We study flat Friedmann-Lemaitre-Robertson-Walker cosmological models for ascalar field coupled nonminimally to teleparallel gravity with generic couplingand potential functions. The goal of this paper is to determine the conditionsunder which the cosmological evolution tends to the limit where the variationof the gravitational "constant" ceases and the system evolves close to generalrelativity. These conditions can be read off from the approximate analyticalsolutions describing the process in matter and potential domination eras. Onlythose models where the GR limit exists and is an attractor can be consideredviable. We expect the results to hold in the original "pure tetrad" formulationas well as in the recently suggested covariant formulation of the teleparalleltheory. In the former case the GR attractor simultaneously provides a mechanismhow cosmological evolution suppresses the problematic degrees of freedomstemming from the lack of local Lorentz invariance.
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