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Grade 10-11 (age 15-17)

high school Expanding Universe & Big Bang

Galaxies are not flying through space; the space between them is stretching, so every galaxy is moving away from every other. That is why more distant galaxies recede faster, a relationship called Hubble's law, v = H₀d, and why light from receding galaxies arrives stretched to longer wavelengths, a shift toward red called redshift. Run the expansion backward and the whole universe was extremely hot and dense about 13.8 billion years ago; that idea is the Big Bang theory. In the diagram, raising the scale factor stretches every distance by the same factor, and the three points on the graph below always fall on one straight line through the origin.

The universe is expanding

🎈 Thinking with dots on a balloon
①Draw evenly spaced dots on a balloon and inflate it, and the distance between every pair of dots grows by the same factor
②From any dot, all the other dots move away, so an expanding universe has no special center
③The dots are not racing across the surface; the surface is stretching, and galaxies likewise move apart because space itself stretches
④A dot that started twice as far away moves twice as far in the same time

Seeing the expansion

1.5
💡 What to look for in the diagram
①The top row is the starting state, and the bottom row is the state after space has stretched by the scale factor a
②While the galaxy one step from the central observer moves away by x, the galaxy two steps away moves 2x and the one three steps away moves 3x
③Distance moved in the same time is speed, so recession speed is proportional to present distance
④That is why, whatever a is, the three points on the graph lie on one straight line through the origin, and the slope of that line plays the role of the Hubble constant

Hubble's law and redshift

Hubble's law
v = H₀d
Recession speed (v) is proportional to distance (d); the constant H₀ is the Hubble constant, measured today at about 70 km/s/Mpc.
Redshift
z = Δλ / λ₀ ≈ v / c
Light from a receding galaxy is stretched to longer wavelengths. When the speed is much less than the speed of light, z ≈ v / c gives the speed.
🔴 Speed from redshift, distance from Hubble's law
①Just as an ambulance siren drops in pitch once it passes and moves away, light from a receding source is stretched to longer wavelengths
②Redshift is how far the absorption lines in a galaxy's spectrum have moved toward the red compared with laboratory positions
③Once redshift gives the recession speed, Hubble's law, d = v / H₀, gives an estimate of the distance
④In 1929 Hubble compared the distances and recession speeds of galaxies and published this proportional relationship

The Big Bang theory

The core of the Big Bang theory
an extremely hot, dense state about 13.8 billion years ago → space expands and cools → today's universe
The Big Bang was not an explosion at one point; it was everywhere in the universe beginning to expand together.
Evidence for the Big Bang
① cosmic expansion (Hubble's law) ② cosmic microwave background (about 2.7 K) ③ hydrogen-to-helium mass ratio ≈ 3 : 1
The steady-state theory also accepts expansion, so ② and ③ are what decided between the two; the steady-state theory has trouble explaining either.
📡 The cosmic microwave background
①About 380,000 years after the Big Bang, the universe cooled to about 3000 K; electrons and nuclei combined into atoms, and light could travel freely instead of being blocked by matter
②That light has been stretched by the expansion ever since and now arrives as microwaves at about 2.7 K, almost evenly from every direction in the sky
③In 1965 Penzias and Wilson found it by accident while tracking down noise in an antenna
④The Big Bang theory had predicted this radiation, so its discovery won the theory wide acceptance

Worked Examples and Exam Practice

Example 1
If the Hubble constant is H₀ = 70 km/s/Mpc, how fast does a galaxy 100 Mpc away recede?
1
Put the values into Hubble's law, v = H₀d.
2
v = 70 km/s/Mpc × 100 Mpc = 7,000 km/s.
▸ 7,000 km/s
In the same universe, a galaxy 200 Mpc away recedes twice as fast, at 14,000 km/s. Double the distance, double the recession speed.
Example 2
Of the observations that support the Big Bang theory, which two are hard to explain with the steady-state theory?
1
Cosmic expansion (Hubble's law) is accepted by the steady-state theory too, so it cannot decide between them.
2
The cosmic microwave background (about 2.7 K), light released about 380,000 years after the Big Bang, and the hydrogen-to-helium mass ratio set in the early universe (about 3 : 1) both match what the Big Bang theory predicts.
▸ the cosmic microwave background (about 2.7 K) and the hydrogen-to-helium mass ratio ≈ 3 : 1
The steady-state theory holds that new matter appears as the universe expands, keeping the density constant, so it cannot account for background radiation left over from a time when the whole universe was hot.
CSAT-style problem
Which statement about cosmic expansion and the Big Bang theory is correct?
①Redshift appears when a galaxy is approaching
②According to Hubble's law, more distant galaxies recede faster
③The cosmic microwave background has a temperature of about 270 K
④The universe is about 4.6 billion years old
⑤The cosmic microwave background is observed from only one direction
▸ ② According to Hubble's law, more distant galaxies recede faster
1
In Hubble's law, v = H₀d, recession speed is proportional to distance, so more distant galaxies recede faster.
2
Redshift appears when a galaxy is receding (①), the background radiation is about 2.7 K (③), the universe is about 13.8 billion years old (④), and the background radiation arrives almost evenly from every direction (⑤).

Summary

Expansion and the Big Bang in brief
redshift → recession speed → v = H₀d → cosmic expansion → Big Bang theory
Redshift rising in proportion to distance established that the universe is expanding, and the background radiation and the share of light elements support the Big Bang theory.
🎯 Exam Points
①Hubble's law, v = H₀d: recession speed is proportional to distance
②Redshift: light from a receding galaxy is stretched, and its absorption lines move toward the red
③Cosmic expansion has no center; from any galaxy, the others move away
④The evidence for the Big Bang is the cosmic microwave background (about 2.7 K, light released about 380,000 years after the Big Bang) and the hydrogen-to-helium mass ratio of about 3 : 1
⑤The universe is about 13.8 billion years old
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