Nonmetricity theories and aspects of gauge symmetry

Understand

In this paper we discuss on the phenomenological viability of nonmetricity theories of gravity which are based in the class of generalized Weyl spacetimes -- denoted by $W_4$ -- where arbitrary nonmetricity is allowed.

• This class of geometry includes the so called teleparallel spaces $Z_4$, which are the geometric basement of the symmetric teleparallel theories (STTs).
• The guiding principle in our discussion is Weyl gauge symmetry (WGS), which is a manifest symmetry of $W_4$ spaces.
• Here we derive the master equation that drives the gauge invariant variations of the length of vectors during parallel transport in $W_4$.