Saoussen Mbarek and Manu Paranjape at the Université de Montréal in Canada have published a paper that details the conditions for negative mass to exist in our Universe without the need to include exotic particles. In their calculations negative mass is allowed in the General Relativity solution of a Schwarzschild-De Sitter geometry. This geometry corresponds to a curved space time with a cosmological constant.
This letter is quite interesting and there’s plenty to be excited about since negative mass has several interesting consequences. Negative mass could be dampening the elusive gravitational waves but there needs to be a great amount in the Universe, so we need to conceive a reasonable mechanism for negative mass formation during inflation (where our universe had a Schwarzschild-De Sitter geometry). Negative mass also has interesting consequences in general relativity, where it allows stable wormholes, naked singularities, and time loops.
But before we run to build our TARDISes, we need to understand that this is a theoretical work. Just because something is allowed to happen under the strict conditions imposed by us, does not mean that it has happened in the past.
Negative mass bubbles in de Sitter space-time, Saoussen Mbarek & Manu Paranjape http://arxiv.org/abs/1407.1457