Cosmological bouncing scenarios in symmetric teleparallel gravity

Nonmetricity theories and aspects of gauge symmetry

“…The above results leave the recently proposed cosmological models that are based in symmetric teleparallel theories [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] in quite a difficult situation. In particular, if we follow the first way above, and we consider the only geometrically (and phenomenologically) acceptable nonmetricity: Q αµν = Q α g µν , in the coincident gauge of symmetric teleparallel geometry, we will be able to demonstrate that, independent of the given theory of gravity, the only possible metric is the conformally flat one.…”

“…Nevertheless, Weyl geometry has gotten back to scene through proposals to unify the standard model of particles with gravity [59,60,[62][63][64][65]102] and also by looking for applications in cosmology [103,104], among other interesting physical implications. This is not to mention recent resurrection of Weyl's ideas through a generalization of the nonmetricity condition: ∇ α g µν = −Q αµν , which together with the requirement (17), are the basis of the symmetric teleparallel theories of gravity [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][91][92][93][94][95][96][97][98][99], including the so called coincident general relativity [89,100,101]. It is clumsy that, but a very few works [55,57] one can not find even a mention of the SCE in none of these papers.…”

“…In order to obtain the above equations, in (46) and (51) we have made the following replacements (recall that i is the imaginary unit):…”

“…The whole picture can be described in the following way. Whenever one works in Weyl geometric backgrounds such as W 4 , or any of it subclasses as Z 4 , one accepts that the units of measure, represented by the length of given vectors v i of weight w i (i = 1, 2, ..., N ): ||v i || 2 = g µν v µ i v ν i , inevitably vary during parallel transport along the curves C i , according to (46):…”

“…Theories that are based in Weitzenböck space A 4 are known as teleparallel theories of gravity . In this new wave of post-Riemannian theories a branch known as nonmetricity theories or, also, as symmetric teleparallel theories (STTs) [32][33][34][35][36][37][38][39], play a central role mostly in what regards to their applications in the cosmological context [40][41][42][43][44][45][46].…”