No, it is not possible. Cosmological models are actually tightly constrained by data. Even in the late 80s, when we did not have such good data, I remember being amazed at the fact that primordial nucleosynthesis calculations together with observational data were enough to conclude that the number of light "normal" neutrino species was 3, while there were still speculations in Particle Physics that we could have more than 3 generations of particles. The data accumulated over the last 30 years has constrained things even more.
If some other explanation than invoking some new type of matter that can not be seen was possible to explain the observational data, don't you think that Physicists would use that instead of coming up with postulating that the Universe is dominated by "dark matter" and "dark energy" which we have not seen yet?