The Higgs field and early universe cosmology: a (brief) review

We consider low scale slow roll inflation driven by the gauge-invariant flat directions udd and LLe of the minimally supersymmetric standard model at the vicinity of a saddle point of the scalar potential. We study the stability of the saddle point and the slow roll regime by considering radiative and supergravity corrections. The latter are found to be harmless, but the former require a modest fine-tuning of the saddle point condition. We show that, while the inflaton decays almost instantly, full thermalization occurs late, typically at a temperature T ≈10 7 GeV, so that there is no gravitino problem. We also compute the renormalization group running of the inflaton mass and relate it to slepton masses that may be within the reach of the LHC and could be precisely determined in a future linear collider experiment.

We assume that the Boson which has recently been measured by the LHC experiments is the lightest Higgs boson of such model, while for the second Higgs Boson we consider a mass range of 600 ​ GeV ≤ m H ≤ 1 ​ TeV 600\,{\rm GeV}\,\leq\,m_{H}\,\leq\,1\,{\rm TeV} , i.e. outside the range of the direct searches presented so far. In this light, we study the impact of perturbative unitarity limits, Renormalisation Group Equations analysis and experimental constraints (Electro-Weak Precision Tests, measurements of the light Higgs coupling at the Large Hadron Collider). We show that, in the case of no additional hidden sector contributions, the largest constraints for higher Higgs masses stem from the assumption of perturbativity as well as vacuum stability for scales on the order of the SM metastability scale, and that the allowed mixing range is severely restricted .

Assuming that the particle with mass $\ensuremath{\sim}126\text{ }\text{ }\mathrm{GeV}$ discovered at LHC is the standard model Higgs boson, we find that the stability of the electroweak (EW) vacuum strongly depends on new physics interaction at the Planck scale ${M}_{P}$, despite of the fact that they are higher-dimensional interactions, apparently suppressed by inverse powers of ${M}_{P}$. In particular, for the present experimental values of the top and Higgs boson masses, if $\ensuremath{\tau}$ is the lifetime of the EW vacuum, new physics can turn $\ensuremath{\tau}$ from $\ensuremath{\tau}\ensuremath{\gg}{T}_{U}$ to $\ensuremath{\tau}\ensuremath{\ll}{T}_{U}$, where ${T}_{U}$ is the age of the Universe, thus, weakening the conclusions of the so called metastability scenario.

We perform an in-depth analysis of the Higgs sector in the minimal left-right symmetric model and compute the scalar mass spectrum and associated mixings, offering simple physical and symmetry arguments in support of our findings. We identify the tree-level quartic and cubic potential couplings in terms of the physical states and compute the quantum corrections for the latter ones. The deviations from the standard model prediction of the cubic Higgs doublet coupling are considered. Moreover we discuss the possible implications concerning the stability of the potential under the renormalization-group-equations evolution. In particular we examine three possible energy scales of parity restoration: LHC reach, next hadronic collider and very high energy relevant for grand unification.

The one-loop renormalization of the action for a set of Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in a geometric formulation that preserves at all stages the symmetries of the action. The result is then applied to Higgs effective field theory to obtain the renormalization group evolution. In the standard model limit of this effective field theory the renormalization group evolution equations collapse into a smaller linearly independent set; this allows to probe the dynamics of the scalar discovered at LHC via de-correlations in the running of couplings.