Using the formalism of Boucher we derive the conditions under which gravity can stabilize otherwise metastable or unstable scalar field configurations. For the case of a double-welled potential we rederive the stability criteria first obtained by Coleman and DeLuccia. Our derivation does not require the assumption of 0(4) symmetry or the thin-walled approximation used in their work. We also giv...

We derive constraints on scalar field theories coupled to gravity by using recently developed positivity bounds in the presence of gravity. It is found that a canonically normalized real cannot have an arbitrarily flat potential unless some new physics enters well below Planck scale. An upper bound scale determined loop corrections self-energy. Our result provides swampland condition for potent...

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of generalized vector and scalar Hartmann potentials. This is done provided the vector and scalar potentials hold some relation. Namely, one must be equals to or minus the other. Finally the case of some quasi-exactly solvable potentials are briefly commented.

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

The results on chaos in FRW cosmology with a massive scalar field are extended to another scalar field potential. It is shown that for sufficiently steep potentials the chaos disappears. A simple and rather accurate analytical criterion for the chaos to disappear is given. On the contrary, for gently sloping potentials the transition to a strong chaotic regime can occur. Two examples, concernin...