What Is the Universe Made Of? The 5% We See

Imagine you have a giant toy box that contains everything in the universe—stars, planets, galaxies, gas clouds, and even the space between them. If you carefully sorted through this box and counted only the things made of atoms (the same stuff that makes up you, your dog, and your school), you would find that they make up just 5% of the total contents. The other 95% is completely invisible and made of something we don’t fully understand yet. This chapter is your guide to that surprising 5%—the ordinary matter we can see. We will explore how scientists precisely measured this number using two cosmic detective tools: the afterglow of the Big Bang (the Cosmic Microwave Background, or CMB) and the primordial element recipe from the first few minutes of the universe (Big Bang Nucleosynthesis, or BBN). By the end, you’ll know why the universe’s inventory forces us to accept the existence of dark matter and dark energy, setting the stage for the mysteries explored in later chapters.

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The Cosmic Inventory: How Do We Weigh the Universe?

Before we dive into the technical details, let’s establish the basic framework modern cosmologists use to describe the universe’s content. The foundation is the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, which assumes the universe is homogeneous and isotropic on large scales. Einstein’s field equations then simplify to the Friedmann equations:

$$H^2(t) = \frac{8\pi G}{3} \rho(t) - \frac{k c^2}{a^2(t)} + \frac{\Lambda c^2}{3}$$

Here, $H(t)$ is the Hubble parameter (expansion rate), $a(t)$ is the scale factor, $\rho(t)$ is the total energy density, $k$ is the curvature, and $\Lambda$ is the cosmological constant. The total density $\rho$ is split into components: ordinary matter (baryons), dark matter, dark energy, and radiation. Each component’s contribution is expressed as a density parameter $\Omega_i = \rho_i / \rho_c$, where $\rho_c = 3H^2/(8\pi G)$ is the critical density—the exact density needed for a flat universe ($k=0$). Current measurements from the Planck satellite give $H_0 \approx 67.4\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$, so $\rho_c \approx 8.5 \times 10^{-27}\ \mathrm{kg\ m^{-3}}$ (about five hydrogen atoms per cubic meter!).

The “cosmic pie chart” is then defined by these $\Omega$ values:

• $\Omega_b$: baryonic (ordinary) matter
• $\Omega_c$: cold dark matter
• $\Omega_\Lambda$: dark energy (cosmological constant)
• $\Omega_r$: radiation (photons and neutrinos)
• $\Omega_k$: curvature

Observations consistently show $\Omega_k \approx 0$, meaning the universe is spatially flat. Thus, the sum of all $\Omega_i$ equals 1. The stunning result from multiple independent probes is:

$$\Omega_b \approx 0.05,\quad \Omega_c \approx 0.27,\quad \Omega_\Lambda \approx 0.68$$

So, ordinary matter—everything made of atoms—is just 5% of the universe’s total energy budget. But how do we know $\Omega_b$ so precisely? The two pillars are Cosmic Microwave Background anisotropies and Big Bang Nucleosynthesis.

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Pillar 1: The Cosmic Microwave Background – The Universe’s Baby Picture

What is the CMB?

About 380,000 years after the Big Bang, the universe cooled enough for protons and electrons to combine into neutral hydrogen atoms. This event, called recombination, made the universe transparent for the first time. Photons that were previously scattered by free electrons could now travel freely. These photons have been crossing the cosmos ever since, stretched by the expansion of the universe into the microwave band we detect today. This is the Cosmic Microwave Background (CMB)—a nearly uniform glow at a temperature of $2.725\ \mathrm{K}$ coming from all directions.

But the CMB isn’t perfectly smooth. Tiny fluctuations in temperature (about 1 part in 100,000) encode a wealth of information about the universe’s composition and geometry. These anisotropies were first mapped by the COBE satellite (1992), then with exquisite precision by WMAP (2001-2010) and Planck (2009-2013). The CMB power spectrum—a plot of temperature variation versus angular scale—is like a cosmic fingerprint.

How Baryons Leave Their Fingerprint on the CMB

The key physics involves photon-baryon fluid acoustic oscillations before recombination. In the hot, dense early universe, photons and baryons (protons and neutrons) were tightly coupled by Thomson scattering. Overdense regions (slightly higher gravity) would pull baryons inward, but photon pressure pushed back, creating sound waves. The competition between gravity and pressure sets up standing waves. When recombination happens, these waves freeze, imprinting a characteristic pattern on the CMB temperature map.

The baryon density $\Omega_b h^2$ (where $h = H_0/(100\ \mathrm{km\ s^{-1}\ Mpc^{-1}})$) crucially affects these oscillations:

1. Peak Heights: Baryons add inertia to the photon-baryon fluid. This enhances the compression phases of the sound waves relative to the rarefaction phases. Specifically, the odd-numbered peaks (first, third, etc.) in the angular power spectrum are boosted compared to the even-numbered ones. The ratio of the first to second peak heights is a sensitive baryometer. 2. Peak Positions: The overall scale of the acoustic horizon (the distance sound waves traveled before recombination) depends on the expansion history, which involves $\Omega_b$ and other components. The peak locations tell us about the universe’s geometry (flatness), while their relative heights tease apart $\Omega_b$, $\Omega_c$, and other parameters.

Extracting $\Omega_b$ from CMB Data: A Technical Walkthrough

Cosmologists fit the observed CMB power spectrum to theoretical models computed with Boltzmann codes like CAMB or CLASS. These codes solve the coupled Einstein-Boltzmann equations for photons, baryons, dark matter, and neutrinos. The main parameters include:

• $\Omega_b h^2$: physical baryon density
• $\Omega_c h^2$: physical cold dark matter density
• $\theta_s$: angular size of the sound horizon (related to curvature)
• $\tau$: optical depth to reionization
• $n_s$: scalar spectral index
• $A_s$: amplitude of primordial fluctuations

The Planck 2018 results gave:

$$\Omega_b h^2 = 0.02237 \pm 0.00015$$

With $h = 0.674 \pm 0.005$, this translates to:

$$\Omega_b = \frac{\Omega_b h^2}{h^2} = \frac{0.02237}{(0.674)^2} \approx 0.0493 \pm 0.0005$$

So, baryons constitute 4.93% of the universe’s total energy density, with an uncertainty of only about 1%! This precision is possible because the CMB anisotropies are measured across a wide range of angular scales (multipoles $\ell \sim 2$ to $2500$), and the acoustic peak pattern is starkly sensitive to $\Omega_b h^2$.

Practical Example: Simulating the CMB Power Spectrum

Let’s illustrate with a simple conceptual experiment using a Python-like pseudocode (real calculations require sophisticated codes). Suppose we want to see how changing $\Omega_b h^2$ affects the first two peaks.

```python

Pseudocode: Varying baryon density in a CMB spectrum model

import cosmology_toolkit as ct

Baseline: Planck best-fit

params_baseline = { 'omega_b_h2': 0.02237, 'omega_c_h2': 0.1200, 'theta_s': 1.0411e-2, 'tau': 0.054, 'n_s': 0.965, 'A_s': 2.1e-9 } cl_baseline = ct.compute_cmb_spectrum(params_baseline)

Higher baryon density

params_high_b = params_baseline.copy() params_high_b['omega_b_h2'] = 0.030 # 34% higher cl_high_b = ct.compute_cmb_spectrum(params_high_b)

Lower baryon density

params_low_b = params_baseline.copy() params_low_b['omega_b_h2'] = 0.015 # 33% lower cl_low_b = ct.compute_cmb_spectrum(params_low_b)

Compare first peak height (l~200) and first/second peak ratio

Result: Higher Ω_b h^2 -> first peak boosted, second peak suppressed.

Lower Ω_b h^2 -> first peak lower, second peak relatively higher.

```

In a real analysis, a Markov Chain Monte Carlo (MCMC) algorithm explores the parameter space, comparing m