Expanding Universe & Big Bang

The universe expands as space itself stretches, like dots on an inflating balloon moving apart. More distant galaxies recede faster; that is Hubble's law v = H₀d, and light from receding galaxies stretches to longer wavelengths as redshift. The Big Bang, about 13.8 billion years ago from an ultra-hot, ultra-dense state, is supported by cosmic expansion, the microwave background (about 2.7 K), and the hydrogen-to-helium ratio. Here you can raise the scale-factor slider and watch galaxies recede from the observer.

The universe is expanding

🎈 Balloon analogy

①Mark dots on a balloon and inflate — all dots move apart

②From any dot, the rest appear to move away

③This is cosmic expansion! Space itself stretches

Visualizing cosmic expansion

Scale factor1

💡 Key observations

①Increasing the scale factor moves all galaxies away from the observer

②Galaxies further away recede faster (longer arrows)

③This is the heart of Hubble's law: recession speed proportional to distance

Hubble's Law

v = H₀d

recession velocity (v) = Hubble constant (H₀) × distance (d) — farther → faster

Redshift

z = Δλ / λ₀ = v / c

light from a receding galaxy → wavelength stretches (redshift) → measure recession speed

🔴 Measuring distance via redshift

①Approaching ambulance siren: high pitch → low pitch (Doppler effect)

②Light from receding galaxies stretches similarly — appears redder

③Larger redshift → faster recession → farther galaxy

Big Bang cosmology

Big Bang cosmology core

about 13.8 billion years ago, the universe began as an ultra-hot, ultra-dense point that exploded → expanding

after the Big Bang the universe expanded and cooled → current universe

Three pillars of Big Bang evidence

① Hubble's law (cosmic expansion) ② Cosmic microwave background (2.7K) ③ Hydrogen:helium = 3:1

only the Big Bang theory explains all three observations

📡 Cosmic Microwave Background (CMB)

①About 380,000 years after the Big Bang — universe cooled enough for light to travel freely

②That light, stretched by expansion, is now microwaves observed from all directions

③Temperature: ~2.7K — discovered by Penzias and Wilson in 1965

Worked Examples and Exam Practice

Example 1

If the Hubble constant is H₀ = 70 km/s/Mpc, what is the recession speed of a galaxy 100 Mpc away?

Use Hubble's law, v = H₀d.

v = 70 km/s/Mpc × 100 Mpc = 7,000 km/s.

▸ 7,000 km/s

The farther a galaxy is, the faster it recedes, in proportion to distance.

Example 2

Name three key observations that support Big Bang cosmology.

Cosmic expansion (Hubble's law), confirmed by the redshift of receding galaxies, is the first.

The cosmic microwave background (about 2.7 K), light from about 380,000 years after the Big Bang, and the light-element ratio (hydrogen : helium ≈ 3 : 1) also support it.

▸ Cosmic expansion (Hubble's law), the cosmic microwave background (about 2.7 K), and a hydrogen : helium mass ratio ≈ 3 : 1

All three are explained consistently only by the Big Bang theory.

CSAT-style

Which statement about cosmic expansion and Big Bang cosmology is correct?

①Redshift appears when a galaxy approaches

②By Hubble's law, more distant galaxies recede faster

③The cosmic microwave background temperature is about 270 K

④The age of the universe is about 4.6 billion years

⑤The cosmic microwave background is observed from only one direction

▸ ② By Hubble's law, more distant galaxies recede faster

In Hubble's law v = H₀d, recession speed is proportional to distance, so farther galaxies recede faster.

Redshift appears when receding (①), the background is about 2.7 K (③), the universe is about 13.8 billion years old (④), and the background is observed uniformly from all directions (⑤).

Summary

Cosmic expansion & Big Bang core

v = H₀d (Hubble's law) / Big Bang → expansion → current universe

redshift measures recession speed, which is proportional to distance → evidence of expansion

🎯 Exam Points

①Hubble's law: v = H₀d — recession speed proportional to distance

②Redshift: receding galaxy → wavelength increase (toward red)

③Three Big Bang evidences: expansion, CMB (2.7K), hydrogen:helium ≈ 3:1

④CMB: light from 380,000 years after Big Bang, observed isotropically

⑤Age of universe: ~13.8 billion years (estimated from Hubble constant)

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