Scaling cosmologies, geodesic motion and pseudo-susy

Understand

One-parameter solutions in supergravity carried by scalars and a metric trace out curves on the scalar manifold.

• In ungauged supergravity these curves describe a geodesic motion.
• It is known that a geodesic motion sometimes occurs in the presence of a scalar potential and for time-dependent solutions this can happen for scaling cosmologies.
• This note contains a further study of such solutions in the context of pseudo-supersymmetry for multi-field systems whose first-order equations we derive using a Bogomol'nyi-like method.