Avik DeTee-How LooEmmanuel N. Saridakis2024-12-262024-12-262024-03-0110.1088/1475-7516/2024/03/050https://dspace-cris.utar.edu.my/handle/123456789/8133<jats:title>Abstract</jats:title> <jats:p>We formulate <jats:italic>f</jats:italic>(<jats:italic>Q,C</jats:italic>) gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar <jats:italic>Q</jats:italic> we incorporate in the Lagrangian the boundary term <jats:italic>C</jats:italic> of its difference from the standard Levi-Civita Ricci scalar  <jats:italic>R̊</jats:italic>. We extract the general metric and affine connection field equations, we apply them at a cosmological framework, and adopting three different types of symmetric teleparallel affine connections we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.</jats:p>journal-article