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f(R) gravity — the fRn1 suite

The f(R) (n = 1) twin campaign re-runs the 64 ΛCDM design cosmologies with a fifth parameter logf_R0 = log10(|f_R0|) ∈ [−7, −4], reusing the matched ΛCDM initial-condition seeds. Address it with gravity="fRn1" and a 5-parameter θ:

th5 = [0.31, 0.677, 0.967, 0.83, -5.0]   # [Omega_m, h, n_s, S_8, logf_R0]
xi  = reg.predict("xi_mm", "fRn1", 0.25, th5)

Every gate of the ΛCDM sections runs unchanged at the fRn1 key.

How the f(R) artifacts are built

Most f(R) artifacts emulate the modified-gravity boost over the matched ΛCDM twin, not the absolute quantity, because the shared seeds let the difference cancel cosmic variance:

\[X_{f(R)}(\theta_5) = B(\theta_5)\, X_{\Lambda\mathrm{CDM}}(\theta_5[:4])\]
Property f(R) representation
hmf multiplicative boost (MGBoostEmulator)
pk_mm multiplicative boost
xi_mm additive Δξ boost
vel_* (7/8) additive δ boost, arcsinh
vel_m10 direct 5-parameter GP
b_cum direct 5-parameter peak-height GP

Boost artifacts pin the sha256 of their ΛCDM base; retraining the base forces a re-pin. The choice of boost vs direct GP per property is evidence-based — see Representations.

Out-of-sample references

Two 100-box fiducials at the GR fiducial background, with independent seeds, are the sharp out-of-sample tests (not limited by the 5-box sampling floor):

  • F5n1 — logf_R0 = −5 (get_cosmology("fRn1", 0)).
  • F6n1 — logf_R0 = −6 (get_cosmology("fRn1", -1)).

Accuracy (z = 0.25)

  • Composed boosts 0.5–0.9 % LOO.
  • hmf fiducial OOS 0.3–0.5 % with the screened tail resolved (see HMF).
  • ξ_hh 2.0–2.6 % to 60 Mpc/h.
  • Velocity moments: low/3rd moments χ ≈ 1; high even moments χ ≈ 1.4–2.3 (a design-sampling limit).

Improving the f(R) emulators with new simulations

The high even velocity moments (c02, c40, c22, c04) plateau because 64 design points are sparse in 5D. A learning-curve experiment (velocity_frn1_learning_curve.py) shows the design is still in the undersampled regime: adding new f(R) + ΛCDM simulation pairs gives roughly a 10–15 % χ reduction for +8 pairs and 20–25 % for +16, enough to bring c40/c02/c22 near the floor but not, by itself, to break the c04 plateau (which needs tens of pairs).

A sequential maximin infill design provides an ordered list of new 5D cosmologies, each filling the largest remaining hole, biased toward the chameleon screening transition (logf_R0 ~ −5.5 to −6, where the response is steepest):

micromamba run -n cosemu python3 haloemu/properties/generate_frn1_infill.py \
    --n-new 64 --out doc/frn1_infill_design.csv

Each row is one simulation pair — the f(R) run at the five parameters plus a matched-seed ΛCDM twin at the four background parameters, with new IC seeds (ibox ≥ 6). Run the top K for whatever budget you have. Full recipe and numbers: doc/frn1_new_runs_velocity.tex and the methods paper.

Caveats specific to f(R)

  • The frozen-seed large-scale offset affects ξ / ξ_hh for fRn1 as for ΛCDM — confirmed at both independent-seed fiducials. See Caveats.
  • Near the GR limit logf_R0 → −7 the f(R) response → ΛCDM, so the boost carries little information there.