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‎notebooks/00_sanity.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "0",
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"metadata": {},
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"source": [
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"# 00 — sanity\n",
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"Quick import + TT luminality smoke (should be exactly 1 at LO)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"from palatini_pt.gw.quadratic_action import tensor_action_coeffs\n",
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"from palatini_pt.spurion.pt_even import project_scalar\n",
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"from palatini_pt.spurion.profile import constant_gradient"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2",
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"metadata": {},
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"outputs": [],
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"source": [
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"k = np.logspace(-3, -1, 64)\n",
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"deps = constant_gradient([0.0, 0.0, 1.0]) # ∂ε 指向 z\n",
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"Seps = project_scalar(np.dot(deps, deps))\n",
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"\n",
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"K, G = tensor_action_coeffs(Seps)\n",
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"cT2 = G / K\n",
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"print(\"K(LO)=\", K, \"G(LO)=\", G, \"c_T^2(LO)=\", cT2)\n",
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"assert np.allclose(cT2, 1.0), \"locked LO must be luminal\""
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "kernelspec,language_info"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎notebooks/10_c2_symbolic_demo.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "0",
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"metadata": {},
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"source": [
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"# 10 — C2 symbolic demo\n",
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"Show DBI / closed-metric reduce to A_* * I_T at quadratic order."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy as sp\n",
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"from palatini_pt.equivalence.coeff_extractor import reduce_to_IT\n",
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"\n",
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"lam, eta, Seps = sp.symbols(\"lambda eta Seps\", positive=True)\n",
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"res_dbi = reduce_to_IT(route=\"dbi\", lam=lam, eta=eta, Seps=Seps)\n",
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"res_cm = reduce_to_IT(route=\"closed_metric\", lam=lam, eta=eta, Seps=Seps)\n",
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"sp.simplify(res_dbi - res_cm)"
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "kernelspec,language_info"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎notebooks/20_flux_ratio.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "0",
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"metadata": {},
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"source": [
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"# 20 — Flux ratio R_{X/Y}(R) -> 1\n",
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"Finite-domain FRW ball visualization."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np, matplotlib.pyplot as plt\n",
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"from palatini_pt.equivalence.flux_ratio import flux_ratio_FRW\n",
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"\n",
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"R = np.linspace(5.0, 80.0, 60)\n",
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"out = flux_ratio_FRW(R, {\"flux\": {\"sigma\": 1.0, \"c\": 0.5}})\n",
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"plt.plot(out[\"R\"], out[\"R_DBI_CM\"])\n",
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"plt.axhline(1.0, ls=\"--\")\n",
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"plt.xlabel(\"R\"); plt.ylabel(r\"$\\mathcal R_{X/Y}$\")\n",
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"plt.title(\"Flux ratio → 1 with $R^{-\\sigma}$ tail\")\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "kernelspec,language_info"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎notebooks/30_nlo_offsets.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "0",
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"metadata": {},
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"source": [
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"# 30 — NLO offsets\n",
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"δc_T^2(k) ~ b k^2 / Λ^2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np, matplotlib.pyplot as plt\n",
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"from palatini_pt.gw.nlo import predict_offsets\n",
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"\n",
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"k = np.logspace(-3, -1, 200)\n",
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"cfg = {\"nlo\": {\"gradT_sq_eff\": 1.0, \"Ricci_deps_deps_eff\": 0.3, \"Lambda2\": 1e6}}\n",
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"out = predict_offsets(k, cfg)\n",
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"\n",
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"plt.loglog(k, np.abs(out[\"delta_cT2\"]), label=r\"$|\\delta c_T^2|$\")\n",
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"plt.loglog(k, (out[\"delta_cT2\"][0]/(k[0]**2))*k**2, ls=\"--\", label=r\"$\\propto k^2$\")\n",
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"plt.legend(); plt.xlabel(\"k\"); plt.ylabel(r\"$|\\delta c_T^2|$\")\n",
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"plt.title(\"NLO: $k^2/\\\\Lambda^2$\")\n",
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"plt.show()"
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "-all",
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"main_language": "python",
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"notebook_metadata_filter": "kernelspec,language_info"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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