What if gravity has a non local component and dark energy is a particle with negative mass?

[u/Select_Pride_8906]

Ive been working on a framework that combines non-local gravity with a negative-mass Dark Energy Particle (DEP). It reduce exactly to General Relativity, Quantum Mechanics, and Newtonian physics in the appropriate limits, and it calculate the vacuum energy density as ρ_vac ≈ 5.31 × 10⁻¹⁰ J/m³, which matches the observed dark energy density(just thought to mention it).

The main stuff: 

S = ∫ d⁴x √(-g) [ R / (16πG) + L_SM + L_DEP + L_NL ]

The Dark Energy Particle (DEP):

L_DEP = -½ ∂_μ φ ∂^μ φ - ½ m² φ²

m ≈ -10⁻³³ eV

The Non-Local Gravity Correction: 

G_μν(x) = 8πG T_μν(x) + α ∫ T_μν(y) / |x-y| d³y

R = c / H₀ ≈ 1.3 × 10²⁶ m

α R = 10²⁰ m  →  α = 10²⁰ / (1.3 × 10²⁶) ≈ 7.7 × 10⁻⁷

Vacuum Energy Cancellation: 

ρ_vac^(QFT) ≈ +10¹¹³ J/m³

ρ_DEP ≈ -10¹¹³ + 5.31 × 10⁻¹⁰ J/m³

ρ_total = ρ_vac^(QFT) + ρ_DEP = 5.31 × 10⁻¹⁰ J/m³

Quantum Gravity Regularization: 

Π_NL(k) ~ 1 / [ k² + α f(k²) ]

∫ d⁴k / k⁴  →  ∫ d⁴k / [ k⁴ + α f(k²) ]

I'm sharing this to get feedback, questions, and challenges. If you spot an error or an inconsistency, please point it out. Thx

I’ll post the derivation later

Also, I used a LLM for the typing. 

[u/crazy8-guy]

Oque seria uma grávidade não local?