Linear Perturbations and Multi-Probe Diagnostics in Dark-Sector Selective $f(R,T_χ)$ Gravity

We develop a dark-sector selective trace-coupled extension of gravity in which the matter–curvature coupling depends exclusively on the trace of the dark-matter energy–momentum tensor, $T_χ$, defined from a canonical dark-matter field $χ$. This construction provides a microphysically specified trace sector, removes the usual matter-Lagrangian ambiguity of $f(R,T)$-type models, and preserves minimal coupling of visible matter by design. We derive the full field equations, the exact dark-sector exchange structure, and the linear scalar-perturbation system in gauge-ready form. In the sub-horizon regime, we derive effective modified-gravity functions governing structure growth and light deflection, and show that the model generically produces correlated, scale- and time-dependent departures from General Relativity in growth and lensing observables. Building on this structure, we formulate a perturbation-focused multi-probe framework based on redshift-space distortions, weak lensing, and CMB lensing, explicitly targeting degeneracy breaking beyond background-expansion tests. The analysis establishes the action-level and perturbation-level foundations of the model and provides a conservative, reproducible framework for translated linear-regime constraints within a dark-sector selective modified-gravity setting.

💡 Research Summary

The authors introduce a novel modification of gravity in which the trace‑coupling of the gravitational Lagrangian is restricted solely to the dark‑matter sector. In practice the theory is defined by the action
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