Ambiguity in matter sector for modified gravity involving δ 2 ℒm/δ gμ ν δ gα β and its implications to astrophysics and cosmology
- 1Universitas Indonesia
Abstract
Matter density (ρ) and radial pressure (p) are often used as the matter Lagrangian density (ℒm) because both are thermodynamically consistent and produce the same Einstein field equation (EFE) in general relativity (GR). New gravity models with explicit links between matter and geometry instead involve second-order derivatives of ℒm relative to the metric tensor. So, picking either p or −ρ for ℒm gives different effective EFEs. This confusion appears because one usually treats the four-velocity (uμ) and the metric tensor (gμ ν ) as independent. Here, we revisit the basics and offer a consistent framework by relaxing that assumption, thereby making the modified gravity theory independent of the choice of ℒm. Finally, we test this approach on neutron and quark stars (ultraviolet region) and on cosmological situations with matter-dominated or dust (p=0), radiation-dominated (p=ρ /3), and vacuum energy (p=−ρ) equations of state (infrared region), showing how it clarifies the ambiguity in picking ℒm for gravity models.
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BibTeX
@article{jayawiguna2026ambiguity,
title = {{Ambiguity in matter sector for modified gravity involving $$\delta ^2 \mathcal L_m/\delta g^\mu \nu \delta g^\alpha \beta $$ and its implications to astrophysics and cosmology}},
author = {B. N. Jayawiguna and A. Sulaksono},
journal = {The European Physical Journal C},
year = {2026},
month = nov,
doi = {10.1140/epjc/s10052-026-16443-z},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16443-z},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Ambiguity in matter sector for modified gravity involving δ ^2 ℒ_m/δ g^μ ν δ g^α β and its implications to astrophysics and cosmology
AU - B. N. Jayawiguna
AU - A. Sulaksono
PY - 2026
DA - 2026/11/03
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16443-z
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16443-z
AB - Matter density (ρ) and radial pressure (p) are often used as the matter Lagrangian density (ℒ_m) because both are thermodynamically consistent and produce the same Einstein field equation (EFE) in general relativity (GR). New gravity models with explicit links between matter and geometry instead involve second-order derivatives of ℒ_m relative to the metric tensor. So, picking either p or −ρ for ℒ_m gives different effective EFEs. This confusion appears because one usually treats the four-velocity (u_μ) and the metric tensor (g_μ ν ) as independent. Here, we revisit the basics and offer a consistent framework by relaxing that assumption, thereby making the modified gravity theory independent of the choice of ℒ_m. Finally, we test this approach on neutron and quark stars (ultraviolet region) and on cosmological situations with matter-dominated or dust (p=0), radiation-dominated (p=ρ /3), and vacuum energy (p=−ρ) equations of state (infrared region), showing how it clarifies the ambiguity in picking ℒ_m for gravity models.
SN - 1434-6052
ER -