<h1>The Mobley Framework</h1>
<p>Cosmology from Self-Observation: U² = -∞</p>
<div class="tabs">
<button class="tab active" onclick="switchTab('simulation')">🔬 Simulation</button>
<button class="tab" onclick="switchTab('paper')">📄 Paper</button>
<button class="tab" onclick="switchTab('math')">📊 Interactive Math</button>
<button class="tab" onclick="switchTab('comparison')">⚖️ vs ΛCDM</button>
</div>
</div>
<!-- SIMULATION TAB -->
<div id="simulation" class="content active">
<div class="simulation-container">
<div class="canvas-container">
<div id="threejs-canvas"></div>
</div>
<div class="controls-panel">
<div class="control-group">
<h3>Controls</h3>
<button class="btn btn-primary" onclick="toggleSimulation()">
<span id="play-pause-text">▶ Play</span>
</button>
<button class="btn btn-secondary" onclick="resetSimulation()">🔄 Reset</button>
<button class="btn btn-success" onclick="exportData()">💾 Export Data</button>
</div>
<div class="control-group">
<h3>Parameters</h3>
<div class="control-item">
<label>Observer Growth Rate (λ)</label>
<input type="range" id="lambda-slider" min="0.01" max="0.5" step="0.01" value="0.1" oninput="updateLambda(this.value)">
<div class="value-display" id="lambda-value">0.100</div>
</div>
<div class="control-item">
<label>Turbulence Intensity</label>
<input type="range" id="turbulence-slider" min="0" max="1" step="0.1" value="0.5" oninput="updateTurbulence(this.value)">
<div class="value-display" id="turbulence-value">0.5</div>
</div>
<div class="control-item">
<label>View Mode</label>
<select id="view-mode" onchange="updateViewMode(this.value)" style="width: 100%; padding: 0.5rem; background: #374151; color: #e0e0e0; border: none; border-radius: 0.25rem;">
<option value="magnitude">|U| Magnitude</option>
<option value="real">Re(U) Real Part</option>
<option value="imaginary">Im(U) Imaginary Part</option>
<option value="phase">Phase</option>
<option value="turbulence">Turbulent Flow</option>
</select>
</div>
</div>
<div class="control-group">
<h3>Current State</h3>
<div class="stat-box">
<div class="label">Time</div>
<div class="value" id="time-display">0.00</div>
</div>
<div class="stat-box">
<div class="label">Observers (O)</div>
<div class="value" id="observers-display">0.01</div>
</div>
<div class="stat-box">
<div class="label">U²</div>
<div class="value" id="usquared-display" style="color: #ef4444;">-0.10</div>
</div>
<div class="stat-box">
<div class="label">Effective Dimension</div>
<div class="value" id="dimension-display">10.00</div>
</div>
<div class="stat-box">
<div class="label">Hubble Parameter (H)</div>
<div class="value" id="hubble-display">0.00</div>
</div>
<div style="margin-top: 1rem;">
<div style="color: #9ca3af; font-size: 0.85rem; margin-bottom: 0.5rem;">Progress to Singularity</div>
<div class="progress-bar">
<div class="progress-fill" id="progress-fill" style="width: 0%"></div>
</div>
<div style="color: #9ca3af; font-size: 0.75rem; text-align: right; margin-top: 0.25rem;" id="progress-text">0.0000%</div>
</div>
</div>
<div class="control-group">
<h3>Interpretation</h3>
<div id="interpretation-text" style="font-size: 0.9rem; line-height: 1.6; color: #d1d5db;">
🌌 Early universe: High dimensional, quantum foam
</div>
</div>
</div>
</div>
</div>
<!-- PAPER TAB -->
<div id="paper" class="content">
<div class="paper-container" id="paper-content">
<div class="paper-header">
<h1 class="paper-title">Cosmology from Self-Observation:<br>The U² = -∞ Framework</h1>
<p class="paper-author">John Alexander Mobley</p>
<p class="paper-date">February 2026</p>
<div style="margin-top: 1.5rem;">
<button class="btn btn-primary" onclick="generatePDF()">📥 Download PDF</button>
<button class="btn btn-secondary" onclick="downloadLaTeX()">📥 Download LaTeX</button>
</div>
</div>
<div class="abstract">
<h2 style="font-size: 1.2rem; margin-bottom: 1rem;">Abstract</h2>
<p>
We propose that the universe satisfies the fundamental equation U² = -∞, where U is a
Clifford multivector representing the cosmic state. This equation implies the universe is
complex-valued (U = iΛ) and evolves through entropy increase driven by observation. From
this single principle, we derive: (i) cosmological expansion, (ii) inflation, (iii) dark
energy, and (iv) cyclic cosmology. The theory predicts w₁ ≈ 7×10⁻⁵, testable by 2027.
</p>
</div>
<div class="paper-section">
<h2>I. Introduction</h2>
<p>
Modern cosmology faces profound puzzles: fine-tuning, the cosmological constant problem,
and the coincidence problem. We propose the universe is a self-referential structure whose
dynamics are determined by a single equation:
</p>
<div class="equation-box">
<div class="equation">
\[ U^2 = -\infty \]
</div>
<div class="equation-number">(1)</div>
</div>
<p>
The universe cannot observe itself completely without encountering a singularity. The
negative sign reflects the complex nature of the cosmic field, while infinity represents
unbounded information that becomes constrained through observation.
</p>
</div>
<div class="paper-section">
<h2>II. Mathematical Framework</h2>
<h3>A. The Observer Field</h3>
<p>
We define observer count O as total entropy:
</p>
<div class="equation-box">
<div class="equation">
\[ O \equiv S_{\text{total}} = \ln(\Omega) \]
</div>
<div class="equation-number">(2)</div>
</div>
<p>
Currently O<sub>now</sub> ≈ 10<sup>120</sup> (Bekenstein bound).
</p>
<h3>B. Solution</h3>
<p>
The universe as Clifford multivector:
</p>
<div class="equation-box">
<div class="equation">
\[ U(S,\Lambda) = i\Lambda \cdot e^{-S^2/2\Lambda^2} \]
</div>
<div class="equation-number">(3)</div>
</div>
<p>
where Λ ≈ 10<sup>122</sup> is maximum entropy.
</p>
</div>
<div class="paper-section">
<h2>III. Cosmological Solutions</h2>
<h3>A. Expansion History</h3>
<p>
Scale factor evolution:
</p>
<div class="equation-box">
<div class="equation">
\[ a(t) \propto e^{S(t)^2/\Lambda^2} \]
</div>
<div class="equation-number">(4)</div>
</div>
<h3>B. Dark Energy</h3>
<p>
Equation of state:
</p>
<div class="equation-box">
<div class="equation">
\[ w(S) = -1 + \frac{2}{3}\left(\frac{S}{\Lambda}\right)^2 \]
</div>
<div class="equation-number">(5)</div>
</div>
<p>
Predicts w(a) = -1 + w₁(1-a) with w₁ ≈ 6.7 × 10⁻⁵.
</p>
<h3>C. Cyclic Universe</h3>
<p>
As S → Λ, U → 0 creates Big Bang singularity. Time to next bang: ~10²⁴ years.
</p>
</div>
<div class="paper-section">
<h2>IV. Testable Predictions</h2>
<ol style="padding-left: 2rem; line-height: 2;">
<li><strong>Dark energy evolution:</strong> w₁ ≈ 7×10⁻⁵ (testable by DESI/Euclid 2027)</li>
<li><strong>Decoherence scaling:</strong> Γ ∝ S<sub>local</sub></li>
<li><strong>Laboratory analogue:</strong> P(k,N) ∝ exp(-αN²)</li>
<li><strong>CMB anomalies:</strong> Hemispherical asymmetry from Im(U)</li>
</ol>
</div>
<div class="paper-section">
<h2>V. Conclusion</h2>
<p>
We have presented a cosmological framework based on U² = -∞, yielding testable predictions.
If validated, this represents a fundamental shift: the universe as a self-observing structure
whose existence is maintained by its inability to completely know itself.
</p>
</div>
<div class="paper-section">
<h2>References</h2>
<ol style="padding-left: 2rem; line-height: 2; font-size: 0.9rem;">
<li>Planck Collaboration, A&A 641, A6 (2020)</li>
<li>Guth, A., Phys. Rev. D 23, 347 (1981)</li>
<li>Weinberg, S., Rev. Mod. Phys. 61, 1 (1989)</li>
<li>Penrose, R., "Cycles of Time" (2010)</li>
<li>Bekenstein, J., Phys. Rev. D 7, 2333 (1973)</li>
</ol>
</div>
</div>
</div>
<!-- MATH TAB -->
<div id="math" class="content">
<div class="math-container">
<h2 style="font-size: 2rem; margin-bottom: 2rem; text-align: center;">Interactive Mathematics</h2>
<div class="interactive-box">
<h3 style="color: #60a5fa; margin-bottom: 1rem;">Adjust Entropy (S)</h3>
<input type="range" id="entropy-slider" min="0" max="100" value="50" oninput="updateMath(this.value)" style="width: 100%; margin-bottom: 1rem;">
<div style="display: flex; justify-content: space-between; color: #9ca3af; font-size: 0.9rem;">
<span>S = <span id="entropy-value">50</span></span>
<span>Λ = 100</span>
</div>
<div class="stats-grid">
<div class="stat-box">
<div class="label">|U|</div>
<div class="value" id="math-u-mag">60.65</div>
</div>
<div class="stat-box">
<div class="label">U²</div>
<div class="value" id="math-u-squared" style="color: #ef4444;">-3679</div>
</div>
<div class="stat-box">
<div class="label">Dimension</div>
<div class="value" id="math-dimension">2.86</div>
</div>
<div class="stat-box">
<div class="label">w (EoS)</div>
<div class="value" id="math-w">-0.833333</div>
</div>
</div>
</div>
<div class="chart-container">
<h3 style="color: #60a5fa; margin-bottom: 1rem;">Evolution Plots</h3>
<canvas id="evolution-chart"></canvas>
</div>
<div class="interactive-box">
<h3 style="color: #60a5fa; margin-bottom: 1rem;">Key Equations</h3>
<div style="background: #0a0e27; padding: 1.5rem; border-radius: 0.5rem; margin-bottom: 1rem;">
<div style="color: #9ca3af; margin-bottom: 0.5rem;">Fundamental:</div>
<div style="font-size: 1.3rem; text-align: center;">
\[ U^2 = -\infty \]
</div>
</div>
<div style="background: #0a0e27; padding: 1.5rem; border-radius: 0.5rem; margin-bottom: 1rem;">
<div style="color: #9ca3af; margin-bottom: 0.5rem;">Solution:</div>
<div style="text-align: center;">
\[ U(S,\Lambda) = i\Lambda \cdot e^{-S^2/2\Lambda^2} \]
</div>
</div>
<div style="background: #0a0e27; padding: 1.5rem; border-radius: 0.5rem;">
<div style="color: #9ca3af; margin-bottom: 0.5rem;">Dark Energy:</div>
<div style="text-align: center;">
\[ w(S) = -1 + \frac{2}{3}\left(\frac{S}{\Lambda}\right)^2 \]
</div>
</div>
</div>
</div>
</div>
<!-- COMPARISON TAB -->
<div id="comparison" class="content">
<div class="math-container">
<h2 style="font-size: 2rem; margin-bottom: 2rem; text-align: center;">Mobley vs ΛCDM</h2>
<div class="comparison-container">
<div class="comparison-box">
<h3>Mobley Framework</h3>
<table class="data-table">
<tr>
<th>Parameter</th>
<th>Value</th>
</tr>
<tr>
<td>Fundamental Equation</td>
<td>U² = -∞</td>
</tr>
<tr>
<td>Free Parameters</td>
<td>1 (Λ)</td>
</tr>
<tr>
<td>w₀ (today)</td>
<td>-0.9999</td>
</tr>
<tr>
<td>w₁ (evolution)</td>
<td>6.7×10⁻⁵</td>
</tr>
<tr>
<td>Inflation</td>
<td>Natural (S≈0)</td>
</tr>
<tr>
<td>Fine-tuning</td>
<td>None</td>
</tr>
<tr>
<td>Consciousness</td>
<td>Fundamental</td>
</tr>
<tr>
<td>Ultimate Fate</td>
<td>Cyclic (Bang)</td>
</tr>
</table>
</div>
<div class="comparison-box">
<h3>ΛCDM</h3>
<table class="data-table">
<tr>
<th>Parameter</th>
<th>Value</th>
</tr>
<tr>
<td>Fundamental Equation</td>
<td>GR + Λ</td>
</tr>
<tr>
<td>Free Parameters</td>
<td>6 (Ωₘ, Ωᵦ, h, σ₈, nₛ, Λ)</td>
</tr>
<tr>
<td>w₀ (today)</td>
<td>-1 (exactly)</td>
</tr>
<tr>
<td>w₁ (evolution)</td>
<td>0 (constant)</td>
</tr>
<tr>
<td>Inflation</td>
<td>Separate mechanism</td>
</tr>
<tr>
<td>Fine-tuning</td>
<td>10⁻¹²⁰ problem</td>
</tr>
<tr>
<td>Consciousness</td>
<td>Emergent/Irrelevant</td>
</tr>
<tr>
<td>Ultimate Fate</td>
<td>Heat Death</td>
</tr>
</table>
</div>
</div>
<div class="chart-container">
<h3 style="color: #60a5fa; margin-bottom: 1rem;">Expansion History: H(z)</h3>
<canvas id="comparison-chart"></canvas>
</div>
<div class="chart-container">
<h3 style="color: #60a5fa; margin-bottom: 1rem;">Dark Energy Evolution: w(a)</h3>
<canvas id="w-evolution-chart"></canvas>
</div>
<div class="interactive-box">
<h3 style="color: #60a5fa; margin-bottom: 1.5rem;">Key Differences</h3>
<div style="line-height: 1.8;">
<p style="margin-bottom: 1rem;">
<strong style="color: #60a5fa;">1. Testable Difference:</strong>
Mobley predicts time-varying w(a), ΛCDM predicts constant w = -1.
<span style="color: #10b981;">DESI/Euclid will distinguish by 2027.</span>
</p>
<p style="margin-bottom: 1rem;">
<strong style="color: #60a5fa;">2. Philosophical:</strong>
Mobley makes consciousness fundamental, ΛCDM treats it as emergent.
</p>
<p style="margin-bottom: 1rem;">
<strong style="color: #60a5fa;">3. Explanatory Power:</strong>
Mobley explains fine-tuning via cyclic self-organization. ΛCDM requires anthropic reasoning.
</p>
<p>
<strong style="color: #60a5fa;">4. Ultimate Fate:</strong>
Mobley: universe rebirths at S=Λ. ΛCDM: eternal expansion and heat death.
</p>
</div>
</div>
</div>
</div>
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if (tabName === 'math') {
setTimeout(() => {
createEvolutionChart();
MathJax.typesetPromise();
}, 100);
} else if (tabName === 'comparison') {
setTimeout(() => {
createComparisonCharts();
MathJax.typesetPromise();
}, 100);
} else if (tabName === 'paper') {
setTimeout(() => {
MathJax.typesetPromise();
}, 100);
}
}
function toggleSimulation() {
isRunning = !isRunning;
document.getElementById('play-pause-text').textContent = isRunning ? '⏸ Pause' : '▶ Play';
}
function resetSimulation() {
time = 0;
observers = 0.01;
dataHistory = [];
updateDisplay();
}
function updateLambda(value) {
lambda = parseFloat(value);
document.getElementById('lambda-value').textContent = lambda.toFixed(3);
}
function updateTurbulence(value) {
turbulenceIntensity = parseFloat(value);
document.getElementById('turbulence-value').textContent = turbulenceIntensity.toFixed(1);
}
function updateViewMode(mode) {
viewMode = mode;
}
// Export data
function exportData() {
if (dataHistory.length === 0) {
alert('No data to export. Run the simulation first.');
return;
}
// CSV export
let csv = 'Time,Observers,U_Squared,Dimension,w,Hubble\n';
dataHistory.forEach(d => {
csv += `${d.time},${d.observers},${d.uSquared},${d.dimension},${d.w},${d.hubble}\n`;
});
const blob = new Blob([csv], { type: 'text/csv' });
const url = URL.createObjectURL(blob);
const a = document.createElement('a');
a.href = url;
a.download = 'mobley_simulation_data.csv';
a.click();
URL.revokeObjectURL(url);
// Also export JSON
const json = JSON.stringify(dataHistory, null, 2);
const jsonBlob = new Blob([json], { type: 'application/json' });
const jsonUrl = URL.createObjectURL(jsonBlob);
const jsonA = document.createElement('a');
jsonA.href = jsonUrl;
jsonA.download = 'mobley_simulation_data.json';
jsonA.click();
URL.revokeObjectURL(jsonUrl);
}
// PDF generation
async function generatePDF() {
const { jsPDF } = window.jspdf;
const pdf = new jsPDF('p', 'mm', 'a4');
const element = document.getElementById('paper-content');
// Show loading
const originalText = event.target.textContent;
event.target.textContent = '⏳ Generating...';
event.target.disabled = true;
try {
const canvas = await html2canvas(element, {
scale: 2,
useCORS: true,
logging: false
});
const imgData = canvas.toDataURL('image/png');
const imgWidth = 210; // A4 width in mm
const pageHeight = 297; // A4 height in mm
const imgHeight = (canvas.height * imgWidth) / canvas.width;
let heightLeft = imgHeight;
let position = 0;
pdf.addImage(imgData, 'PNG', 0, position, imgWidth, imgHeight);
heightLeft -= pageHeight;
while (heightLeft >= 0) {
position = heightLeft - imgHeight;
pdf.addPage();
pdf.addImage(imgData, 'PNG', 0, position, imgWidth, imgHeight);
heightLeft -= pageHeight;
}
pdf.save('Mobley_Framework.pdf');
} catch (error) {
console.error('PDF generation error:', error);
alert('Error generating PDF. Please try again.');
} finally {
event.target.textContent = originalText;
event.target.disabled = false;
}
}
// LaTeX download
function downloadLaTeX() {
const latex = `\\documentclass{article}\usepackage{amsmath} \usepackage{amssymb} \usepackage{graphicx}
\title{Cosmology from Self-Observation: The \(U^2 = -\\infty\) Framework} \author{John Alexander Mobley} \date{February 2026}
\begin{document}
\maketitle
\begin{abstract} We propose that the universe satisfies the fundamental equation \(U^2 = -\\infty\), where \(U\) is a Clifford multivector representing the cosmic state. This equation implies the universe is complex-valued (\(U = i\\Lambda\)) and evolves through entropy increase driven by observation. From this single principle, we derive: (i) cosmological expansion, (ii) inflation, (iii) dark energy, and (iv) cyclic cosmology. The theory predicts \(w_1 \\approx 7\\times10^{-5}\), testable by 2027. \end{abstract}
\section{Introduction} Modern cosmology faces profound puzzles: fine-tuning, the cosmological constant problem, and the coincidence problem. We propose the universe is a self-referential structure whose dynamics are determined by a single equation:
\begin{equation} U^2 = -\infty \end{equation}
\section{Mathematical Framework}
\subsection{The Observer Field} We define observer count \(O\) as total entropy:
\begin{equation} O \equiv S_{\text{total}} = \ln(\Omega) \end{equation}
\subsection{Solution} The universe as Clifford multivector:
\begin{equation} U(S,\Lambda) = i\Lambda \cdot e{-S2/2\Lambda^2} \end{equation}
\section{Cosmological Solutions}
\subsection{Expansion History} Scale factor evolution:
\begin{equation} a(t) \propto e{S(t)2/\Lambda^2} \end{equation}
\subsection{Dark Energy} Equation of state:
\begin{equation} w(S) = -1 + \frac{2}{3}\left(\frac{S}{\Lambda}\right)^2 \end{equation}
\section{Testable Predictions} \begin{enumerate} \item Dark energy evolution: \(w_1 \\approx 7\\times10^{-5}\) \item Decoherence scaling: \(\\Gamma \\propto S_{\\text{local}}\) \item Laboratory analogue: \(P(k,N) \\propto e^{-\\alpha N^2}\) \end{enumerate}
\section{Conclusion} We have presented a cosmological framework based on \(U^2 = -\\infty\), yielding testable predictions. If validated, this represents a fundamental shift: the universe as a self-observing structure whose existence is maintained by its inability to completely know itself.
\end{document}`;
const blob = new Blob([latex], { type: 'text/plain' });
const url = URL.createObjectURL(blob);
const a = document.createElement('a');
a.href = url;
a.download = 'Mobley_Framework.tex';
a.click();
URL.revokeObjectURL(url);
}
// Math tab functions
function updateMath(value) {
const S = parseFloat(value);
const LAMBDA = 100;
document.getElementById('entropy-value').textContent = S;
const U_mag = LAMBDA * Math.exp(-S*S / (2*LAMBDA*LAMBDA));
const U_squared = -LAMBDA * LAMBDA * Math.exp(-S*S / (LAMBDA*LAMBDA));
const dimension = 10 / (1 + S*S / (LAMBDA*LAMBDA));
const w = -1 + (2/3) * (S/LAMBDA) * (S/LAMBDA);
document.getElementById('math-u-mag').textContent = U_mag.toFixed(2);
document.getElementById('math-u-squared').textContent = U_squared.toFixed(0);
document.getElementById('math-dimension').textContent = dimension.toFixed(2);
document.getElementById('math-w').textContent = w.toFixed(6);
}
let evolutionChart = null;
function createEvolutionChart() {
const ctx = document.getElementById('evolution-chart');
if (!ctx) return;
const LAMBDA = 100;
const sValues = [];
const uMagValues = [];
const dimensionValues = [];
const wValues = [];
for (let s = 0; s <= LAMBDA; s += 1) {
sValues.push(s);
uMagValues.push(LAMBDA * Math.exp(-s*s / (2*LAMBDA*LAMBDA)));
dimensionValues.push(10 / (1 + s*s / (LAMBDA*LAMBDA)));
wValues.push(-1 + (2/3) * (s/LAMBDA) * (s/LAMBDA));
}
if (evolutionChart) {
evolutionChart.destroy();
}
evolutionChart = new Chart(ctx, {
type: 'line',
data: {
labels: sValues,
datasets: [
{
label: '|U| (scaled ×0.1)',
data: uMagValues.map(v => v * 0.1),
borderColor: '#60a5fa',
backgroundColor: 'rgba(96, 165, 250, 0.1)',
tension: 0.4
},
{
label: 'Dimension',
data: dimensionValues,
borderColor: '#a78bfa',
backgroundColor: 'rgba(167, 139, 250, 0.1)',
tension: 0.4
},
{
label: 'w + 1 (×10)',
data: wValues.map(v => (v + 1) * 10),
borderColor: '#f87171',
backgroundColor: 'rgba(248, 113, 113, 0.1)',
tension: 0.4
}
]
},
options: {
responsive: true,
maintainAspectRatio: true,
plugins: {
legend: {
labels: {
color: '#e0e0e0'
}
}
},
scales: {
x: {
title: {
display: true,
text: 'Entropy (S)',
color: '#e0e0e0'
},
ticks: {
color: '#9ca3af'
},
grid: {
color: '#374151'
}
},
y: {
title: {
display: true,
text: 'Value',
color: '#e0e0e0'
},
ticks: {
color: '#9ca3af'
},
grid: {
color: '#374151'
}
}
}
}
});
}
// Comparison charts
let comparisonChart = null;
let wEvolutionChart = null;
function createComparisonCharts() {
// H(z) comparison
const ctx1 = document.getElementById('comparison-chart');
if (ctx1 && !comparisonChart) {
const zValues = [];
const mobleyH = [];
const lcdmH = [];
for (let z = 0; z <= 5; z += 0.1) {
zValues.push(z.toFixed(1));
const a = 1 / (1 + z);
// Mobley: H(z) depends on S(a)
const S = 50 * a; // Simplified
const H_mob = Math.sqrt(0.3 * Math.pow(1+z, 3) + 0.7 * Math.exp(S*S/10000));
mobleyH.push(H_mob);
// ΛCDM
const H_lcdm = Math.sqrt(0.3 * Math.pow(1+z, 3) + 0.7);
lcdmH.push(H_lcdm);
}
comparisonChart = new Chart(ctx1, {
type: 'line',
data: {
labels: zValues,
datasets: [
{
label: 'Mobley',
data: mobleyH,
borderColor: '#60a5fa',
backgroundColor: 'rgba(96, 165, 250, 0.1)',
tension: 0.4
},
{
label: 'ΛCDM',
data: lcdmH,
borderColor: '#f87171',
backgroundColor: 'rgba(248, 113, 113, 0.1)',
tension: 0.4,
borderDash: [5, 5]
}
]
},
options: {
responsive: true,
plugins: {
legend: {
labels: { color: '#e0e0e0' }
}
},
scales: {
x: {
title: { display: true, text: 'Redshift (z)', color: '#e0e0e0' },
ticks: { color: '#9ca3af' },
grid: { color: '#374151' }
},
y: {
title: { display: true, text: 'H(z) (normalized)', color: '#e0e0e0' },
ticks: { color: '#9ca3af' },
grid: { color: '#374151' }
}
}
}
});
}
// w(a) evolution
const ctx2 = document.getElementById('w-evolution-chart');
if (ctx2 && !wEvolutionChart) {
const aValues = [];
const mobleyW = [];
const lcdmW = [];
const w1 = 0.000067;
for (let a = 0.2; a <= 1; a += 0.01) {
aValues.push(a.toFixed(2));
mobleyW.push(-1 + w1 * (1 - a));
lcdmW.push(-1.0);
}
wEvolutionChart = new Chart(ctx2, {
type: 'line',
data: {
labels: aValues,
datasets: [
{
label: 'Mobley',
data: mobleyW,
borderColor: '#60a5fa',
backgroundColor: 'rgba(96, 165, 250, 0.1)',
tension: 0.4
},
{
label: 'ΛCDM (w = -1)',
data: lcdmW,
borderColor: '#f87171',
backgroundColor: 'rgba(248, 113, 113, 0.1)',
tension: 0,
borderDash: [5, 5]
}
]
},
options: {
responsive: true,
plugins: {
legend: {
labels: { color: '#e0e0e0' }
}
},
scales: {
x: {
title: { display: true, text: 'Scale Factor (a)', color: '#e0e0e0' },
ticks: { color: '#9ca3af' },
grid: { color: '#374151' }
},
y: {
title: { display: true, text: 'w(a)', color: '#e0e0e0' },
ticks: { color: '#9ca3af' },
grid: { color: '#374151' },
min: -1.001,
max: -0.999
}
}
}
});
}
}
// Initialize on load
window.addEventListener('load', () => {
initThreeJS();
updateDisplay();
updateMath(50);
// Trigger MathJax rendering
if (typeof MathJax !== 'undefined') {
MathJax.typesetPromise();
}
});
</script>