It is hard to take space-time seriously. What is the consequence for the four-dimensional shape of our universe?

For better understanding, this article uses 2-d sections to visualize Einstein’s first model. This static model used a cosmological constant which Einstein later withdrew. The authors present a new 3-sphere space-time model which abides all observations, the perfect cosmological principle and Noether’s theorem.

As a consequence, the density is about 20 times higher, which wipes out dark energy.

The Pioneer 10&11 anomaly is solved and this new model needs a lot less dark matter.