Tee-How Loo

While conformal transformations in metric scalar-tensor theories recover General Relativity, this feature is notably absent in standard non-metricity-based theories. We demonstrate that by introducing the boundary term C, a non-metricity scalar-tensor theory can recover Symmetric Teleparallel Equivalent of General Relativity (STEGR) in the Einstein frame. Motivated by this, we propose a novel gravity model where a scalar field couples nonminimally to both the non-metricity scalar Q and the boundary term C. We focus in the cosmological scenario where we present the covariant formulation and a unified autonomous system framework that treats generic affine-connection choices, including coincident and non-coincident gauges, on an equal footing. Our dynamical analysis across three connection branches reveals standard thermal histories and stable de Sitter attractors. These results show that boundary-term couplings provide a well-posed, geometrically flexible route to addressing late-time cosmic acceleration.

The symmetric teleparallel theory offers an alternative gravitational formulation which can elucidate events in the early and late universe without requiring the physical existence of dark matter or dark energy. In this formalism, f ( Q,C ) gravity has been recently introduced by incorporating the boundary term C with the non-metricity scalar Q . In this paper, we develop the theory of cosmological scalar perturbation for f ( Q,C ) gravity, and retrieve that of f ( R̊ ) and f ( Q ) gravity from our result. The analysis assumes a model-independent approach within these theories that adheres to the conventional continuity equation at the background level. We derive the density contrast equation by employing some standard cosmological approximations, where the f ( Q,C ) theory is encoded in the effective Newtonian constant G _eff . Finally, we derive the evolution equation of density growth f _g .

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat Friedmann–Lemaître–Robertson–Walker background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard ΛCDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe’s evolution while providing new phenomenology that can be tested by upcoming surveys.

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard $Λ$CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.

The vanishing affine connections have been used solely while adopting the modified f(Q) gravity theory to the cosmology. Consequently, researchers could not get beyond what is already known in f(T) theory earlier. To alleviate this problem, in the present manuscript we investigate a recently proposed construction of f(Q) theory using non-vanishing affine connection in the spatially flat FLRW spacetime. We then investigate the cosmological solutions of f(Q) theory for a perfect fluid through the phase space analysis. We introduce few variables and dimensionless parameters to construct the corresponding equations suitable for the dynamical system approach. The conservation of the energy-momentum tensor leads to a constraint equation that relates the dynamical variables. Briefly, both unstable and stable de Sitter solutions appear which correspond to early and late times accelerated expansions. Also, unstable points corresponding to the matter dominated and radiation dominated eras have been found which do exist for every f(Q) function. As a result, the present discussion shows that f(Q) gravity endowed by non-vanishing affine connections is capable of explaining a true sequence of cosmic eras.