The logotropic dark fluid as an energy diffusion in unimodular gravity
Abstract
We show that the logotropic dark fluid, proposed as a single-fluid unification of dark matter and dark energy, is exactly dissipative unimodular gravity with pressureless matter and the logarithmic energy diffusion function Q(a)=3Aln a+Qc. The correspondence is exact at the level of the homogeneous background, rather than asymptotic, and introduces no parameters beyond those already present in either description. It provides a dynamical reinterpretation of the logotropic temperature A, whose origin was left open in the original proposal: up to the expansion rate, A is the rate at which energy is diffused from matter into the geometric sector, Q̇=3AH. The adiabatic sound speed of the effective fluid is cs2=A/ρ, where ρ is the unimodular matter energy density, and reaches the speed of light at as=aM/21/3; the matter energy density then vanishes and changes sign at aM, which is precisely the scale factor at which the model is known to become phantom. Since ρ coincides with the enthalpy density ε+P of the logotropic fluid, the phantom branch is the branch on which the matter sector carries negative energy density and on which the apparent horizon entropy decreases. Finally, we show that a one-parameter saturating diffusion law removes these late-time pathologies while preserving the low-redshift phenomenology.
Related
- Unimodular Gravity with Arbitrary Diffusion Function: A Dynamical System Reconstruction Approach
- Observational constraints on Diffusion Cosmologies in Unimodular Gravity from DESI DR2
- Lifshitz Phase of Quantum Gravity: The Infrared Fixed Point of the (2+1)D Unimodular Hořava-Chern-Simons Model
- Spherical thin shells with charge in unimodular gravity
- Dymnikova Black Holes in Unimodular Gravity: Maxwell Sources and Vacuum Contributions
BibTeX
@misc{cruz2026logotropic,
title = {{The logotropic dark fluid as an energy diffusion in unimodular gravity}},
author = {Miguel Cruz and Samuel Lepe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21006},
eprint = {2609.21006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21006},
}
RIS
TY - UNPB
TI - The logotropic dark fluid as an energy diffusion in unimodular gravity
AU - Miguel Cruz
AU - Samuel Lepe
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.21006
UR - https://arxiv.org/abs/2609.21006
AB - We show that the logotropic dark fluid, proposed as a single-fluid unification of dark matter and dark energy, is exactly dissipative unimodular gravity with pressureless matter and the logarithmic energy diffusion function Q(a)=3Aln a+Q_c. The correspondence is exact at the level of the homogeneous background, rather than asymptotic, and introduces no parameters beyond those already present in either description. It provides a dynamical reinterpretation of the logotropic temperature A, whose origin was left open in the original proposal: up to the expansion rate, A is the rate at which energy is diffused from matter into the geometric sector, Q̇=3AH. The adiabatic sound speed of the effective fluid is c_s^2=A/ρ, where ρ is the unimodular matter energy density, and reaches the speed of light at a_s=a_M/2^1/3; the matter energy density then vanishes and changes sign at a_M, which is precisely the scale factor at which the model is known to become phantom. Since ρ coincides with the enthalpy density ε+P of the logotropic fluid, the phantom branch is the branch on which the matter sector carries negative energy density and on which the apparent horizon entropy decreases. Finally, we show that a one-parameter saturating diffusion law removes these late-time pathologies while preserving the low-redshift phenomenology.
ER -