The Gravitational Wave Background and Higgs False Vacuum Inflation

For a narrow band of values of the top quark and Higgs boson masses, the Standard Model Higgs potential develops a shallow local minimum at energies of about $10^{16}$ GeV, where primordial inflation could have started in a cold metastable state. For each point of that band, the highness of the Higgs potential at the false minimum is calculable, and there is an associated prediction for the inflationary gravitational wave background, namely for the tensor to scalar ratio $r$. We show that the recent measurement of $r$ by the BICEP2 collaboration, $r=0.16 _{-0.05}^{+0.06}$ at $1\sigma$, combined with the most up-to-date measurements of the top quark and Higgs boson masses, reveals that the hypothesis that a Standard Model shallow false minimum was the source of inflation in the early Universe is viable.Comment: 4 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1112.543

Higgs boson and Top quark masses as tests of Electroweak Vacuum Stability

The measurements of the Higgs boson and top quark masses can be used to extrapolate the Standard Model Higgs potential at energies up to the Planck scale. Adopting a NNLO renormalization procedure, we: i) find that electroweak vacuum stability is at present allowed, discuss the associated theoretical and experimental errors and the prospects for its future tests; ii) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the Planck scale, which is a stable configuration that might have been relevant for primordial inflation; iii) derive a conservative upper bound on type I seesaw right-handed neutrino masses, following from the requirement of electroweak vacuum stability.Comment: v1: 22 pages, 9 figures; v2: 26 pages, 11 figures: improved text, added detailed comparison with previous literature results, version matching the PRD articl

Stationary configurations of the Standard Model Higgs potential: electroweak stability and rising inflection point

We study the gauge-independent observables associated with two interesting stationary configurations of the Standard Model Higgs potential (extrapolated to high energy according to the present state of the art, namely the NNLO): i) the value of the top mass ensuring stability of the SM electroweak minimum, and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, finding that: i) stability of the SM is compatible with the present data at the 1.5 sigma level; ii) despite the large theoretical error plaguing the value of the Higgs potential at a rising inflection point, application of such configuration to models of primordial inflation displays a 3 sigma tension with the recent bounds on the tensor-to-scalar ratio of cosmological perturbations.Comment: v1: 21 pages, 6 figures; v2: 22 pages, 7 figures, text improved, figure and references added, matches published versio

The Higgs mass range from Standard Model false vacuum Inflation in scalar-tensor gravity

If the Standard Model is valid up to very high energies it is known that the Higgs potential can develop a local minimum at field values around $10^{15}-10^{17}$ GeV, for a narrow band of values of the top quark and Higgs masses. We show that in a scalar-tensor theory of gravity such Higgs false vacuum can give rise to viable inflation if the potential barrier is very shallow, allowing for tunneling and relaxation into the electroweak scale true vacuum. The amplitude of cosmological density perturbations from inflation is directly linked to the value of the Higgs potential at the false minimum. Requiring the top quark mass, the amplitude and spectral index of density perturbations to be compatible with observations, selects a narrow range of values for the Higgs mass, $m_H=126.0\pm 3.5$ GeV, where the error is mostly due to the theoretical uncertainty of the 2-loop RGE. This prediction could be soon tested at the Large Hadron Collider. Our inflationary scenario could also be further checked by better constraining the spectral index and the tensor-to-scalar ratio.Comment: v1: 14 pages, 4 figures; v2: 18 pages, 8 figures, text improved, new section and figures adde

Electroweak vacuum stability and finite quadratic radiative corrections

If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale $\Lambda$ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff $\Lambda_i$. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs $\Lambda_i$, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.Comment: 36 pages, 5 figures; v2: logarithm corrections included, figures improved, references adde

Ruling out Critical Higgs Inflation?

We consider critical Higgs inflation, namely Higgs inflation with a rising inflection point at smaller field values than those of the plateau induced by the non-minimal coupling to gravity. It has been proposed that such configuration is compatible with the present CMB observational constraints on inflation, and also with primordial black hole production accounting for the totality or a fraction of the observed dark matter. We study the model taking into account the NNLO corrections to the Higgs effective potential: such corrections are extremely important to reduce the theoretical error associated to the calculation. We find that, in the 3 sigma window for the relevant low energy parameters, which are the strong coupling and the Higgs mass (the top mass follows by requiring an inflection point), the potential at the inflection point is so large (and so is the Hubble constant during inflation) that the present bound on the tensor-to-scalar ratio is violated. The model is viable only allowing the strong coupling to take its upper 3-4 sigma value. In our opinion, this tension shows that the model of critical Higgs inflation is likely to be not viable: neither inflation nor black holes as dark matter can be originated in this version of the model.Comment: v1: 21 pages, 5 figures; v2: 23 pages, 5 figures, improved text and figures, results unchange

The problem of neutrino masses in extensions of the Standard Model

We review the problem of neutrino masses and mixings in the context of Grand Unified Theories. After a brief summary of the present experimental status of neutrino physics, we describe how the see-saw mechanism can automatically account for the large atmospheric mixing angle. We provide two specific examples where this possibility is realized by means of a flavour symmetry. We then review in some detail the various severe problems which plague minimal GUT models (like the doublet-triplet splitting and proton-decay) and which force to investigate the possibility of constructing more elaborate but realistic models. We then show an example of a quasi-realistic SUSY SU(5) model which, by exploiting the crucial presence of an abelian flavour symmetry, does not require any fine-tuning and predicts a satisfactory phenomenology with respect to coupling unification, fermion masses and mixings and bounds from proton decay.Comment: 140 pages, 6 figures; based on PhD thesis work; accepted by Int. Jour. of Mod. Phys.