivative theories. The renormalization of the theory is also reviewed and the final form of the full renormalization group equations in the presence of a generic renormalizable QFT is presented. The theory can be extrapolated up to infinite energy through the renormalization group if all matter couplings flow to a fixed point (either trivial or interacting). Moreover, besides reviewing the above-mentioned topics some further insight on the ghost issue and the infinite energy extrapolation is provided. There is the hope that in the future this scenario might provide a phenomenologically viable and UV complete relativistic field theory of all interactions.Comment: 46 pages, 4 figures, 2 tables. Review article prepared for Frontiers; v2 matches version published in Frontier

Quantum mechanics of 4-derivative theories

A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalisable wave functions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.Comment: 25 pages. v2: clarifications added, final published versio

Agravity up to infinite energy

The self-interactions of the conformal mode of the graviton are controlled, in dimensionless gravity theories (agravity), by a coupling $f_0$ that is not asymptotically free. We show that, nevertheless, agravity can be a complete theory valid up to infinite energy. When $f_0$ grows to large values, the conformal mode of the graviton decouples from the rest of the theory and does not hit any Landau pole provided that scalars are asymptotically conformally coupled and all other couplings approach fixed points. Then, agravity can flow to conformal gravity at infinite energy. We identify scenarios where the Higgs mass does not receive unnaturally large physical corrections. We also show a useful equivalence between agravity and conformal gravity plus two extra conformally coupled scalars, and give a simpler form for the renormalization group equations of dimensionless couplings as well as of massive parameters in the presence of the most general matter sector.Comment: 24 pages, 1 figure; v2: revised version to appear in the European Physical Journal