Dark Energy vs Modified Gravity

Current Values

Instructions

• Background expansion H(z) depends on energy content (Ω_m, Ω_Λ)
• Growth of structure depends on gravity theory via growth index γ
• GR predicts γ ≈ 0.55, modified gravity predicts γ ≠ 0.55
• Degeneracy: different theories can have same H(z) but different growth
• Observable fσ₈(z) from redshift-space distortions tests gravity

Physics

Dark energy and modified gravity both explain cosmic acceleration but differ in structure growth.

Background: H(z) = H₀√[Ω_m(1+z)³ + Ω_Λ]

Growth rate: f(z) = Ω_m(z)^γ
where Ω_m(z) = Ω_m(1+z)³/[Ω_m(1+z)³ + Ω_Λ]

Growth index:
• γ ≈ 0.55 for ΛCDM/GR
• γ ≠ 0.55 for modified gravity (f(R), DGP, etc.)

Observable: fσ₈(z) = f(z) × σ₈(z) measured from galaxy surveys