  Phenomenological models are widely used in cosmology in relation to
constraining different cosmological models, with two common examples being
cosmographic expansions and modeling the equation-of-state parameter of dark
energy. This work presents a study of how using different phenomenological
expressions for observables and physical quantities versus using physically
motivated, derived expressions affects cosmological parameter constraints. The
study includes the redshift-distance relation and Hubble parameter as
observables, and the dark energy equation-of-state parameter as a physical
quantity, and focuses on constraining the cosmological parameter
$\Omega_{\Lambda}$. The observables and equation-of-state parameter are all
modeled both using the physical, derived expressions and a variety of
phenomenological models with different levels of accuracy and complexity. The
results suggest that the complexity of phenomenological expressions only has
minor impact on the parameter constraints unless the complexity is very high.
The results also indicate that statistically significantly different results
can be expected from parameter constraints using different phenomenological
models if the models do not have very similar accuracy. This suggests that a
good practice is to use multiple phenomenological models when possible, in
order to assess the model dependence of results. Straightforward examples of
this is that results obtained using cosmographic expansions should always be
checked against similar results obtained with expansions of other order, and
when using phenomenological models such as for the equation-of-state
parameters, robustness of results could be assessed using fitted models from
symbolic regression, similar to what is done in this study.
