We consider two models of interacting dark energy, both of which interact only through momentum exchange. One is a phenomenological one-parameter extension to $w$CDM, and the other is a coupled quintessence model described by a Lagrangian formalism. Using a variety of high and low redshift data sets, we perform a global fitting of cosmological parameters and compare to $Lambda$CDM, uncoupled quintessence, and $w$CDM. We find that the models are competitive with $Lambda$CDM, even obtaining a better fit when certain data sets are included.
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