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Abstract In the framework of metric-affine gravity, we consider the role of the boundary term in Symmetric Teleparallel Gravity assuming f (Q, B) models where f is a smooth function of the non-metricity scalar Q and the related boundary term B. Starting from a variational approach, we derive the field equations and compare them with respect to those of f (Q) gravity in the limit of B 0 B → 0. It is possible to show that f (Q, B) =f (Q-B) f (Q, B) = f (Q - B) models are dynamically equivalent to f (R) gravity as in the case of teleparallel f (B-T) f (B ~ - T) gravity (where B B B ≠ B ~). Furthermore, conservation laws are derived. In this perspective, considering boundary terms in f (Q) gravity represents the last ingredient towards the Extended Geometric Trinity of Gravity, where f (R), f (T, B) f (T, B ~), and f (Q, B) can be dealt under the same standard. In this perspective, we discuss also the Gibbons–Hawking–York boundary term of General Relativity comparing it with B in f (Q, B) gravity.
Capozzıello et al. (Tue,) studied this question.