Nonzero Spatial Curvature in Symmetric Teleparallel Cosmology

Abstract: We consider the symmetric teleparallel $f\left( Q\right) $-gravity in Friedmann--Lema^{\i}tre--Robertson--Walker cosmology with nonzero spatial curvature. For a nonlinear $f\left( Q\right) $ model there exist always the limit of General\ Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models $f_{A}\left( Q\right) \simeq Q^{\frac{\alpha}{\alpha-1}}% ~,~f_{B}\left( Q\right) \simeq Q+f_{1}Q^{\frac{\alpha}{\alpha-1}}$ and $f_{C}\left( Q\right) \simeq Q+f_{1}Q\ln Q$ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.