  In the paper we check whether the contribution of $(-)(1+z)^6$ type in the
Friedmann equation can be tested. We consider some astronomical tests to
constrain the density parameters in such models. We describe different
interpretations of such an additional term: geometric effects of Loop Quantum
Cosmology, effects of braneworld cosmological models, non-standard cosmological
models in metric-affine gravity, and models with spinning fluid. Kinematical
(or geometrical) tests based on null geodesics are insufficient to separate
individual matter components when they behave like perfect fluid and scale in
the same way. Still, it is possible to measure their overall effect. We use
recent measurements of the coordinate distances from the Fanaroff-Riley type
IIb (FRIIb) radio galaxy (RG) data, supernovae type Ia (SNIa) data, baryon
oscillation peak and cosmic microwave background radiation (CMBR) observations
to obtain stronger bounds for the contribution of the type considered. We
demonstrate that, while $\rho^2$ corrections are very small, they can be tested
by astronomical observations -- at least in principle. Bayesian criteria of
model selection (the Bayesian factor, AIC, and BIC) are used to check if
additional parameters are detectable in the present epoch. As it turns out, the
$\Lambda$CDM model is favoured over the bouncing model driven by loop quantum
effects. Or, in other words, the bounds obtained from cosmography are very
weak, and from the point of view of the present data this model is
indistinguishable from the $\Lambda$CDM one.
