False vacuum energy dominated inflation with large $r$ and the importance of $kappa_s$

We investigate to which extent and under which circumstances false vacuum energy (V0) dominated slow-roll inflation is compatible with a large tensor-to-scalar ratio r=O(0.1), as indicated by the recent BICEP2 measurement. With V0 we refer to a constant contribution to the inflaton potential, present before a phase transition takes place and absent in the true vacuum of the theory, like e.g. in hybrid inflation. Based on model-independent considerations, we derive an upper bound on the possible amount of V0 domination and highlight the importance of higher-order runnings of the scalar spectral index (beyond αs) in order to realise scenarios of V0 dominated inflation. We study the conditions for V0 domination explicitly with an inflaton potential reconstruction around the inflaton field value 50 e-folds before the end of inflation, taking into account the present observational data. To this end, we provide the up-to-date parameter constraints within ΛCDM + r + αs + κs using the cosmological parameter estimation code Monte Python together with the Boltzmann code CLASS