Cosmological reconstruction and Lambda CDM universe in f(Q, C) gravity

Symmetric Teleparallel Gravity allows for the reformulation of gravity in the form of nonmetricity by vanishing the contorsion term in the generic affine connection. Our focus is on investigating a recently proposed extension of this theory in which the Lagrangian has the form f(Q, C) by incorporating the boundary term C. In this work, we first use a reconstruction approach in f(Q, C) gravity that might admit the Lambda CDM expansion history. Furthermore, we perform a novel approach for cosmological reconstruction of f(Q, C) gravity in terms of e-folding, and it shows how any FLRW cosmology can arise from a specific f(Q, C) gravity. A variety of instances are provided using this approach in which f(Q, C) gravity is reconstructed to yield the well-known cosmic evolution: Lambda CDM era, acceleration/deceleration era which is equivalent to the presence of phantom and non-phantom matter, late-time acceleration with the crossing of phantom-divide line and transient phantom era.