Reproducing ΛCDM-like solutions in <i>f</i>(<i>Q</i>) gravity: a comprehensive study across all connection branches

Abstract Given the remarkable success of the ΛCDM model in fitting various cosmological observations, a pertinent question in assessing the phenomenological viability of modified gravity theories is whether they can reproduce an exactly ΛCDM-like cosmic background evolution. In this paper, we address this question in the context of f ( Q ) gravity, where Q denotes the nonmetricity scalar. It is known that there are three possible symmetric teleparallel connection branches that respect the cosmological principles of spatial homogeneity, isotropy, and global spatial flatness. By enforcing a ΛCDM-like background evolution via the cosmographic condition j ( z ) = 1, where j is the jerk parameter, we reconstruct the ΛCDM-mimicking f ( Q ) theory for each of the three possible connection branches. For the first connection branch, also known as the “coincident gauge” in cosmology, we recover the previously known result that a theory of the form f ( Q ) = -2Λ + αQ + β √ Q can exactly reproduce a ΛCDM-like cosmic evolution. Furthermore, we establish that the stability of the ΛCDM-like cosmic solution within this reconstructed f ( Q ), as well as the robustness of the reconstructed f ( Q ) form with respect to small errors in the astrophysical measurements of the jerk parameter. For the second connection branch, we analytically reconstruct the ΛCDM-mimicking f ( Q ) to be of the form f ( Q ) = -2Λ + αQ - βQ 2 . For the third connection branch, we could decouple the evolution equation for the dynamical connection function, which enabled us to perform a numerical reconstruction. Our analysis proves that, at least at the background level, it is possible to obtain ΛCDM-mimicking f ( Q ) models for all the three possible connection branches. These models effectively reduce to (STE)GR in the past while possessing a positive effective gravitational coupling throughout.