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We study the observational implications of a class of inflationary models
wherein the inflaton is coupled to the Einstein tensor through a generalized
non-minimal derivative coupling (GNMDC). In particular, we explore whether
these models can generate suitable features in the primordial spectrum of
curvature perturbations as a possible explanation for the large-scale anomalies
associated with the angular power spectrum of CMB temperature anisotropies. We
derive model-independent constraints on the GNMDC function for such a scenario,
considering both the scalar and tensor perturbations. We modify CosmoMC to
accommodate our GNMDC framework and investigate different classes of
inflationary models using a fully consistent numerical approach. We find that
the hilltop-quartic model with a specific choice of the GNMDC function provides
a considerable improvement over the best-fit reference $\Lambda$CDM model with
a nearly scale-invariant power spectrum. While the large-scale structure
observations should be able to provide independent constraints, future CMB
experiments, such as CMB-S4 and CMB-Bharat, are expected to constrain further
the parameter space of such beyond canonical single-field inflationary models.
