Construct the framework for non-coincident f(Q) cosmology

Construct an analogous unified dynamical-system formulation for the non-coincident branches of f(Q) cosmology, including the genuinely dynamical connection function and its coupling to the cosmological variables.

Background

The analysis in the paper is restricted to the coincident-gauge branch of f(Q) cosmology, where the connection structure permits the algebraic eliminations used to obtain finite-dimensional systems. Other symmetric-teleparallel branches contain a genuinely dynamical connection function, so the simplifications underlying the coincident-gauge treatment no longer apply directly.

The authors identify the construction of a corresponding formulation for these non-coincident branches as a distinct unresolved problem requiring special care. This is a concrete extension of the framework, not merely a general aspiration, because it must accommodate the additional dynamical connection degree of freedom and determine an appropriate closed dynamical-system representation.

References

Non-coincident gauges are attracting significant phenomenological attention at present , and constructing an analogous formulation for them requires special care; we reserve this problem, too, for future work.

— Formalizing a unified dynamical system framework for $f(R)$ and $f(Q)$ gravity  (2609.24733 - Chakraborty, 21 Sep 2026) in Section Summary and Outlook