Higgs Stability and the 750 GeV Diphoton Excess

We study the implications of a possible unstable particle with mass $M_X<$ TeV for the Higgs stability, naturalness and inflation. We pay particular attention to the case $M_X\approx$ 750 GeV, suggested by recent results of ATLAS and CMS on diphoton final states, and work within the minimal model: we add to the Standard Model field content a pseudoscalar and a vector-like fermion carrying both color and electric charge. This can stabilize the electroweak vacuum without invoking new physics at very high energies, which would give an unnaturally large contribution to the Higgs mass. We also show that inflation can be obtained via a UV modification of General Relativity.