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This theoretical study examines how energy and momentum are distributed between different components in modified gravity cosmological models, specifically analyzing a two-fluid system where matter sectors may exchange energy. The researchers demonstrate that without specifying the underlying physical action, conservation laws become ambiguous, leading to mathematical singularities where the standard general relativity limit cannot be smoothly recovered. They solve the mathematical structure of these models and identify conditions where the density reconstruction breaks down, revealing that phenomenological assumptions about energy transfer can produce artifacts that don't reflect genuine physical predictions.
Why it matters
This work establishes critical mathematical consistency checks for modified gravity theories that attempt to explain dark energy and cosmic acceleration. By distinguishing between predictions derived from fundamental physics versus those arising from ad-hoc mathematical assumptions, it helps theorists avoid interpreting spurious features as real physical effects in alternative cosmological models.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: In multi-fluid, matter-type gravity, the Bianchi identity constrains the divergence of the total effective stress tensor but does not, by itself, determine the currents assigned to its constituent sectors. Those currents are selected only after the off-shell matter action and equations, or an additional phenomenological closure, have been specified. We formulate this distinction and examine a spatially flat two-fluid background inspired by scale-independent EMSG. The case study combines an algebraic perfect-fluid prescription with a vanishing contracted-Hessian contribution, together with separate conservation of the total conventional and modification sectors. Because neither assumption is derived here from a concrete off-shell fluid action, the resulting system is an effective background closure rather than a microscopic EMSG model. For unequal EoS and every $alphane0$, the closure yields a Barrow-Clifton system whose transfer coefficients depend on $(w_1,w_2)$ but not on $alpha$. Hence the nonzero-$alpha$ family is singular: its $alphato0$ limit does not recover the uncoupled GR conservation laws. We solve the two density eigenmodes and derive the associated modified Li’enard equation for $H$. We also prove that the discriminant governing rank loss of the density-reconstruction map is strictly positive for every finite $w_1ne w_2$. Thus each genuinely quadratic case has two distinct real rank-degenerate couplings. Exact vacuum and stiff-fluid families illustrate modal cancellation. When today’s conventional densities are positive, the intervals on which both remain positive generally terminate at finite endpoints in the parameter ranges analyzed explicitly. These results provide a consistency diagnostic for separating action-level predictions from closure artifacts in multi-fluid, matter-type gravity; they do not establish an observationally viable EMSG model.