We consider general relativity with matter and radiation, with one of these fluids being coupled to a vacuum. We find that the Universe dynamics starts by an inflation phase if the coupled fluid has a negative energy density at an early time. Then, there is always a finite scale factor singularity except when vacuum and matter are coupled and matter density behaves like a negative radiation density. Moreover, the convergence to the $\mathrm{\Lambda }CDM$ model is clearly easier to reach when a vacuum is coupled to matter rather than to radiation. Two classes of theories are studied to illustrate these results.

• Received 30 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.063514