From c4df9645336fb3ba30c301a5fbece81c0fd02cd1 Mon Sep 17 00:00:00 2001 From: SethulekshmiBeena Date: Mon, 2 Nov 2026 22:06:28 +0000 Subject: [PATCH 1/4] Add scripts/validate.py: x_e and g(z) residuals against CAMB/RECFAST Reports the residual in three parts (last-scattering window, most negative, most positive over z = 200-2000) for the pure Peebles model and the F = 1.14 variant, plus the helium-era minimum and the tau-integrator cross-check. Adds residual tolerance tests (measured values, not targets) and an explicit check that the visibility function integrates to 1 within 1e-6. No change to the physics or numerical methods. Co-Authored-By: Claude Opus 5.5 --- figures/validation.pdf | Bin 0 -> 35804 bytes figures/validation.png | Bin 0 -> 270962 bytes results/validation.json | 97 +++++++++++++ results/validation.md | 23 +++ scripts/validate.py | 265 ++++++++++++++++++++++++++++++++++ src/cmb_decoupling/results.py | 104 +++++++++++++ tests/test_regression.py | 20 ++- tests/test_visibility.py | 7 + 8 files changed, 515 insertions(+), 1 deletion(-) create mode 100644 figures/validation.pdf create mode 100644 figures/validation.png create mode 100644 results/validation.json create mode 100644 results/validation.md create mode 100644 scripts/validate.py diff --git a/figures/validation.pdf b/figures/validation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6a677e94a400f594f2b95f5721d7d287cc3df09c GIT binary patch literal 35804 zcma&N19WBEw(niBZQHhOTNSR@b_EqXso1tFs@S$|+h%>Kz4tly-1hGG?rUjntue;z zV~&6CbFSGk`s_b4MNx4&CVEzAvWhjr@)l?&LPkP6LrZ90UP1;{4|@|r1`&WWz}n7? zkU8Lha9GMa4g*n7BI=GDz8c zN)Z0%TjZZ_DMH=FMX`oCvx8o-Sl-Yxmh> z`ZM=Gqx0wRzrrbNVr%AXPRR6+1aS-N&j1iIh+BU~MbyN|&e-ISA5PAWCIA~~_l$F0 z?HJ=mhmE#}>Z9Z@UkO)7U-yX+um_b9y97yLt^#&KG?Nppm!s*(nBPusz14WVCA0YX zW_jvX{D``kUCR*c)cVVapKG38HalKA?K+=MW@9d+JD={i?_U-%HVMwIAD=GAr*VB_ ze*5sQ><)f*y0@wY@cm&Z%&ei&eSH>xV`U1c8O4Dt!}@wVae8^XzY|eE;|KBcme`da!1%artxEHw9e>|<|Cn!Cn#XV)dt%A1;92>h zKs9J-1U*mi`(^%`V^9E3-}h*0Hh?SWYh?9A-j}86-_O@ihv~iD|R+N zZ=WIrNWZ|{1;e4Si)Q&LA(X`DQ^I7!yYY;}i4jJq@Vf0@6q_a>Y@<3+TVSh7bf$iq zIGN7v9|RL$rYh0*$4hMb<3P+$+nLURoMd3RG&koCy_zNjVF{wS#Q8{cW-2`{HUsAR z|F%!!gTE8VU*?OqGo5W`n~-f;QrF+&t1Agc@x=t@`(~A~>{L_P(RB+@s-igbX7jn3r+GKUzgH8FX?DyVXw4j0f&xuR=Jtc~c)Pwz z1_7DV0N1sznx}&u&GokOzaM1yaBq5z%%yumQy#v4T22mGBv{U88=UOm_qyuo;PrWU z6(NpS67FDpI|#ridPg>75~o3+P^Cg^GFrG{*ei#uAt8qMp_(9H!O-h?+BXYP*vNJd z7%x5xkBWEad8ypNE7R%cS#WQhT_W6Q9%8!&KV500e}2O4JIxAkH{#|x?BV^!^D@43 zUVhfcGxx`ia-(!e?OJ@b1CB8~)7{DOp*?hwAL6gQKEwx|U^E#<)^TpcH+pO-9mbVUC0h7P!#IrUyg92m?>}G)Hp3FZC<0yXiQS(#; zF0aN2hsI-8TtCmwhYPC&&Z_3Hw!%i@(P~Qg zoy}AH=+-W2Ok$f&J`Gbn6Z-LLXtDXz;M_p!e~k!kpXIH{x%vHjWThl!;b#baj7`O! 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zQ(P74<3IodcmyVJyWcfP+{ljQo)PDtBFxyzgKGc^CD%#>PkhU%se>dZ5Z7c+mA;0B z5A=t{yvp{1!^tGkPepqaSD219(Vf;@@)AL5hfRhu<8&KItSG`+7Hg-lE&vvo1Axda zsAH{LD`u?Bf&zlL7oZ zasS>us!G}(?b@55#lmfei~ zWSn{Zd6bg4(1>OOolqJW-P%?WMykC1JuqPq2ofFRMi1qtijyiJX=x#rqDy&l<%2C( zK9FX;R;UGu~TVm`Jzd|(^#ZpfK0SA zVKfb=*r-sb@{CH5Jbm`}6{(=`^9PJt31Sn2k=~I(D;#t<%GN)pG~GE|8Q>{5$Q}KU zW|J72=V8QvG>^Z~D3g&2R*(Kwq00x{>l*};s6EXw&#poO&yq}!CR(IFW2nApAYE)A}n6Zv8BEv<5(>+%gqjn!D z*}De)ITro~WidN8xD$_@+kbq^dev9g=uSax+dC_q`X?suT-Rixw`WCH5|+n!m4Fk- z_wF$qD9nsULM1q0a}qgLACZa^;SB&>^R+F dict[str, object]: + """Run both codes and collect every number reported by this script.""" + cosmo = PLANCK2018 + ref = camb_reference(cosmo) + x_e = { + "camb": ref.x_e, + "peebles": solve_peebles(cosmo).x_e, + "peebles_fudge": solve_peebles(cosmo, fudge=RECFAST_FUDGE).x_e, + } + ls = {k: last_scattering(f, cosmo) for k, f in x_e.items()} + last_sc = {k: {"z_star": v.z_tau_one(), "z_peak": v.z_peak(), "fwhm": v.fwhm()[0]} for k, v in ls.items()} + resid = {k: residual_summary(x_e[k], ref.x_e, cosmo).as_dict() for k in MODELS} + for k in MODELS: + resid[k]["residual_at_freeze_out"] = float( + fractional_residual(x_e[k], ref.x_e, np.array(Z_FREEZE_OUT)) + ) + # Hydrogen-only era (Peebles ODE region) and the helium era beyond the main range. + z_switch = DEFAULT_Z_SWITCH + hydrogen_era = { + k: residual_summary(x_e[k], ref.x_e, cosmo, z_min=Z_VALIDATION_MIN, z_max=z_switch).as_dict() + for k in MODELS + } + z_he = np.linspace(z_switch, Z_HELIUM_MAX, N_HELIUM) + r_he = fractional_residual(x_e["peebles"], ref.x_e, z_he) + i_he = int(np.argmin(r_he)) + saha = last_scattering(lambda z: x_e_saha_full(z, cosmo), cosmo) + rec = ref.params.Recomb + recfast = { + "fudge": rec.RECFAST_fudge, + "Hswitch": bool(rec.RECFAST_Hswitch), + "gauss_centres_z": [float(np.exp(rec.zGauss1) - 1.0), float(np.exp(rec.zGauss2) - 1.0)], + } + return { + "x_e": x_e, + "ls": ls, + "numbers": { + "camb_version": __import__("camb").__version__, + "camb_recombination": ref.recombination_model, + "last_scattering": last_sc, + "camb_recfast_settings": recfast, + "residuals_vs_camb": resid, + "residuals_hydrogen_era": hydrogen_era, + "residuals_helium_era": { + "z_min": z_switch, + "z_max": Z_HELIUM_MAX, + "min_residual": float(r_he[i_he]), + "z_min_residual": float(z_he[i_he]), + }, + "tau_integrator_check": { + "z_star_from_camb_xe": ls["camb"].z_tau_one(), + "z_star_camb_internal": ref.z_star, + }, + "saha": {"z_star": saha.z_tau_one(), "z_peak": saha.z_peak()}, + }, + } + + +def make_figure(data: dict[str, object]) -> None: + """Three-panel validation figure: x_e, fractional residual, visibility function.""" + x_e, ls, num = data["x_e"], data["ls"], data["numbers"] + window = ( + num["residuals_vs_camb"]["peebles"]["window_lo"], + num["residuals_vs_camb"]["peebles"]["window_hi"], + ) + z = np.geomspace(Z_VALIDATION_MIN, Z_VALIDATION_MAX, N_PLOT) + + fig = plt.figure(figsize=(6.4, 8.4)) + # Row 2 is an empty spacer: panel (c) has its own redshift axis. + gs = fig.add_gridspec(4, 1, height_ratios=[2.0, 1.4, 0.55, 2.0], hspace=0.08) + ax_x = fig.add_subplot(gs[0]) + ax_r = fig.add_subplot(gs[1], sharex=ax_x) + ax_g = fig.add_subplot(gs[3]) + + for k in ("camb", *MODELS): + ax_x.plot(z, x_e[k](z), **STYLES[k]) + ax_x.set_yscale("log") + ax_x.set_ylabel(r"Free-electron fraction $x_e = n_e/n_{\rm H}$") + ax_x.legend(loc="lower left") + ax_x.tick_params(labelbottom=False) + + for ax in (ax_x, ax_r): + ax.axvspan(*window, color=GUIDE_COLOR, alpha=0.15, lw=0) + ax_r.axhline(0.0, color=GUIDE_COLOR, lw=0.8) + for k in MODELS: + ax_r.plot(z, 100.0 * fractional_residual(x_e[k], x_e["camb"], z), **STYLES[k]) + ax_r.set_ylabel(r"$\Delta x_e / x_e^{\rm CAMB}$ [%]") + ax_r.text( + np.sqrt(window[0] * window[1]), 0.95, "last-scattering\nwindow", transform=ax_r.get_xaxis_transform(), + ha="center", va="top", fontsize=8, color="#404040", + ) # fmt: skip + ax_r.set_xscale("log") + ax_r.set_xlim(Z_VALIDATION_MAX, Z_VALIDATION_MIN) + ax_r.set_xticks(Z_TICKS, [str(t) for t in Z_TICKS]) + ax_r.xaxis.set_minor_locator(plt.NullLocator()) + ax_r.set_xlabel(r"Redshift $z$") + + ax_g.axvspan(*window, color=GUIDE_COLOR, alpha=0.15, lw=0, label="FWHM of CAMB $g(z)$") + for k in ("camb", *MODELS): + ax_g.plot(ls[k].z, ls[k].g * 1e3, **STYLES[k]) + ax_g.set_xlim(*G_PLOT_RANGE[::-1]) + ax_g.set_ylim(bottom=0) + ax_g.set_xlabel(r"Redshift $z$") + ax_g.set_ylabel(r"$g(z) = \frac{d\tau}{dz}\,e^{-\tau}$ [$10^{-3}$ per unit $z$]") + ax_g.legend(loc="upper left") + + # Panel tags placed where no curve passes. + for ax, tag, y, va in ((ax_x, "a", 0.95, "top"), (ax_r, "b", 0.06, "bottom"), (ax_g, "c", 0.95, "top")): + ax.text(0.98, y, f"({tag})", transform=ax.transAxes, ha="right", va=va, fontsize=11) + save(fig, FIG_DIR, "validation") + + +def write_tables(num: dict[str, object]) -> str: + """Write results/validation.{json,md} and return the Markdown.""" + ls, res = num["last_scattering"], num["residuals_vs_camb"] + cols = ("peebles", "peebles_fudge", "camb") + head = f"| | {LABELS['peebles']} | {LABELS['peebles_fudge']} | CAMB {num['camb_version']} (RECFAST) |" + lines = [head, "|---|---|---|---|"] + for key, label in ( + ("z_star", r"$z_\ast$ where $\tau = 1$"), + ("z_peak", "Peak of $g(z)$ per unit $z$"), + ("fwhm", "FWHM of $g(z)$"), + ): + lines.append(f"| {label} | " + " | ".join(f"{ls[c][key]:.2f}" for c in cols) + " |") + + def pct(x: float) -> str: + return f"{100 * x:+.2f}%" + + p = res["peebles"] + lines += [ + "", + r"Residuals $\Delta x_e/x_e = x_e/x_e^{\rm CAMB} - 1$ " + f"on $z = {p['z_min']:.0f}$–${p['z_max']:.0f}$ (grid spacing $\\Delta z = 0.1$). " + "Last-scattering window = FWHM of CAMB's $g(z)$, " + f"$z = {p['window_lo']:.1f}$–${p['window_hi']:.1f}$.", + "", + f"| | {LABELS['peebles']} | {LABELS['peebles_fudge']} |", + "|---|---|---|", + ] + rows = ( + ( + r"(a) max $\lvert\Delta x_e/x_e\rvert$ in the last-scattering window", + "max_abs_window", + "z_max_abs_window", + True, + ), + ("(b) most negative residual", "min_residual", "z_min_residual", False), + ("(c) most positive residual", "max_residual", "z_max_residual", False), + ) + for label, key, zkey, absolute in rows: + cells = [ + (f"{100 * res[m][key]:.2f}%" if absolute else pct(res[m][key])) + f" at $z = {res[m][zkey]:.1f}$" + for m in MODELS + ] + lines.append(f"| {label} | " + " | ".join(cells) + " |") + lines.append( + f"| residual at $z = {Z_FREEZE_OUT:.0f}$ | " + + " | ".join(pct(res[m]["residual_at_freeze_out"]) for m in MODELS) + + " |" + ) + h_era = num["residuals_hydrogen_era"] + he = num["residuals_helium_era"] + lines.append( + f"| range on $z = {Z_VALIDATION_MIN:.0f}$–${DEFAULT_Z_SWITCH:.0f}$ (hydrogen only) | " + + " | ".join(f"{pct(h_era[m]['min_residual'])} to {pct(h_era[m]['max_residual'])}" for m in MODELS) + + " |" + ) + tc = num["tau_integrator_check"] + rf = num["camb_recfast_settings"] + lines += [ + "", + f"Helium era, $z = {he['z_min']:.0f}$–${he['z_max']:.0f}$: most negative residual " + f"{pct(he['min_residual'])} at $z = {he['z_min_residual']:.1f}$ (both models; helium is in Saha).", + "", + "$\\tau$-integrator check: CAMB's $x_e$ through this code gives " + f"$z_\\ast = {tc['z_star_from_camb_xe']:.4f}$; " + f"CAMB's internal value is {tc['z_star_camb_internal']:.4f} " + f"(difference {tc['z_star_from_camb_xe'] - tc['z_star_camb_internal']:+.4f}).", + "", + f"CAMB RECFAST settings: $F = {rf['fudge']}$, Hswitch = {rf['Hswitch']} " + f"(Gaussian corrections centred at $z \\approx {rf['gauss_centres_z'][0]:.0f}$ " + f"and {rf['gauss_centres_z'][1]:.0f}).", + ] + saha = num["saha"] + lines += [ + "", + f"Saha (H + He) for comparison: $z_\\ast = {saha['z_star']:.2f}$, " + f"peak of $g(z)$ at {saha['z_peak']:.2f}.", + ] + md = "\n".join(lines) + "\n" + RES_DIR.mkdir(exist_ok=True) + (RES_DIR / "validation.json").write_text(json.dumps(num, indent=2) + "\n", encoding="utf-8") + (RES_DIR / "validation.md").write_text(md, encoding="utf-8") + return md + + +def main() -> None: + """Compute, plot and tabulate the validation against CAMB.""" + if hasattr(sys.stdout, "reconfigure"): + sys.stdout.reconfigure(encoding="utf-8") + use_style() + data = compute() + make_figure(data) + print(write_tables(data["numbers"])) + + +if __name__ == "__main__": + main() diff --git a/src/cmb_decoupling/results.py b/src/cmb_decoupling/results.py index e2fa736..58ea5d8 100644 --- a/src/cmb_decoupling/results.py +++ b/src/cmb_decoupling/results.py @@ -4,6 +4,9 @@ from dataclasses import asdict, dataclass +import numpy as np +from numpy.typing import NDArray + from .cosmology import Cosmology from .visibility import XeFunction, decoupling_redshift, last_scattering @@ -12,6 +15,12 @@ #: approximation of this package becomes poor (see docs/theory.md). Z_FREEZE_OUT: float = 200.0 +#: Redshift range over which x_e is compared with the reference (scripts/validate.py). +Z_VALIDATION_MIN: float = 200.0 +Z_VALIDATION_MAX: float = 2000.0 +#: Number of points of the uniform comparison grid (spacing 0.1 in z). +N_VALIDATION: int = 18001 + @dataclass(frozen=True) class KeyResults: @@ -69,3 +78,98 @@ def key_results(x_e: XeFunction, cosmo: Cosmology) -> KeyResults: x_e_freeze_out=float(x_e(Z_FREEZE_OUT)), x_e_today=float(x_e(0.0)), ) + + +def fractional_residual(x_e: XeFunction, x_e_ref: XeFunction, z: NDArray[np.float64]) -> NDArray[np.float64]: + """Fractional residual Delta x_e / x_e = x_e(z) / x_e_ref(z) - 1 [dimensionless]. + + Parameters + ---------- + x_e, x_e_ref : callable + Ionisation history under test and reference ionisation history, x_e(z) = n_e / n_H. + z : ndarray + Redshifts at which to compare. + """ + return x_e(z) / x_e_ref(z) - 1.0 + + +@dataclass(frozen=True) +class ResidualSummary: + """Where and by how much an ionisation history departs from a reference. + + All residuals are fractional, Delta x_e / x_e = x_e / x_e_ref - 1 [dimensionless]. + + Attributes + ---------- + window_lo, window_hi : float + Last-scattering window: the half-maximum redshifts of the *reference* g(z). + max_abs_window : float + Largest |Delta x_e / x_e| inside the last-scattering window. + z_max_abs_window : float + Redshift where ``max_abs_window`` occurs. + min_residual, z_min_residual : float + Most negative residual over the full comparison range, and its redshift. + max_residual, z_max_residual : float + Most positive residual over the full comparison range, and its redshift. + z_min, z_max : float + Comparison range. + """ + + window_lo: float + window_hi: float + max_abs_window: float + z_max_abs_window: float + min_residual: float + z_min_residual: float + max_residual: float + z_max_residual: float + z_min: float + z_max: float + + def as_dict(self) -> dict[str, float]: + """Return the summary as a plain dictionary.""" + return asdict(self) + + +def residual_summary( + x_e: XeFunction, + x_e_ref: XeFunction, + cosmo: Cosmology, + z_min: float = Z_VALIDATION_MIN, + z_max: float = Z_VALIDATION_MAX, + n: int = N_VALIDATION, +) -> ResidualSummary: + """Summarise the fractional x_e residual against a reference. + + Extrema are taken on a uniform grid of ``n`` points over [``z_min``, ``z_max``] + (no interpolation between grid points). + + Parameters + ---------- + x_e, x_e_ref : callable + Ionisation history under test and reference, x_e(z) = n_e / n_H. + cosmo : Cosmology + Background cosmology (used to compute the reference visibility function). + z_min, z_max : float, optional + Comparison range in redshift. + n : int, optional + Number of grid points. + """ + z = np.linspace(z_min, z_max, n) + r = fractional_residual(x_e, x_e_ref, z) + _, w_lo, w_hi = last_scattering(x_e_ref, cosmo).fwhm() + in_window = (z >= w_lo) & (z <= w_hi) + i_w = int(np.argmax(np.abs(r[in_window]))) + i_min, i_max = int(np.argmin(r)), int(np.argmax(r)) + return ResidualSummary( + window_lo=float(w_lo), + window_hi=float(w_hi), + max_abs_window=float(np.abs(r[in_window][i_w])), + z_max_abs_window=float(z[in_window][i_w]), + min_residual=float(r[i_min]), + z_min_residual=float(z[i_min]), + max_residual=float(r[i_max]), + z_max_residual=float(z[i_max]), + z_min=z_min, + z_max=z_max, + ) diff --git a/tests/test_regression.py b/tests/test_regression.py index 2f1e53f..1a94c3d 100644 --- a/tests/test_regression.py +++ b/tests/test_regression.py @@ -9,7 +9,7 @@ import pytest -from cmb_decoupling.results import key_results +from cmb_decoupling.results import key_results, residual_summary @pytest.fixture(scope="module") @@ -34,6 +34,24 @@ def test_freeze_out_against_camb(ours, ref): assert ours.x_e_freeze_out == pytest.approx(ref.x_e_freeze_out, rel=0.25) +@pytest.fixture(scope="module") +def residuals(cosmo, peebles, camb_ref): + return residual_summary(peebles.x_e, camb_ref.x_e, cosmo) + + +def test_xe_residual_in_last_scattering_window(residuals): + # Measured: 1.08% (z = 966.5-1170.5, the FWHM of CAMB's g(z)); see scripts/validate.py. + assert residuals.max_abs_window < 0.02 + + +def test_xe_residual_full_range(residuals): + # Measured on z = 200-2000: -3.58% (helium in Saha, z = 2000) and +14.05% + # (three-level atom at late times, z = 200). Bounds describe this, not a target. + assert -0.05 < residuals.min_residual < 0.0 + assert 0.0 < residuals.max_residual < 0.20 + assert residuals.z_max_residual == pytest.approx(200.0) + + def test_self_regression(ours): # Values recorded on 2026-10-22 (results/key_results.json). assert ours.z_tau_one == pytest.approx(1089.44, abs=0.05) diff --git a/tests/test_visibility.py b/tests/test_visibility.py index 957f0a6..95f39df 100644 --- a/tests/test_visibility.py +++ b/tests/test_visibility.py @@ -29,6 +29,13 @@ def test_visibility_normalisation(cosmo, peebles): assert trapezoid(ls.g, ls.z) == pytest.approx(1 - np.exp(-ls.tau[-1]), rel=1e-6) +def test_visibility_integrates_to_one(cosmo, peebles): + # tau(z_max = 3000) >> 1, so e^{-tau} is negligible and g(z) is a normalised density. + ls = last_scattering(peebles.x_e, cosmo) + assert ls.tau[-1] > 100.0 + assert trapezoid(ls.g, ls.z) == pytest.approx(1.0, abs=1e-6) + + def test_grid_convergence(cosmo, peebles): coarse = last_scattering(peebles.x_e, cosmo, n=15001) fine = last_scattering(peebles.x_e, cosmo, n=60001) From 57b67a349fd734c5266380432a2fae4aed3d5354 Mon Sep 17 00:00:00 2001 From: SethulekshmiBeena Date: Mon, 2 Nov 2026 22:06:29 +0000 Subject: [PATCH 2/4] CI: run validate.py and check committed results tables match the code Co-Authored-By: Claude Opus 5.5 --- .github/workflows/tests.yml | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml index 528b5ca..6448628 100644 --- a/.github/workflows/tests.yml +++ b/.github/workflows/tests.yml @@ -35,6 +35,13 @@ jobs: run: python scripts/make_figures.py env: MPLBACKEND: Agg + - name: Run validation against CAMB + run: python scripts/validate.py + env: + MPLBACKEND: Agg + - name: Check committed results tables match the code + if: matrix.python-version == '3.13' + run: git diff --exit-code -- results/key_results.md results/validation.md - name: Execute notebook top to bottom run: jupyter nbconvert --to notebook --execute --output /tmp/executed.ipynb notebooks/recombination_and_decoupling.ipynb @@ -54,3 +61,7 @@ jobs: run: python scripts/make_figures.py env: MPLBACKEND: Agg + - name: Run validation against CAMB + run: python scripts/validate.py + env: + MPLBACKEND: Agg From 5264e4bfbd39bd66081e01d95d10ddf90baed6a1 Mon Sep 17 00:00:00 2001 From: SethulekshmiBeena Date: Mon, 2 Nov 2026 22:06:33 +0000 Subject: [PATCH 3/4] Restructure README around the validation; correct archived Saha peak to 1283.6 README: summary, key results, physics with equations, limitations, install/quick start, tests and CI, roadmap (planned), citation. Every number is printed by scripts/validate.py or scripts/make_figures.py. Co-Authored-By: Claude Opus 5.5 --- README.md | 378 ++++++++++++++++++++++++++++++++-------------- archive/README.md | 5 +- 2 files changed, 271 insertions(+), 112 deletions(-) diff --git a/README.md b/README.md index 26f16f7..4b19593 100644 --- a/README.md +++ b/README.md @@ -3,104 +3,229 @@ [![tests](https://github.com/sethuastro/CMB_Decoupling/actions/workflows/tests.yml/badge.svg)](https://github.com/sethuastro/CMB_Decoupling/actions/workflows/tests.yml) [![License: MIT](https://img.shields.io/badge/License-MIT-blue.svg)](LICENSE) -When is the cosmic microwave background actually emitted, and how thick is the "surface" it -comes from? This project is my attempt to answer that from first principles, by following the -free-electron fraction of the Universe, $`x_e(z)`$, through hydrogen recombination. - -I started with the Saha equation, which is the textbook answer, and quickly found that it puts last -scattering at $`z \approx 1291`$, about 200 in redshift too early. The reason is that recombination is -a bottleneck rather than an equilibrium process. An electron captured straight into the ground state -emits a photon that ionises the next atom, and Lyman-α photons are trapped by resonant scattering. -So I implemented the Peebles three-level atom, in which hydrogen reaches the ground state only through -two slow channels: Lyman-α photons redshifting out of the line, and the two-photon 2s→1s decay. From -the resulting $`x_e(z)`$ I compute the Thomson scattering rate, the optical depth $\tau(z)$ and the -visibility function $`g(z)`$, which is the probability distribution for when a CMB photon last scattered. - -Everything uses Planck 2018 parameters, and I check each step against CAMB, which uses the RECFAST -recombination code. +When is the cosmic microwave background actually emitted, and how thick is the "surface" it comes +from? I built this code to learn recombination physics from first principles by following the +free-electron fraction $`x_e(z)`$ through hydrogen recombination. I started with Saha equilibrium, +which puts last scattering at $`z_\ast = 1291`$, far too early. I then implemented the Peebles +three-level atom, and from its $`x_e(z)`$ I computed the Thomson optical depth $\tau(z)$ and the +visibility function $`g(z)`$. I validated every step against CAMB, which uses the RECFAST +recombination code, run on exactly the same Planck 2018 background. The plain Peebles model, with no +fudge factor, reproduces CAMB's last-scattering redshift to 0.45 and the width of last scattering to +0.67 in redshift. Its residual ionisation at $`z = 200`$ is 14.05% too high, and I explain why below. + +## Key results

- Free-electron fraction x_e(z) from Saha, Peebles and CAMB, with residuals relative to CAMB + Validation against CAMB: (a) x_e(z), (b) fractional residual for the pure Peebles model and the F = 1.14 variant, (c) visibility function g(z)

-

- Visibility function g(z) and optical depth tau(z) compared with CAMB -

- -*Top: the free-electron fraction for each model, with the residual relative to CAMB underneath. -Bottom: the visibility function (FWHM shaded) and the optical depth. Saha equilibrium recombines far -too early; the Peebles model sits almost on top of CAMB through last scattering.* -## Results +*(a) Free-electron fraction from CAMB/RECFAST, my Peebles model and the Peebles model with the +RECFAST fudge factor $`F = 1.14`$. (b) Fractional residual relative to CAMB; the grey band is the +last-scattering window (the FWHM of CAMB's $`g(z)`$). (c) The visibility function.* -Planck 2018 cosmology, no reionisation. "This work" is the plain Peebles model, with no fudge factor. -I ran CAMB with exactly the same background, so the differences come from the recombination physics -alone. +Planck 2018 background, no reionisation. CAMB 2.0.5 is run with the same parameters (massless +neutrinos, same $`Y_p`$ and $`T_0`$), so the differences come from the recombination physics alone. +Nothing has been tuned to match CAMB. -| | This work | CAMB 2.0.5 (RECFAST) | Difference | +| | Peebles (this work) | Peebles, $`F = 1.14`$ (this work) | CAMB 2.0.5 (RECFAST) | |---|---|---|---| -| Last-scattering redshift $`z_\ast`$ ($`\tau = 1`$) | 1089.44 | 1089.89 | −0.45 | -| Peak of $`g(z)`$, per unit redshift | 1078.80 | 1078.37 | +0.43 | -| Peak of visibility, per unit conformal time | 1089.11 | 1088.78 | +0.32 | -| Width of last scattering (FWHM of $`g`$) | 203.3 | 204.0 | −0.7 | -| $`z_{\rm dec}`$, where $`\Gamma_T = H`$ | 903.2 | 903.6 | −0.4 | -| Residual ionisation $`x_e(z = 200)`$ | 3.85 × 10⁻⁴ | 3.38 × 10⁻⁴ | +14% | -| Residual ionisation $`x_e(z = 0)`$ | 2.67 × 10⁻⁴ | 1.74 × 10⁻⁴ | +53% | - -For comparison, Saha alone gives $`z_\ast = 1291`$. - -The last-scattering numbers agree with CAMB to better than one unit of redshift. That's because the -Peebles model tracks RECFAST to within about 2% between $z \approx 1000$ and 1500, which is where -$\tau$ builds up. The late-time residual ionisation is a different story: my model is 14% high at -$`z = 200`$. I think this comes from two simplifications rather than a bug. First, a three-level atom -recombines too slowly at late times, which is why RECFAST introduced a fudge factor; with their -$F = 1.14$ my value drops to within 1% of CAMB. Second, I assume the gas stays at the radiation -temperature, while in reality it cools faster below $`z \sim 300`$. Helium is the other visible gap. -I treat it in Saha equilibrium, so at $`z \approx 1800\text{–}2800`$ my $`x_e`$ is up to 6% lower than CAMB's, -where helium recombination is delayed. - -A detail worth pointing out: the familiar "$`z \approx 1090`$" is not where $g(z)$ peaks when you -plot it per unit redshift. That peak is at 1079. The 1090 comes from the $\tau = 1$ definition, or -from the visibility per unit conformal time. I report all three in the table, and -[`docs/theory.md`](docs/theory.md#63-which-redshift-of-last-scattering) explains why they differ. - -To make sure my optical-depth integrator wasn't hiding errors, I also fed CAMB's own $`x_e(z)`$ into -it. It recovers CAMB's internal $`z_\ast = 1089.892`$ to within 0.01. - -## How it's organised +| $`z_\ast`$, where $\tau = 1$ | 1089.44 | 1090.28 | 1089.89 | +| Peak of $`g(z)`$ per unit redshift | 1078.80 | 1079.05 | 1078.37 | +| Peak of visibility per unit conformal time | 1089.11 | 1089.32 | 1088.78 | +| Width of last scattering (FWHM of $`g`$) | 203.33 | 202.73 | 204.00 | +| $`z_{\rm dec}`$, where $`\Gamma_T = H`$ | 903.18 | 904.44 | 903.55 | +| $`x_e(z = 200)`$ | 3.849 × 10⁻⁴ | 3.404 × 10⁻⁴ | 3.375 × 10⁻⁴ | +| $`x_e(z = 0)`$ | 2.665 × 10⁻⁴ | 2.351 × 10⁻⁴ | 1.738 × 10⁻⁴ | + +**How far $`x_e`$ is from CAMB.** Fractional residual $`\Delta x_e/x_e = x_e/x_e^{\rm CAMB} - 1`$ +on $`z = 200\text{–}2000`$, sampled every $\Delta z = 0.1$: + +| | Peebles (this work) | Peebles, $`F = 1.14`$ (this work) | +|---|---|---| +| (a) Largest $`\lvert\Delta x_e/x_e\rvert`$ in the last-scattering window, $`z = 966.5\text{–}1170.5`$ | 1.08% (at $`z = 1170.5`$) | 1.04% (at $`z = 1170.5`$) | +| (b) Most negative residual | −3.58% (at $`z = 2000`$) | −3.58% (at $`z = 2000`$) | +| (c) Most positive residual | +14.05% (at $`z = 200`$) | +1.46% (at $`z = 1264`$) | +| Range over the hydrogen-only era, $`z = 200\text{–}1800`$ | −0.33% to +14.05% | −1.46% to +1.46% | + +**(a) Last scattering.** This is the part that matters for the CMB. Across the window that holds half +the visibility, my $`x_e`$ is within 1.08% of CAMB's. That is why $`z_\ast`$ and the width agree to +better than one unit of redshift. The largest value sits at the window's upper edge, because just +above the window both curves in panel (b) rise to a bump, which reaches +1.46% at $`z = 1264`$ for +the $`F = 1.14`$ run. +CAMB's RECFAST has two corrections that my model lacks: its own fudge factor $`F = 1.125`$, and two +Gaussian corrections to the recombination rate centred at $`z \approx 1452`$ and 867 (the +`RECFAST_Hswitch` option, fitted to multi-level calculations). I think these are the likely origin of +the bump, but I have not isolated it. + +**(b) Helium.** Above $`z = 1800`$ I treat helium in Saha equilibrium, while RECFAST evolves helium +recombination with a rate equation. Real helium recombination lags Saha, so my $`x_e`$ is too low. +The −3.58% minimum on this range sits at its upper edge, $`z = 2000`$. Beyond that range the gap +reaches −5.81% at $`z = 2299`$. Helium has recombined well before last scattering, so this does not +affect $`z_\ast`$. + +**(c) Late times.** Below the last-scattering window the plain Peebles residual grows steadily, +reaching +14.05% at $`z = 200`$. The largest value over the whole range therefore sits at +the lower end of the range I chose. There, $`C_r \to 1`$ and the freeze-out value of $`x_e`$ is set by +the recombination rate $`\alpha_B`$. A three-level atom with the case-B rate recombines too slowly +compared with a full multi-level atom. Seager, Sasselov & Scott (1999) introduced the fudge factor +$`F = 1.14`$ on $`\alpha_B`$ to correct for exactly this. With $`F = 1.14`$, my residual stays within +±1.46% over the whole hydrogen era, and the excess at $`z = 200`$ drops from +14.05% to +0.87%. So the +late-time excess is the three-level approximation, not a numerical error. + +The comparison is not fully independent, because CAMB's RECFAST is itself a fudged three-level model. +The fudge also moves $`z_\ast`$ slightly *away* from CAMB, from 1089.44 to 1090.28, which is why I +keep the plain Peebles model as my headline result. The small positive residual that remains at the lowest +redshifts with $`F = 1.14`$ (+0.87% at $`z = 200`$) is what I would expect from my second simplification. I keep the +gas at the radiation temperature, while RECFAST lets it cool faster, and cooler gas recombines faster. +By $`z = 0`$ this matters a lot: even with $`F = 1.14`$, my $`x_e(0)`$ is 2.351 × 10⁻⁴ against CAMB's +1.738 × 10⁻⁴. + +**Two more checks.** +- I fed CAMB's own $`x_e(z)`$ into my optical-depth integrator. It gives $`z_\ast = 1089.8901`$, + against CAMB's internal 1089.8923, so the integrator is not hiding anything. +- The familiar "$`z \approx 1090`$" is $`z_\ast`$ or the peak per unit conformal time. The peak of + $`g(z)`$ per unit *redshift* is about 10 lower, at 1078.80. + [`docs/theory.md`](docs/theory.md#63-which-redshift-of-last-scattering) explains why. + +Every number above is printed by `python scripts/validate.py` (written to `results/validation.md`) or +`python scripts/make_figures.py` (written to `results/key_results.md`). + +## Physics + +The full derivations, with each approximation stated where it is made, are in +[`docs/theory.md`](docs/theory.md). These are the equations the code solves. + +**Background.** Flat ΛCDM with $`H(z) = H_0\sqrt{\Omega_m(1+z)^3 + \Omega_r(1+z)^4 + \Omega_\Lambda}`$, +radiation temperature $`T = T_0(1+z)`$ and hydrogen density $`n_{\rm H} = (1 - Y_p)\,\rho_b/m_{\rm H}`$. +Here $`Y_p`$ is the helium mass fraction, $`\rho_b`$ the baryon density and $`m_{\rm H}`$ the hydrogen +atom mass. The parameters are Planck 2018 VI, Table 2 (TT,TE,EE+lowE+lensing). + +### Saha equilibrium, with helium + +If ionisation and recombination are in balance, the ionised fraction $`x_e = n_e/n_{\rm H}`$ of pure +hydrogen obeys + +```math +\frac{x_e^2}{1 - x_e} = \frac{1}{n_{\rm H}}\left(\frac{m_e k_B T}{2\pi\hbar^2}\right)^{3/2} e^{-E_{\rm ion}/k_BT}, +``` + +where $`m_e`$ is the electron mass, $`k_B`$ Boltzmann's constant, $`\hbar`$ the reduced Planck constant +and $`E_{\rm ion} = 13.598`$ eV the hydrogen ionisation energy. Helium adds two more equilibria: +```math +\frac{n_{\rm He\,II}\, n_e}{n_{\rm He\,I}} = 4\left(\frac{m_ek_BT}{2\pi\hbar^2}\right)^{3/2} e^{-\chi_{\rm He\,I}/k_BT}, +\qquad +\frac{n_{\rm He\,III}\, n_e}{n_{\rm He\,II}} = \left(\frac{m_ek_BT}{2\pi\hbar^2}\right)^{3/2} e^{-\chi_{\rm He\,II}/k_BT}. ``` -src/cmb_decoupling/ the package - cosmology.py Planck 2018 parameters (defined once), H(z), n_H(z) - constants.py physical and atomic constants, with sources - saha.py Saha equilibrium for hydrogen and helium - peebles.py Peebles three-level atom (stiff ODE) - visibility.py Thomson rate, tau(z), g(z), peak and width - reference.py the CAMB comparison run -notebooks/ a walk-through from Saha to last scattering -scripts/ make_figures.py rebuilds every figure and the results table -tests/ 38 tests: physical limits, convergence, comparison with CAMB -docs/theory.md the derivations, step by step, with references -archive/ my original scripts, kept as they were + +Here $`\chi_{\rm He\,I} = 24.587`$ eV and $`\chi_{\rm He\,II} = 54.418`$ eV are the helium ionisation +energies, and 4 and 1 are statistical-weight factors. These are closed by charge neutrality: + +```math +x_e = x_{\rm H\,II} + f_{\rm He}\,(y_{\rm He\,II} + 2y_{\rm He\,III}), ``` -The derivations in [`docs/theory.md`](docs/theory.md) go from the Boltzmann distribution to the Saha -equation, then through the rate balance for the $n = 2$ level to the Peebles equation and the $`C_r`$ -factor, and finally to $\tau(z)$ and $`g(z)`$. I've tried to state each approximation at the point -where it's made. +with $`x_{\rm H\,II} = n_p/n_{\rm H}`$, $`y_i = n_i/n_{\rm He}`$ and $`f_{\rm He} = n_{\rm He}/n_{\rm H}`$. +Saha fails during recombination for two reasons: +- A direct capture to the ground state emits a photon that immediately ionises a neighbouring atom. +- Lyman-α photons are trapped by resonant scattering. + +### The Peebles three-level atom + +Below $`z = 1800`$ the code integrates the Peebles (1968) equation. It treats hydrogen as a ground +state, an $n = 2$ level and the continuum: + +```math +\frac{dx_e}{dz} = \frac{C_r}{(1+z)H(z)}\left[\alpha_B\, n_{\rm H}\, x_e^2 - \beta_B\,(1 - x_e)\, e^{-E_{{\rm Ly}\alpha}/k_BT}\right], +\qquad +C_r = \frac{\Lambda_{2s1s} + \Lambda_\alpha}{\Lambda_{2s1s} + \Lambda_\alpha + \beta_B}. +``` + +- $`\alpha_B(T)`$ is the case-B recombination coefficient: recombinations to $n \ge 2$ only (Péquignot, + Petitjean & Boisson 1991 fit, multiplied by a fudge factor $F$, which is 1 by default). +- $`\beta_B = \alpha_B\,(m_ek_BT/2\pi\hbar^2)^{3/2}\,e^{-E_{\rm ion}/4k_BT}`$ is the photo-ionisation rate + from $n = 2$, fixed by detailed balance. +- $`E_{{\rm Ly}\alpha} = \tfrac34 E_{\rm ion}`$ is the Lyman-α energy. +- $`\Lambda_{2s1s} = 8.22458\ {\rm s^{-1}}`$ is the two-photon 2s → 1s decay rate. +- $`\Lambda_\alpha = 8\pi H/(\lambda_\alpha^3\, n_{1s})`$ is the rate at which Lyman-α photons redshift + out of the line, with $`\lambda_\alpha`$ the Lyman-α wavelength and + $`n_{1s} = (1 - x_e)\,n_{\rm H}`$ the ground-state density. + +$`C_r`$ is the probability that an atom in $n = 2$ reaches the ground state before being +re-ionised. During recombination $`C_r \ll 1`$, and recombination is throttled by the two slow +escape routes. The bracket vanishes exactly at the Saha solution, so the ODE starts from Saha at +$`z = 1800`$. It is stiff, so it is integrated with the implicit Radau method. + +### Thomson optical depth + +Photons scatter off free electrons at the rate $`\Gamma_T = n_e\sigma_T c`$, where $`\sigma_T`$ is the +Thomson cross-section and $c$ the speed of light. The optical depth back to redshift $z$ is + +```math +\tau(z) = \int_0^z \frac{n_e(z')\,\sigma_T\, c}{(1+z')\,H(z')}\,dz', \qquad n_e = x_e\, n_{\rm H}. +``` + +I define the last-scattering redshift $`z_\ast`$ by $`\tau(z_\ast) = 1`$, as Planck does. + +### Visibility function + +$`e^{-\tau(z)}`$ is the probability that a photon seen today has not scattered since $z$. So the +probability density that it last scattered at $z$ is + +```math +g(z) = \frac{d\tau}{dz}\,e^{-\tau(z)}, \qquad \int_0^{z} g\,dz' = 1 - e^{-\tau(z)} \to 1 . +``` + +Its full width at half maximum is the thickness of the last-scattering surface. + +

+ Free-electron fraction x_e(z) from Saha, Peebles and CAMB, with residuals relative to CAMB +

+ +*Saha equilibrium (orange, pink) recombines far too early. The Peebles model sits almost on top of +CAMB through last scattering. More figures: [`figures/visibility_function.png`](figures/visibility_function.png) +(also shows $`\tau(z)`$) and [`figures/rates.png`](figures/rates.png) ($`\Gamma_T/H`$ and $`C_r`$).* + +## Approximations and limitations + +| Approximation | What it does to the result | What would fix it | +|---|---|---| +| Three-level atom with case-B $`\alpha_B`$, no fudge factor | $`x_e`$ too high after recombination: +14.05% at $`z = 200`$ (+0.87% with $F = 1.14$) | multi-level atom (HyRec, CosmoRec) | +| Gas temperature equals radiation temperature | $`x_e`$ too high at late times; $`x_e(0)`$ is 2.351 × 10⁻⁴ vs 1.738 × 10⁻⁴ even with $F = 1.14$ | evolve the matter temperature with Compton heating | +| Helium in Saha equilibrium; neutral below $`z = 1800`$ | $`x_e`$ too low in the helium era: −5.81% at $`z = 2299`$ | helium rate equations (as in RECFAST) | +| No Lyman-series feedback, Raman scattering or two-photon corrections; none of RECFAST's extra rate corrections | ~1% wiggles in $`x_e`$ around last scattering (e.g. +1.46% at $`z = 1264`$ with $F = 1.14$) | HyRec / CosmoRec | +| No reionisation | $\tau$ is the optical depth to recombination only; reionisation adds a further optical depth at low redshift | add a reionisation model | +| Massless neutrinos | none in the comparison (CAMB uses the same) | massive-neutrino background | -## Running it +CAMB's RECFAST includes helium rate equations, matter-temperature evolution, $`F = 1.125`$ and further +corrections. HyRec and CosmoRec are not in the pip-installed CAMB, so I could not compare with them. +The code is a learning tool and a check of the physics. It is not a replacement for those codes in +parameter estimation. -You'll need Python 3.10 or newer. +## Installation and quick start + +You'll need Python 3.10 or newer. With pip: ```bash git clone https://github.com/sethuastro/CMB_Decoupling.git cd CMB_Decoupling python -m venv .venv source .venv/bin/activate # on Windows: .venv\Scripts\activate +pip install -e ".[dev]" # or, for the exact versions I used: pip install -r requirements.txt && pip install -e . --no-deps +``` + +With conda: + +```bash +conda create -n cmb python=3.13 && conda activate cmb pip install -e ".[dev]" +``` -pytest # run the tests -python scripts/make_figures.py # rebuild figures/ and results/ +Reproduce the validation figure and tables (well under a minute): + +```bash +python scripts/validate.py # figures/validation.{png,pdf}, results/validation.{md,json} +python scripts/make_figures.py # the other figures, results/key_results.{md,json} ``` Or, from Python: @@ -108,52 +233,83 @@ Or, from Python: ```python from cmb_decoupling import PLANCK2018, solve_peebles, last_scattering -history = solve_peebles(PLANCK2018) -ls = last_scattering(history.x_e, PLANCK2018) -print(ls.z_tau_one(), ls.z_peak(), ls.fwhm()[0]) # 1089.44 1078.80 203.33 +history = solve_peebles(PLANCK2018) # Peebles x_e(z) on the Planck 2018 background +ls = last_scattering(history.x_e, PLANCK2018) # tau(z) and g(z) +print(f"{ls.z_tau_one():.2f} {ls.fwhm()[0]:.2f}") # 1089.44 203.33 +``` + +**How it's organised** + +``` +src/cmb_decoupling/ the package + cosmology.py Planck 2018 parameters (defined once), H(z), n_H(z) + constants.py physical and atomic constants, with sources + saha.py Saha equilibrium for hydrogen and helium + peebles.py Peebles three-level atom (stiff ODE) + visibility.py Thomson rate, tau(z), g(z), peak and width + results.py summary numbers and residuals against a reference + reference.py the CAMB comparison run +scripts/ validate.py (comparison with CAMB), make_figures.py (all other figures) +tests/ pytest suite +notebooks/ a walk-through from Saha to last scattering +docs/theory.md the derivations, step by step, with references +archive/ my original scripts, kept as they were ``` -## How I tested it +## Tests and CI + +```bash +pytest +``` -The tests check things that physics says must be true: -- $`x_e \to 1`$ at early times; +There are 41 tests. Some check things that physics says must be true: +- $`x_e \to 1`$ at high redshift in Saha; - the Peebles rate vanishes exactly at the Saha solution (detailed balance); - charge is conserved in the hydrogen–helium Saha solution; -- $`\int g\,dz = 1 - e^{-\tau}`$. +- $`\int g\,dz = 1 - e^{-\tau}`$ exactly, and $`\int g\,dz = 1`$ to $10^{-6}$ since $`\tau(3000) \gg 1`$. -They also check that the answers don't change when I tighten the ODE tolerances, refine the redshift -grid, or move the point where the ODE takes over from Saha. The comparison tests against CAMB use -tolerances that describe the agreement I actually measured; I didn't adjust the model to pass them. -GitHub Actions runs the tests, rebuilds the figures and runs the notebook on every push. +Others check that the answers don't change when I tighten the ODE tolerances, refine the redshift +grid or move the Saha-to-Peebles switch. -## What it doesn't do (yet) +The comparison tests against CAMB use tolerances that describe the agreement I measured, not targets +I tuned the model to meet: +- $`z_\ast`$, the peak and $`z_{\rm dec}`$ within 2; +- the FWHM within 3; +- $`\lvert\Delta x_e/x_e\rvert < 2\%`$ in the last-scattering window. -- **A multi-level hydrogen atom.** This would fix most of the late-time excess. HyRec and CosmoRec do - this properly. -- **A proper helium recombination equation** instead of Saha. -- **Evolving the matter temperature** separately from the radiation temperature. -- **Reionisation.** The optical depth here stops at recombination; Planck measures an extra - $\tau \approx 0.054$ from reionisation. -- **Parameter sensitivity.** I'd like to look at how $`z_\ast`$ and the width of last scattering respond - to $`\Omega_b h^2`$ and $`Y_p`$. +GitHub Actions runs on every push (badge at the top): +- lint (ruff); +- tests on Linux (Python 3.11 and 3.13) and on Windows; +- both scripts, rebuilt from scratch; +- a check that the committed results tables match the code; +- the notebook, run top to bottom. -## References +## Roadmap -- Peebles, P. J. E. 1968, *ApJ* **153**, 1 -- Zel'dovich, Ya. B., Kurt, V. G. & Sunyaev, R. A. 1968, *Zh. Eksp. Teor. Fiz.* **55**, 278 -- Seager, S., Sasselov, D. D. & Scott, D. 1999, *ApJ* **523**, L1 -- Seager, S., Sasselov, D. D. & Scott, D. 2000, *ApJS* **128**, 407 -- Planck Collaboration 2020, *A&A* **641**, A6 (Planck 2018 results VI) -- Lewis, A., Challinor, A. & Lasenby, A. 2000, *ApJ* **538**, 473 (CAMB) -- Dodelson, S. & Schmidt, F. 2020, *Modern Cosmology*, 2nd ed. -- Péquignot, D., Petitjean, P. & Boisson, C. 1991, *A&A* **251**, 680 +These are **planned, not done**: -The full list is at the end of [`docs/theory.md`](docs/theory.md#9-references). +1. **Sound horizon $`r_s(z_\ast)`$**: the comoving distance a sound wave in the photon–baryon fluid + travels before last scattering. This sets the angular scale of the acoustic peaks. +2. **Angular power spectrum $`C_\ell`$**: starting from the visibility function computed here. -## About me +## Citation and licence -I'm Sethulekshmi Beena, an MSc Astrophysics student at the University of Hertfordshire. +If you use this code, please cite it with the metadata in [`CITATION.cff`](CITATION.cff); GitHub's +"Cite this repository" button generates BibTeX from it. The code is released under the +[MIT licence](LICENSE). + +**References:** +- Peebles 1968, *ApJ* **153**, 1 +- Zel'dovich, Kurt & Sunyaev 1968, *Zh. Eksp. Teor. Fiz.* **55**, 278 +- Seager, Sasselov & Scott 1999, *ApJ* **523**, L1 +- Seager, Sasselov & Scott 2000, *ApJS* **128**, 407 +- Péquignot, Petitjean & Boisson 1991, *A&A* **251**, 680 +- Planck Collaboration 2020, *A&A* **641**, A6 +- Lewis, Challinor & Lasenby 2000, *ApJ* **538**, 473 (CAMB) +- Dodelson & Schmidt 2020, *Modern Cosmology*, 2nd ed. + +The full list is in [`docs/theory.md`](docs/theory.md#9-references). + +**About me.** I'm Sethulekshmi Beena, MSc Astrophysics (Distinction), University of Hertfordshire. ORCID [0009-0004-4767-2733](https://orcid.org/0009-0004-4767-2733) · [homepage](https://sethuastro.github.io/) - -If this is useful to you, there's a [`CITATION.cff`](CITATION.cff) file. The code is MIT-licensed. diff --git a/archive/README.md b/archive/README.md index 3161f3b..c61e63e 100644 --- a/archive/README.md +++ b/archive/README.md @@ -18,7 +18,10 @@ Known issues, fixed in the package: - cosmological parameters and constants were duplicated across files without sources. -Using the Saha x_e, the visibility function peaks at z ≈ 1277, much earlier +Using the Saha x_e, the visibility function peaks at z = 1283.6 (`python scripts/validate.py`), much earlier than the z ≈ 1080 obtained once the Peebles model is used. This is the physical failure of Saha equilibrium at late times, not a coding error; see `docs/theory.md`. + +An earlier version of this note gave z ≈ 1277; that figure came from the archive scripts above +(before the fixes listed), not from the package. From c11d4e30e5a910f177d3e9b0db16113351708268 Mon Sep 17 00:00:00 2001 From: SethulekshmiBeena Date: Mon, 2 Nov 2026 22:06:33 +0000 Subject: [PATCH 4/4] Prepare v1.0.0 release metadata Co-Authored-By: Claude Opus 5.5 --- CITATION.cff | 4 ++-- pyproject.toml | 2 +- src/cmb_decoupling/__init__.py | 2 +- 3 files changed, 4 insertions(+), 4 deletions(-) diff --git a/CITATION.cff b/CITATION.cff index 7979c3d..8655793 100644 --- a/CITATION.cff +++ b/CITATION.cff @@ -10,8 +10,8 @@ authors: website: "https://sethuastro.github.io/" repository-code: "https://github.com/sethuastro/CMB_Decoupling" license: MIT -version: 0.1.0 -date-released: 2026-10-22 +version: 1.0.0 +date-released: 2026-11-02 keywords: - cosmology - cosmic microwave background diff --git a/pyproject.toml b/pyproject.toml index c5ded50..a777599 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta" [project] name = "cmb-decoupling" -version = "0.1.0" +version = "1.0.0" description = "Hydrogen recombination (Saha, Peebles) and CMB photon decoupling, validated against CAMB/RECFAST" readme = "README.md" requires-python = ">=3.10" diff --git a/src/cmb_decoupling/__init__.py b/src/cmb_decoupling/__init__.py index 015a99b..b9c65f1 100644 --- a/src/cmb_decoupling/__init__.py +++ b/src/cmb_decoupling/__init__.py @@ -19,4 +19,4 @@ "x_e_saha_hydrogen", ] -__version__ = "0.1.0" +__version__ = "1.0.0"