Big Bang Theory

Q: Did the Big Bang happen at a particular point in space?

No — the Big Bang happened EVERYWHERE simultaneously. The universe was hot and dense at every point. Expansion isn't outward from a center; it's stretching of space itself. There is no 'edge' to the universe and no preferred location.

Q: What was the universe expanding INTO?

Nothing — there is no 'outside'. The expansion describes the evolving geometry of spacetime itself; distances between fixed coordinates grow with time. Asking what's outside is like asking what's north of the North Pole.

Q: How can we 'see' back to 380,000 years after the Big Bang?

Before $z \approx 1090$, the universe was an opaque plasma (free electrons scattered photons). When it cooled below ~3000 K, electrons combined with nuclei to form neutral atoms — recombination — and photons streamed freely. Those photons, redshifted by ~1100×, are the CMB we observe at 2.725 K microwave wavelengths.

Q: Why is dark energy 'discovered' if we can't see it?

It's inferred from acceleration: distant Type Ia supernovae appear dimmer than expected for a decelerating universe, indicating that expansion is speeding up. To explain this within Friedmann's equation requires a repulsive component — Λ or 'dark energy' — comprising ~68% of the universe.

Q: Why is the CMB temperature so uniform?

Inflation: a brief epoch of exponential expansion ($t \sim 10^{-35}$ s) stretched a tiny region to vastly larger than the observable universe, smoothing out inhomogeneities. The tiny remaining ~10⁻⁵ fluctuations seeded today's galaxies.

Section 02

The Idea, Step by Step

Start simple: everything is rushing apart

Picture raisins baked into a loaf of bread as it rises. The dough swells, and every raisin drifts away from every other raisin — and from any one raisin's point of view, the more distant raisins move away fastest. No raisin is the "center"; the whole loaf is simply getting bigger. Our universe does the same thing: distant galaxies are all moving apart from one another. Now run the movie backward. If everything is flying apart today, then long ago it was all crammed together — unimaginably hot and dense. That squeezed-together beginning, about 13.8 billion years ago, is the Big Bang. It was not an explosion at one spot inside space; space itself has been stretching ever since, everywhere at once.

Build it up: how fast is "apart"?

Edwin Hubble measured two things for many galaxies: how far away each one sits (distance $d$) and how fast it is receding (velocity $v$). He found a beautifully simple rule — the farther the galaxy, the faster it flees:

Hubble's Law

$$v = H_0\,d$$

The constant $H_0$ (the Hubble constant, about $70\ \text{km/s/Mpc}$) is just the present-day expansion rate. Quick number: a galaxy $100$ Mpc away recedes at $v \approx 70 \times 100 = 7000\ \text{km/s}$. We read that speed off the galaxy's redshift: as light crosses expanding space, its wavelength is stretched, sliding toward the red end of the spectrum.

Go deeper (AP / intro-college): the scale factor and Friedmann's equation

Cosmologists track the expansion with one number, the scale factor $a(t)$ — the relative size of space, with $a=1$ today. Stretched light ties straight to it: $1+z = a_{\text{now}}/a_{\text{emit}}$, so a redshift of $z=1$ means space has doubled since that light set out. What sets the expansion rate is the universe's contents, through the Friedmann equation $H^2 = \tfrac{8\pi G}{3}\rho + \tfrac{\Lambda c^2}{3}$. Matter (relative density $\Omega_m$) gravitates and tries to slow the expansion down; dark energy ($\Omega_\Lambda$) pushes the other way and speeds it up. In the sim, the $H_0$, $\Omega_m$, and $\Omega_\Lambda$ sliders feed directly into $a(t)$.

Try this in the simulation above

In Expansion History mode, set $\Omega_\Lambda = 0$ and watch the $a(t)$ curve bend over — a gravity-only universe always decelerates. Then raise $\Omega_\Lambda$ back up and see the curve sweep upward as dark energy takes over. Switch to Hubble Diagram mode and drag $H_0$: the slope of the $v$–$d$ line tilts right along with it. Finally, open CMB Map mode to see the $\sim 10^{-5}$ temperature ripples — the seeds of every galaxy — frozen into the oldest light in the universe.

Section 03

Equations & Derivation

The Big Bang theory describes the universe as expanding from an extremely hot, dense initial state ~13.8 billion years ago. Friedmann's equations from Einstein's general relativity govern the expansion; the cosmic microwave background (CMB) and Big Bang nucleosynthesis (BBN) provide observational confirmation.

Friedmann Equation (flat universe)

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

Symbol	Meaning	SI Unit
$a(t)$	Scale factor	—
$H = \dot{a}/a$	Hubble parameter	s⁻¹
$H_0$	Today's Hubble constant	km/s/Mpc
$\rho$	Energy density	kg/m³
$\Lambda$	Cosmological constant	m⁻²
$\Omega_m,\Omega_\Lambda$	Matter, dark-energy density (relative)	—
$z$	Redshift	—

Step 1 — Hubble's Law

$$v = H_0 d$$

Recession velocity is proportional to distance — galaxies don't move through space; space itself stretches.

Step 2 — Redshift & scale factor

$$1 + z = \frac{a(\text{now})}{a(\text{emission})} = \frac{\lambda_{\text{obs}}}{\lambda_{\text{emit}}}$$

Step 3 — Friedmann's equations

From Einstein's GR for a homogeneous, isotropic universe (FLRW metric):

$$\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}$$

Step 4 — Density parameters

$$\Omega_m + \Omega_\Lambda + \Omega_k = 1, \quad \Omega_i = \frac{\rho_i}{\rho_{\text{crit}}}, \quad \rho_{\text{crit}} = \frac{3H_0^2}{8\pi G}$$

Planck 2018 values: $H_0 = 67.4$ km/s/Mpc, $\Omega_m = 0.315$, $\Omega_\Lambda = 0.685$, $\Omega_k \approx 0$ (flat).

Step 5 — CMB & BBN

The CMB at $T = 2.725$ K is relic photons from $z \approx 1090$ ($t \approx 380{,}000$ yr). BBN at $t \sim 3$ min produced $^4$He (~24% by mass), D, $^3$He, $^7$Li in ratios that match observations.

Mapping to the simulation

Expansion mode shows $a(t)$ for chosen $\Omega_m,\Omega_\Lambda$. CMB mode renders the Planck-style temperature anisotropy map. Hubble mode plots $v$ vs $d$ with selectable $H_0$.

Reference: Liddle — An Introduction to Modern Cosmology, 3rd Ed., Wiley 2015; Weinberg — The First Three Minutes, Basic Books 1977; Dodelson — Modern Cosmology, 2nd Ed., Academic Press 2020.

Section 04

Frequently Asked Questions

Expansion mode plots the scale factor $a(t)$ from the Friedmann equation given your choice of densities. CMB mode shows the temperature anisotropies (~10⁻⁵ fluctuations) of the relic radiation. Hubble mode plots the velocity-distance relation $v = H_0 d$.

Cosmic microwave background detected by every WMAP/Planck/CMB-S4 experiment; the abundance of light elements (75% H, 24% He) matches BBN to <1%; supernova distance-redshift measurements (1998 Nobel) detected dark-energy-driven acceleration; LIGO-Virgo gravitational waves from neutron-star mergers measure $H_0$ independently.

No — the Big Bang happened EVERYWHERE simultaneously. The universe was hot and dense at every point. Expansion isn't outward from a center; it's stretching of space itself. There is no 'edge' to the universe and no preferred location.

Nothing — there is no 'outside'. The expansion describes the evolving geometry of spacetime itself; distances between fixed coordinates grow with time. Asking what's outside is like asking what's north of the North Pole.

Before $z \approx 1090$, the universe was an opaque plasma (free electrons scattered photons). When it cooled below ~3000 K, electrons combined with nuclei to form neutral atoms — recombination — and photons streamed freely. Those photons, redshifted by ~1100×, are the CMB we observe at 2.725 K microwave wavelengths.

It's inferred from acceleration: distant Type Ia supernovae appear dimmer than expected for a decelerating universe, indicating that expansion is speeding up. To explain this within Friedmann's equation requires a repulsive component — Λ or 'dark energy' — comprising ~68% of the universe.

Inflation: a brief epoch of exponential expansion ($t \sim 10^{-35}$ s) stretched a tiny region to vastly larger than the observable universe, smoothing out inhomogeneities. The tiny remaining ~10⁻⁵ fluctuations seeded today's galaxies.

Resources: Khan Academy; HyperPhysics; MIT OpenCourseWare; Paul's Physics Notes.

Section 05

Common Misconceptions

❌ Misconception: The Big Bang was an explosion in pre-existing space.

✅ Correction: It wasn't an explosion at all — there was no pre-existing space. The Big Bang is the beginning of space and time themselves. Spacetime expands; nothing 'flies outward' from a central point.

📖 Reference: Weinberg — The First Three Minutes, Basic Books 1977; Liddle — Introduction to Modern Cosmology, 3rd Ed., Wiley 2015, Ch. 1.

❌ Misconception: Galaxies move through space at velocities given by Hubble's law.

✅ Correction: Distant galaxies are essentially stationary in the local frame; the apparent velocity comes from cosmic expansion stretching space between us. For $z > 1$, recession 'velocities' formally exceed $c$ — no relativity violation, because nothing moves faster than light through space locally.

📖 Reference: Davis & Lineweaver — 'Expanding confusion', PASA 21 (2004); Liddle Ch. 3.

❌ Misconception: Redshift is just a Doppler effect.

✅ Correction: Cosmological redshift is fundamentally different: photons aren't 'thrown' from receding galaxies. Their wavelengths stretch with space itself. The Doppler formula gives the right answer at low $z$ but breaks down at high $z$.

📖 Reference: Liddle Ch. 3 'The geometry of the universe'; Misner, Thorne & Wheeler — Gravitation, §29.

❌ Misconception: The Big Bang theory says the universe came from nothing.

✅ Correction: Standard cosmology starts at $t \sim 10^{-43}$ s (Planck time) and tracks evolution forward. What happened before — or whether 'before' is meaningful — requires quantum gravity, which we lack. The theory is silent on the very first moment.

📖 Reference: Hawking — A Brief History of Time, Bantam 1988; Liddle Ch. 11.

❌ Misconception: All matter and energy were created in the Big Bang.

✅ Correction: BBN explains the LIGHT element abundances. Heavier elements (C, N, O, Fe...) were synthesized later in stars and supernovae. So the iron in your blood was forged in a stellar explosion, not the Big Bang.

📖 Reference: Burbidge, Burbidge, Fowler & Hoyle — 'Synthesis of the Elements in Stars', Rev. Mod. Phys. 29 (1957); HRW 10th Ed., §44.

❌ Misconception: The Big Bang theory is just one cosmological model among many equally good ones.

✅ Correction: Big Bang cosmology has overwhelming evidence: CMB blackbody spectrum, light element abundances, large-scale structure formation, expansion (Hubble), redshift-magnitude of supernovae. Steady-state and other competitors fail multiple observational tests.

📖 Reference: Penzias & Wilson — Astrophys. J. 142 (1965) 419 (CMB discovery); WMAP/Planck papers 2003-2018.

Misconception research: Davis & Lineweaver — PASA 21 (2004); Trundle & Bishop — Astron. Education Rev. 11 (2012); Bailey et al. — Phys. Educ. 38 (2003).