A new topological perspective of expanding space-times with applications to cosmology

Abstract

We discuss the possible role of the Tietze extension theorem in providing a rigorous topological base to the expanding space-time in cosmology. A simple toy model has been introduced to show the analogy between the topological extension from a circle $S$ to the whole space $M$ and the cosmic expansion from a non-zero volume to the whole space-time in non-singular cosmological models. A topological analogy to the cosmic scale factor function has been suggested, the paper refers to the possible applications of the topological extension in mathematical physics.

13 pages, 2 figures, https://doi.org/10.1142/S0219887821501309

References in corpus (8)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Quantum Nature of the Big Bang
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Cosmology without inflation
• Singularity free gravitational collapse in an effective dynamical quantum spacetime
• A Cyclic Universe With Varying Cosmological Constant in $f(R,T)$ gravity
• Homotopy approach to quantum gravity
• Singularity-free cosmological solutions in string theories