We explore an extension of the symmetric teleparallel gravity denoted the f(Q) theory, by considering a function of the nonmetricity invariant Q as the gravitational Lagrangian. Some interesting properties could be found in the f(Q) theory by comparing with the f(R) and f(T) theories. The field equations are derived in the f(Q) theory. The cosmological application is investigated. In this theory the accelerating expansion is an intrinsic property of the universe geometry without need of either exotic dark energy or extra fields. And the state equation of the geometrical dark energy can cross over the phantom divide line in the f(Q) theory. In addition, the dynamical system method are investigated. It is shown that there are five critical points in the STG model for taking f(Q)=Q+α Q² . The critical points P₄ and P₅ are stable. P₄ corresponds to the geometrical dark energy dominated de Sitter universe ( wₜₒₜᵉᶠᶠ=-1 ), while P₅ corresponds to the matter dominated universe ( wₜₒₜᵉᶠᶠ=0 ). Given that P₄ represents an attractor, the cosmological constant problems, such as the fine tuning problem, could be solved in the STG model.
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Lu et al. (2019) studied this question.