Physical Basis for the Simplicity of the Cosmic Spacetime

What is it about?

The cosmic spacetime metric is one of the three most famous and often used solutions to Einstein's Equations. Its form is extremely simple, perhaps surprising given its broad cosmological application. For the first time, this paper explores the underlying physics for its high degree of symmetry and simple structure, notably its first coefficient---known as the lapse function---that yields the time dilation measured by an observer using his/her coordinates relative to those in a local free-falling frame.

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Photo by milan degraeve on Unsplash

Photo by milan degraeve on Unsplash

Why is it important?

The dependence of the lapse function on the observer's coordinates is directly related to the local spacetime curvature, and thus the type of mass and energy present in the local medium. Until now, this dependence has been completely ignored, but this paper demonstrates that the equation of state in the cosmic fluid (which relates its pressure to the energy density) directly constrains the permitted form of the lapse function. In other words, this is not a case of ``one size fits all." The simple form often used for the lapse function in the cosmic spacetime metric is not valid for arbitrary choices of the matter and energy content of the Universe.