The following document is to answer if higher dimensions add value to answering fundamental cosmology questions. The results are mixed, 1st with higher dimensions apparently helping in reconstructing and preserving the value of Planck’s constant, and the fine structure constant from a prior to a present universe, while 2nd failing to add anything different from four dimensional cosmological mod...

A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we deene a 2-Hilbert space to be an abelian category enriched over Hilb with a-structure, conjugate-linear on the hom-sets, satisfying hf g; hi = hg; f hi = hf; hg i. We also deene monoidal, braided monoidal, and symmetric monoidal versions of 2-Hilbert spaces, which we call 2-H...

Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures ...

Two-dimensional quantum gravity coupled to conformally invariant matter with central charge c > 25 has been proposed as a toy model for quantum gravity in higher dimensions. The associated “Wheeler-Dewitt equation” is non-linear and unstable to forming a condensate of baby universes. This will occur even in the classical c + co limit. Small fluctuations about this background describe the propag...

These notes give an introductory review on brane cosmology. This subject deals with the cosmological behaviour of a brane-universe, i.e. a three-dimensional space, where ordinary matter is confined, embedded in a higher dimensional spacetime. In the tractable case of a five-dimensional bulk spacetime, the brane (modified) Friedmann equation is discussed in detail, and various other aspects are ...

Brane-world models, where observers are restricted to a brane in a higher dimensional spacetime, offer a novel perspective on cosmology. I discuss some approaches to cosmology in extra dimensions and some interesting aspects of gravity and cosmology in brane-world models. COSMOLOGY AFTER EINSTEIN A century after Einstein first proposed his theory of relativity, it has become a cornerstone of th...