Exact cosmological solutions in vacuum non-coincidence f(Q)-theory

• The non-coincident branch introduces a genuine dynamical scalar degree of freedom from the connection, allowing a scalar-tensor representation of the theory and enabling nontrivial vacuum solutions. • We obtain cosmologically significant analytic solutions including de Sitter, scaling regimes, ΛCDM mimicking dynamics, standard and generalized Chaplygin gas, and CPL parameterizations, all reconstructed within the f ( Q ) framework. • These analytic solutions show that the non-coincident formulation admits a richer solution space than both the coincident gauge and f ( T ) teleparallel limits, capturing both early and late accelerated phases without matter sources. • The results demonstrate that non-coincident f ( Q ) gravity can unify inflation and late acceleration geometrically, offering a promising alternative to dark-energy driven ΛCDM. We study exact cosmological solutions in f ( Q ) gravity formulated beyond the coincident gauge, focusing on the non-coincident connection branch Γ B . Using a minisuperspace approach, the field equations are recast into an equivalent scalar-tensor form, enabling analytic reconstruction of cosmological models. We obtain exact solutions of particular interest, including de Sitter, scaling, ΛCDM, Chaplygin gas, generalized Chaplygin gas, and CPL parameterizations. The corresponding scalar potentials and f ( Q ) functions are derived in closed or parametric form. Our analysis shows that non-coincident f ( Q ) gravity admits a richer solution space than the coincident case and can describe both early-time inflationary dynamics and late-time acceleration within a unified framework. These results open new directions for testing f ( Q ) cosmology against observations and exploring its role as a viable alternative to ΛCDM.