Galaxy Rotation Curves and Dark Energy: A Gravitational Entropy Perspective

We propose a phenomenological framework (the GEE framework) based on gravitational dissipative structures and the holographic principle, in which the observational effects conventionally attributed to dark matter and dark energy are reinterpreted as effective projections of coarse-grained gravitational degrees of freedom. Convention: Throughout this paper we adopt natural units unless otherwise stated. GEE assumes zero particle mass for the dissipative-structure gravitational gradient: . The framework introduces a dimensionless effective gravitational entropy order parameter and a dissipative-structure order parameter , and fuses gravitational relaxation with the holographic principle: gravitational relaxation provides the dynamical background for the formation of dissipative structures, while the holographic principle provides the energy-density formulas for the dissipative-structure gravitational gradient and for the effective energy density driving cosmic accelerated expansion. The two meet through the gravitational entropy . serves as a specified proportionality relation, stipulating that the energy released by gravitational relaxation is proportional to the system mass, but it does not directly enter the fusion equation. Hubble parameter evolution (core revision): In the GEE framework there are two temperatures—the thermodynamic temperature and the gravitational entropy temperature . We define the temperature ratio The core statement is . Temperature conversion drives the Hubble parameter to evolve monotonically from to , with the instantaneous present value . The "Hubble tension" of the standard model does not exist in GEE, because is not a single constant. is the instantaneous value of at the present epoch, not an artificial compromise prior. Holographic dissolution of the dissipative-structure gravitational gradient: GEE does not use particle components. The observational effects conventionally attributed to dark matter are reinterpreted in GEE as the effective projection of the galactic dissipative-structure gravitational gradient under a holographic cutoff. We adopt a holographic model with the Granda-Oliveros (Ricci) cutoff. This cutoff is introduced as a phenomenological assumption (Assumption 19); its first-principles derivation from the first law of thermodynamics on the horizon is left to Sec. 11.1. In a universe containing only baryons and radiation, we assume the effective energy density of the dissipative-structure gravitational gradient evolves as a power law during the dissipative-structure-dominated era, where is an independent phenomenological parameter. The GO cutoff naturally gives in the matter-dominated era; the observational requirement corresponds to , and the difference is absorbed by a phenomenological correction (Sec. 6.1). Through a coarse-graining map and the Poisson equation, an effective gravitational potential correction is derived from local Ricci curvature fluctuations: where is a dimensionless phenomenological coupling. Phenomenological construction of the k-essence Lagrangian: The k-essence Lagrangian is constructed phenomenologically from the holographic energy density and the k-essence definition ( is a phenomenological assumption): During the dissipative-structure-dominated era, taking , the Lagrangian is approximately where has dimensions of energy density. The exponent is determined by observational constraints on the effective sound speed of the dissipative-structure gravitational gradient: A typical value is , corresponding to an effective sound speed which satisfies the observational constraint . corresponds to extreme fine-tuning ; its naturalness is left to Sec. 11.1. The relation between and has been rigorously computed from the k-essence equation of motion given the form of : During the dissipative-structure-dominated era, , , and , approximately mimicking matter behavior. The applicability conditions for this approximation are and , which are satisfied during the dissipative-structure-dominated era. is a consequence of the phenomenological assumption; its applicability requires numerical verification. Dissolution of the effective energy density driving cosmic accelerated expansion: GEE does not use material components. The observational effects conventionally attributed to dark energy are reinterpreted in GEE as the effective energy density driving cosmic accelerated expansion. It is generalized to a two-layer structure consisting of a holographic component and an early peak (EDE) component, coupled to the dissipative-structure gravitational gradient through an interaction. The early peak fraction is dominated by Jeans-mass halos at . Cross-validation using both the Press-Schechter and Sheth-Tormen mass functions yields (PS) and (ST), compatible with the observed value (the ST upper bound touches the boundary and is labeled marginal). The early peak decays after the peak according to a parameterized form (Sec. 7.2), without violating recombination constraints. An interaction between the expansion energy density and the dissipative-structure gravitational gradient is introduced: where controls the delayed onset of the interaction. In the early universe, the gravitational temperature is suppressed by the thermodynamic temperature, , and the interaction is not yet effective; as the universe expands, , the interaction becomes effective at low redshift, flips the sign of , and brings it into agreement with the DESI DR2 (DESI+CMB+SNe) preference. gives , compatible with DESI DR2's at the boundary; gives , closer to the DESI DR2 central value. The model is compatible with current data in this parameter range and requires further testing with future DESI DR3/Euclid data. Unified dissolution equation: where is the energy-momentum tensor of the holographic projection of the dissipative-structure gravitational gradient, is the effective energy-momentum tensor of the expansion energy density, and is the interaction energy-momentum tensor between the expansion energy density and the dissipative-structure gravitational gradient. Key numerical values: (independent phenomenological parameter), (late-universe phenomenological value), (phenomenological correction), , , (PS/ST cross-validation), , , (temperature-conversion evolution values), (energy-density amplitude), (phenomenological range), (phenomenological choice), (definition/phenomenological choice), . Current statistical status: In the Planck+SH0ES combined data, an approximate estimate gives a difference between the GEE and the standard cosmological model of to . This estimate does not include parameter-count penalties; GEE has 10 more phenomenological parameters than the standard cosmological model, and AIC/BIC are expected to penalize GEE. A precise Bayes factor requires a full MCMC analysis, with the calculation scheme given in Sec. 11.4.6. The expectation is , i.e., the standard cosmological model is strongly to decisively preferred, unless the likelihood improvement of GEE far exceeds the current approximate estimate. The currently reportable conclusion is: in the combined data, GEE and the standard cosmological model are statistically indistinguishable; with Planck data alone, the standard cosmological model is preferred.