Baryogenesis from combined Higgs - scalar field inflation
  We study a modification of the Higgs inflation scenario where we introduce an
extra scalar $\phi$, with mass $m$, coupled to the Ricci scalar as $g\phi^2 R$,
and mixed with the Higgs field $h$ by means of the Lagrangian term $\mu \phi
h^2$. Both fields participate in the inflation process in a unitary theory that
predicts values of the cosmological observables in agreement with the results
from the Planck/BICEP/Keck collaborations. In addition, by means of a
$\mathcal{CP}$ odd effective operator that couples $\phi$ to the Chern-Simons
term of the hypercharge gauge group as $f_\phi^{-1}\phi \,Y_{\mu\nu}\tilde
Y^{\mu\nu}$, maximally helical magnetic fields are produced during the last
e-folds of inflation. We found a window in the coupling $ f_\phi$ where these
fields survive all constraints until the electroweak phase transition, and
source the baryon asymmetry of the Universe through the Standard Model chiral
anomaly. From a phenomenological perspective, the model can solve the Standard
Model instability problem at the scale $\mathcal Q_I\simeq 10^{11}$ GeV,
provided that $\mu\lesssim m \lesssim \mathcal Q_I$, and for $m\lesssim
\mathcal{O}$(few) TeV, the $\phi$-$h$ mixing becomes sizable while the theory
turns natural. The latter thus predicts modifications of the trilinear and
quartic couplings that could be explored at the HE-LHC, as well as at future
colliders, and allows for direct $\phi$ production at the LHC followed by decay
into $hh$. Present results from ATLAS and CMS already put (mild) bounds on the
mass of the heavy scalar as $m\gtrsim 0.55$ TeV at 95% CL.
