The Cosmic Spacetime Is The Universe Much Simpler Than we Thought? Fulvio Melia Cosmology today is confronted with several seemingly insoluble puzzles and strange, inexplicable coincidences. But a careful re-examination of the Cosmological principle and the Weyl postulate, foundational elements in this subject, suggests that we may be missing the point. The observations actually reveal a simpler and more elegant Universe than anyone could have imagined. The polish priest Nicolaus Copernicus (1473—1543) started a revolution with his heliocentric cosmology that displaced the Earth from the center of the Universe. His remarkable shift in paradigm continues to this day, the cornerstone of a concept we now call the Cosmological Principle, in which the Universe is assumed to be homogeneous and isotropic, without a center or boundary. But few realize that even this high degree of symmetry is insufficient for cosmologists to build a practical model of the Universe from the equations of General Relativity. The missing ingredient emerged from the work of mathematician Hermann Weyl (1885—1955), who reasoned that on large scales the Universe must be expanding in an orderly fashion. He argued that all galaxies move away from each other, except for the odd collision or two due to some peculiar motion on top of the ``Hubble flow" (figure 1). In this view, the evolution of the universe is a time-ordered sequence of 3-dimensional space-like hypersurfaces, each of which satisfies the Cosmological Principle—an intuitive picture of regularity formally expressed as the Weyl postulate. Together, these two philosophical inputs allow us to use a special time coordinate, called the cosmic time , to represent how much change has occurred since the big bang, irrespective of location. In special relativity, this approach can be confusing because  is the proper time on a clock at rest with respect to the observer, but is not the time she would measure on her synchronized clocks at other locations. But since the physical conditions are presumably the same everywhere,  should track the evolution of the Universe as seen from any vantage point, since the same degree of change will have occurred anywhere on a given time slice shown in figure 1. Figure 1. Illustration of the Weyl postulate. Of course, the Weyl postulate has several other important consequences, particularly in terms of how we interpret the separation between any two points in the cosmic flow. In relativity, the proper distance () between two points is their separation measured simultaneously in a given frame. It is not difficult to convince oneself that if the distance   between frames A and C (figure 2) is twice   , then A and C must be receding from each other at twice the rate of A and B. The Weyl postulate therefore reduces formally to the mathematical expression