The role of the boundary term in $f(Q,B)$ symmetric teleparallel gravity

Understand

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 $B\to0$.
• It is possible to show that $f(Q,B)=f(Q-B)$ models are dynamically equivalent to $f(R)$ gravity as in the case of teleparallel $f(\tilde{B}-T)$ gravity (where $B\neq \tilde{B}$).
• Furtherrmore, conservation laws are derived.