Abstract
The aim of this paper is to highlight the challenges and potential gains surrounding a coherent description of physics from the high-energy scales of inflation down to the lower energy scales probed in particle-physics experiments. As an example, we revisit the way inflation can be realised within an effective Minimal Supersymmetric Standard Model (eMSSM), in which the $LLe$ and $udd$ flat directions are lifted by the combined effect of soft-supersymmetric-breaking masses already present in the MSSM, together with the addition of effective non-renormalizable operators. We clarify some features of the model and address the question of the one-loop Renormalization Group improvement of the inflationary potential, discussing its impact on the fine-tuning of the model. We also compare the parameter space that is compatible with current observations (in particular the amplitude, $A_{\scriptscriptstyle{\mathrm{S}}}$, and the spectral index, $n_{\scriptscriptstyle{\mathrm{S}}}$, of the primordial cosmological fluctuations) at tree level and at one loop, and discuss the role of reheating. Finally we perform combined fits of particle and cosmological observables (mainly $A_{\scriptscriptstyle{\mathrm{S}}}$, $n_{\scriptscriptstyle{\mathrm{S}}}$, the Higgs mass, and the cold-dark-matter energy density) with the one-loop inflationary potential applied to some examples of dark-matter annihilation channels (Higgs-funnel, Higgsinos and A-funnel), and discuss the status of the ensuing MSSM spectra with respect to the LHC searches.