It is suggested that we accept that antiparticles move backward in time, as proposed by Feynman. Then, I show that we have to attribute negative mass and energy to antiparticles. Applying this to the presence of virtual particle-antiparticle pairs in the vacuum, we see that the vacuum has to be considered as containing zero mass-energy, instead of a huge amount of it resulting from considering the antiparticles´ mass-energy being positive. The result is that the cosmological constant has to be taken strictly zero, rather than having a huge value, resulting from taking of the mass-energy content of the vacuum as huge. Then the dark-energy based model universe, presupposing a small but finite cosmological constant, has to be abandoned. The problem then is what it has to be replaced with in order for the observasional data to be explained. To this end, I propose for the Universe a new exact cosmological solution of Einstein´s field equations (with no cosmological term), found by the author, which describes an accelerating expansion of the Universe, and a double rotation of it at the same time, which gives the Universe the shape of an (accelerating expanding) hypertorus. This new metric explains, besides the accelerating expansion of the Universe and the correct age of it, the Ryle effect and the observed large-scale anisotropy of the CMB. It also explains the apparent rotation and the spiral structure of galaxies, which latter one was the motivation underlying the work towards the new metric at the first place. (References under Chaliasos in arXiv.org/find)