A No-Go Theorem for Curvature Neutrality in f(Q) Cosmology?

Résumé

In the framework of $f(Q)$ gravity, we investigate whether spatial curvature can be made dynamically invisible in the cosmological background equations. We consider open spatial sections, $k<0$, on an explicitly specified homogeneous and isotropic symmetric-teleparallel connection branch. For $k\neq0$, the coincident gauge cannot be imposed simultaneously with the standard curved-FLRW coordinate form. Re-deriving the background equations from the minisuperspace action, we show that curvature enters through $x=H+δ\sqrt{-k}/a$ and appears with inequivalent weights in the energy and pressure equations. For $f\in C^3((0,\infty))$, we prove a branch-specific no-go theorem: strict curvature independence for every scale factor and every $k<0$ requires $f=\mathrm{const}$, which contains no metric kinetic term. STEGR is not curvature-neutral, since its Friedmann equation retains the usual $3k/a^2$ contribution. A weaker cancellation, imposed only on backgrounds satisfying $δ\sqrt{-k}/a=cH$, necessarily produces a coasting expansion and yields $f(Q)=A Q^{(c+2)/2}+B$, or $f(Q)=A\ln Q+B$ when $c=-2$. For the illustrative choice $c=-3$, the solution becomes $f=α_1/\sqrt Q+β_1$. Under the conventional positive-coupling assumption $f_Q>0$, the required source violates the null energy condition. Moreover, adding positive radiation or pressureless matter forces a compensating negative-energy component at sufficiently early times. The weak branch is therefore neither curvature-neutral in an invariant sense nor a viable cosmological model. The principal result is the background-level obstruction itself. Perturbative stability and gravitational-wave propagation require a separate analysis including perturbations of the nontrivial affine connection and are not established in this work.

Citer ce document

Accès au document

Texte intégral en lecture en ligne, réservé aux abonnés SPHAERO et aux membres de l'institution. Se connecter

Voir l'article sur le site de la revue

Auteur(s)

Statistiques

Consultations : 1

Téléchargements : 0