Shape and size of the universe: challenging the Standard Model of Cosmology

Abstract The standard model of cosmology (SMC) is based on the Friedmann equations, which are derived from Einstein's field equations of gravity for the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. The Minkowski SpaceTime (MST) metric, which can explain all aspects of special relativity (including time dilation, length contraction, and relative simultaneity), describes SpaceTime far from massive objects. This article contends that the currently accepted mathematical interpretation of the MST metric (as well as the FLRW metric) is incorrect, which has misled cosmologists from reaching a definite conclusion about the true shape and size of the universe. The temporal parts of both metrics are identical, and either metric can be used to determine the shape and size of the universe if the mathematical interpretation is corrected. The universe is like the 3D hypersurface of a 4D hypersphere; or in other words, the shape is like a (hyper) balloon. The shape is not plane (i.e. not 3D flat), and it is not infinite; it is a finite 3D hypersurface. Astronomers are confident that they have measured the universe to be 3D flat using two different methods. However, neither method can measure the extrinsic curvature of a 3D hypersurface. Also, other exotic shapes for the universe, like torus (doughnut) or dodecahedron, need not be considered. The universe is expanding like a balloon. Taking the radial expansion velocity of the universe as c (as dictated by spacetime equations) and the age of the universe as 13.8 billion years, the value of the Hubble constant obtained using this model (71.002 km/s/Mpc) agrees well with the accepted values (69.8 and 74 km/s/Mpc calculated by two different methods). Presently accepted SMC cannot explain why it has this particular value of Hubble constant. SMC cannot provide a satisfactory answer to the question "If the universe is expanding, what is it expanding into?" Additionally, SMC faces embarrassing situation trying to answer "Where is the center of the universe?" The model presented in this paper provides clear answers to both questions. Since the MST metric and Hubble’s law both say the same thing in this presented model, it demonstrates that this model is correct.