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Cosmology with a dynamical dimension of spacetime

Mokhtar Adda-Bedia
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The four-dimensional nature of physical spacetime and the possible existence of hidden dimensions are long-standing and central questions in modern scientific research. They are associated with major theoretical challenges in physics such as the unification of fundamental interactions or the birth and evolution of the universe. In his pioneering work, Ehrenfest concluded that three spatial dimensions are necessary and sufficient for classical fundamental laws of physics to agree with experimental and observational results. Here, we extend Ehrenfest's approach by asking how this particular dimension is selected. To this purpose, we postulate that the current dimension of our physical world results from a dynamical evolution of the spacetime dimension of an expanding universe. Starting from this assumption, we develop a model within the framework of "classical" general relativity. First, we use the generalized action of gravity to any dimension of spacetime and give dimensional arguments for the existence of a physical length scale that characterizes the "spatial" extension of "hidden" components of the metric. Next, we solve a generalized cosmological model in which the dimension n(t) of spacetime is allowed to jump incrementally. Within this approach and under minimal assumptions, we show the existence of a single possible scenario of an expanding universe with a space-time dimension that increases incrementally from n(t) = 2 to an upper limit n(t) = 4. We conclude our study by discussing the results as well as the relevance and possible drawbacks of our approach.
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hal-03859017 , version 1 (18-11-2022)


  • HAL Id : hal-03859017 , version 1


Mokhtar Adda-Bedia. Cosmology with a dynamical dimension of spacetime. 2022. ⟨hal-03859017⟩
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