Proca-stinated cosmology. Part I. A N-body code for the vector Galileon
Christoph Becker, Christian Arnold, Baojiu Li, Lavinia Heisenberg · 2020 · 7 citationsRead the paper
We investigate the nonlinear growth of large-scale structure in the generalised Proca theory, in which a self-interacting massive vector field plays the role of driving the acceleration of the cosmic expansion. Focusing to the Proca Lagrangian at cubic order—the cubic vector Galileon model—we derive the simplified equations for gravity as well as the longitudinal and transverse modes of the vector field under the weak-field and quasi-static approximations, and implement them in a modified version of the ECOSMOG N -body code. Our simulations incorporate the Vainshtein screening effect, which reconciles the fifth force propagated by the longitudinal mode of the cubic vector Galileon model with local tests of gravity. The results confirm that for all scales probed by the simulation, the transverse mode has a negligible impact on structure formation in a realistic cosmological setup. It is well known that in this model the strength of the fifth force is controlled by a free model parameter, which we denote as 3 . By running a suite of cosmological simulations for different values of 3 , we show that this parameter also determines the effectiveness of the Vainshtein screening. The model behaves identically to the cubic scalar Galileon for 0 3 → , in which the fifth force is strong in unscreened regions but is efficiently screened in high-density regions. In the opposite limit, 3 → ∞ , the model approaches its 'quintessence' counterpart, which has a vanishing fifth force but a modified expansion history compared to ΛCDM. This endows the model with rich phenomenology, which will be investigated in future works.
What the full text shows
Working prototype- The transverse mode of the vector field has a negligible impact on structure formation compared to the longitudinal mode. — Power spectrum P(k; ∂i∂2χ) is 15-20 orders of magnitude larger than P(k; ∂2Bi) (All scales probed by the simulation in a realistic cosmological setup)
- The model parameter ˜β3 controls the effectiveness of Vainshtein screening; higher values lead to less efficient screening. — ˜β3 ~ O(100) results in a screening radius nearly an order-of-magnitude smaller than the csG counterpart at a ≈ 1 (At scale factor a ≈ 1)
- The cvG model mimics the cubic scalar Galileon (csG) behavior in the limit of small ˜β3. — Indistinguishable evolution for a < 0.1 and for ˜β3 → 0 (Early times or small ˜β3)
- In the limit of large ˜β3, the model approaches a 'quintessence' counterpart (QCDM). — RV → 0, ϵ → ∞, Geff/G → 1 (˜β3 → ∞)
- Vainshtein screening suppresses the fifth-force, preventing excessive clustering at small scales. — Scales of k ≈ 4 h/Mpc are screened for ˜β3 = (10^-6, 1) at a = 1 (Non-linear regime)
- Setup
- Modified ECOSMOG N-body simulation code; tested across various ˜β3 values (10^-6, 1, 100, 10^2).
- How
- The authors adapted the ECOSMOG N-body code to implement gravity and vector field equations under weak-field and quasi-static approximations. They performed a suite of cosmological simulations varying the ˜β3 parameter to analyze the longitudinal and transverse modes and the Vainshtein screening effect.
- Limitations
- Used weak-field and quasi-static approximations. · Simplified the equation of motion for the transverse mode. · Used a perturbed constraint equation to eliminate time derivatives for the longitudinal mode.
Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it