Higgs inflation and vacuum stability

Inflation is nowadays a well-established paradigm consistent with all the observations. The precise nature of the inflaton is however unknown and its role could be played by any candidate able to imitate a scalar condensate in the slow-roll regime. The discovery of a fundamental scalar in the LHC provides the less speculative candidate. Could the Higgs field itself be responsible for inflation? Do we really need to advocate new physics to explain the properties of the Universe at large scales? Which is the relation between the Standard Model parameters and the inflationary observables? What happens if our vacuum becomes unstable below the scale of inflation? We present an overview of Higgs inflation trying to provide answers to the previous questions with special emphasis on the vacuum stability issue.Comment: 11 pages, 14 figures, contribution to proceedings DISCRETE 201

Higgs-Dilaton cosmology: Universality vs. criticality

The Higgs-Dilaton model is able to produce an early inflationary expansion followed by a dark energy dominated era responsible for the late time acceleration of the Universe. At tree level, the model predicts a small tensor-to-scalar ratio ($0.0021\leq r \leq 0.0034$), a tiny negative running of the spectral tilt ($-0.00057 \leq dn_s/d\ln k \leq -0.00034$) and a nontrivial consistency relation between the spectral tilt of scalar perturbations and the dark energy equation of state, which turns out to be close to a cosmological constant ($0 \leq 1+w_{DE} \leq 0.014$). We reconsider the validity of these predictions in the vicinity of the critical value of the Higgs self-coupling giving rise to an inflection point in the inflationary potential. The value of the inflationary observables in this case strongly depends on the parameters of the model. The tensor-to-scalar ratio can be large [$r\sim {\cal O}(0.1)$] and notably exceed its tree-level value. If that happens, the running of the scalar tilt becomes positive and rather big [$dn_s/d\ln k \sim {\cal O}(0.01)$] and the equation-of-state parameter of dark energy can significantly differ from a cosmological constant [$1+w_{DE}\sim {\cal O}(0.1)$].Comment: 5 pages, 3 figures, published version, added clarifications and references, corrected typo

Quintessential Affleck-Dine baryogenesis with non-minimal couplings

We present a novel Affleck-Dine scenario for the generation of the observed baryon asymmetry of the Universe based on the non-trivial interplay between quintessential inflationary models containing a kinetic dominated post-inflationary era and a non-minimally coupled $U(1)$ field with a weakly broken $B-L$ symmetry. The non-minimal coupling to gravity renders heavy the Affleck-Dine field during inflation and avoids the generation of isocurvature fluctuations. During the subsequent kinetic era the Ricci scalar changes sign and the effective mass term of the Affleck-Dine field becomes tachyonic. This allows the field to dynamically acquire a large expectation value. The symmetry of the Affleck-Dine potential is automatically restored at the onset of radiation domination, when the Ricci scalar approximately equals zero. This inverse phase transition results in the coherent oscillation of the scalar field around the origin of its effective potential. The rotation of the displaced Affleck-Dine field in the complex plane generates a non-zero $B-L$ asymmetry which can be eventually converted into a baryon asymmetry via the usual transfer mechanisms.Comment: 9 pages, 1 figure, minor corrections and clarifications added. Matches the published versio

Endlessly flat scalar potentials and α\alpha-attractors

We consider a minimally-coupled inflationary theory with a general scalar potential $V(f(\varphi))= V(\xi\sum_{k=1}^{n}\lambda_k \varphi^k)$ containing a stationary point of maximal order $m$. We show that asymptotically flat potentials can be associated to stationary points of infinite order and discuss the relation of our approach to the theory of $\alpha$-attractors.Comment: 8 pages, 2 figure

A nonparametric dimension test of the term structure

This paper addresses the problem of conducting a nonparametric test of the dimension of the state variable vector in a continuous-time term structure model. The paper shows that a bivariate diffusion function of the short rate process is a sufficient condition for the term structure to be driven by two stochastic factors. Using an easy-to-implement kernel smoothing method the number of state variables can be tested under very unrestrictive assumptions. The results suggest that continuous-time models for the US interest rates should contain at least two stochastic factors

On the robustness of the primordial power spectrum in renormalized Higgs inflation

We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in critical Higgs inflation scenarios containing a quasi-inflection point along the inflationary trajectory. The interplay of radiative corrections with this quasi-inflection point may translate into a sizable modification of the inflationary observables.Comment: 12 pages, 8 figures - matches the published versio