  In this dissertation, we study two cosmological models based on $f(Q)$
gravity. We resort to mock catalogs of standard siren (SS) events to see
whether data from future gravitational wave (GWs) observatories will be able to
distinguish these models from $\Lambda$CDM.
  The first model is the most general $f(Q)$ formulation that replicates a
$\Lambda$CDM background, with deviations appearing only at the perturbative
level. It has one additional free parameter compared to $\Lambda$CDM, $\alpha$,
which when set to zero falls back to $\Lambda$CDM. We show that LIGO-Virgo is
unable to constrain $\alpha$, due to the high error and low redshift of the
measurements, whereas LISA and the ET will, with the ET outperforming LISA. The
catalogs for both LISA and LIGO-Virgo show non-negligible statistical
fluctuations, where we consider three representative catalogs (the best, median
and worst), whereas for the ET, only a single catalog is considered, as the
number of events is large enough for statistical fluctuations to be neglected.
The best LISA catalog is the one with more low redshift events, while the worst
LISA catalog features fewer low redshift events. Additionally, if we are to
observe a bad LISA catalog, we can rely on data from LIGO-Virgo to improve the
quality of the constrains, bringing it closer to a median LISA catalog.
  The second model attempts to replace dark energy by making use of a specific
form of the function $f(Q)$. We study this model resorting to dynamical system
techniques to show the regions in parameter space with viable cosmologies.
Using model selection criteria, we show that no number of SS events is, by
itself, able to tell this model and $\Lambda$CDM apart. We then show that if we
add current type Ia Supernova (SnIa) data, tensions in this model arise when
compared to the constrains set by the SS events.
