# Cosmology

> Edexcel International GCSE Physics · 4PH1 (2017)
> Source: https://www.owlsprep.com/study/edexcel-igcse-physics-s8-cosmology/

This guide covers all Higher-only cosmology content for Edexcel IGCSE Physics (4PH1), including Big Bang evidence, red-shift calculations, and links between galactic red-shift and universal expansion for Paper 2 exams.

**Prerequisites:** [Understanding of waves, wavelength and frequency (S3_T01)](https://www.owlsprep.com/study/edexcel-igcse-physics-s3-waves/); [Knowledge of galaxies and astronomical scales (S8_T01)](https://www.owlsprep.com/study/edexcel-igcse-physics-s8-astronomical-objects/)

## Learning objectives

- Describe the Big Bang theory and key supporting evidence
- Explain the Doppler effect for moving wave sources relative to observers
- Calculate galactic recessional velocity using the red-shift formula Δλ/λ₀ = v/c
- Link increasing red-shift with galaxy distance to prove universal expansion

## The Big Bang Theory and Supporting Evidence

The Big Bang theory is the leading scientific model for the origin and evolution of the universe. It states that approximately 13.8 billion years ago, all matter and energy in the universe was concentrated in an extremely hot, dense, tiny point. This point then expanded rapidly, and the universe has been expanding and cooling ever since.

**Big Bang Theory** — Model stating the universe began from a single hot, dense point ~13.8 billion years ago and has expanded continuously since.

Two key observational pieces of evidence support the Big Bang theory: red-shift of distant galaxies, and cosmic microwave background (CMB) radiation. CMB is uniform low-energy microwave radiation detected across all directions in space, the leftover 'afterglow' from the hot early universe shortly after the Big Bang.

**Cosmic Microwave Background Radiation** — Uniform microwave radiation across the sky, formed when the early universe cooled enough for atoms to form ~380,000 years after the Big Bang.

**Worked example:** A student claims CMB radiation is direct evidence the universe was once very hot. Explain why this statement is correct.

1. Step 1: Recall that CMB was released when the early universe was extremely hot, at a temperature of ~3000 K.
2. Step 2: At release, this radiation was high-energy visible and gamma radiation, consistent with a very hot environment.
3. Step 3: As the universe expanded, the radiation stretched to longer microwave wavelengths we detect today. Its uniform presence matches Big Bang predictions, confirming the early universe was very hot.

> **Exam tip:** For 6-mark Big Bang evidence questions, you must name both red-shift and CMB, and explain how each supports the theory to gain full marks.

*Calculator:* forbidden

## Doppler Effect and Galactic Red-shift

The Doppler effect describes the change in observed frequency and wavelength of a wave when its source moves relative to an observer. If a source moves away from an observer, waves are stretched, so observed wavelength increases and frequency decreases. If a source moves towards the observer, waves are compressed, so observed wavelength decreases and frequency increases.

**Red-shift** — Increase in observed wavelength of light from distant galaxies, caused by the galaxy moving away (receding) from Earth.

When light from a galaxy is analysed, we compare the observed wavelength of spectral lines to their known rest wavelength (from laboratory measurements). If the galaxy is receding, the lines are shifted to longer, redder wavelengths: this is red-shift. More distant galaxies show larger red-shifts, meaning they are receding faster than closer galaxies.

**Worked example:** Explain why larger red-shifts in more distant galaxies support the idea the universe is expanding.

1. Step 1: Link red-shift to motion: a larger red-shift means a galaxy is receding at a faster speed.
2. Step 2: Relate distance to speed: more distant galaxies recede faster than closer galaxies.
3. Step 3: Connect to expansion: if all galaxies are moving away from each other, and more distant ones move faster, this means the entire universe is expanding, as predicted by the Big Bang theory.

> **Exam tip:** When explaining red-shift as expansion evidence, always make the explicit link between increasing red-shift with distance, increasing recessional speed, and universal expansion to get all available marks.

*Calculator:* allowed

## Red-shift Calculations using \(\frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}\)

You must recall the red-shift formula for your exam, as it is not provided on the formula sheet. The formula relates the change in wavelength of light from a galaxy to its recessional velocity:

$$\frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}$$

Where: \(\Delta \lambda\) = observed wavelength minus rest wavelength (increase in wavelength), \(\lambda_0\) = rest wavelength of the spectral line, \(v\) = recessional velocity of the galaxy (m/s), \(c\) = speed of light (~3 × 10⁸ m/s, given in exam questions if required). Note that \(\Delta \lambda\) and \(\lambda_0\) must be in the same units, as their ratio is dimensionless.

**Worked example:** A spectral line from a distant galaxy has a rest wavelength of 656 nm. The observed wavelength is 689 nm. Calculate the recessional velocity of the galaxy. Use \(c = 3 \times 10^8 \text{ m/s}\).

1. Step 1: Calculate \(\Delta \lambda\): \(\Delta \lambda = 689 - 656 = 33 \text{ nm}\)
2. Step 2: Rearrange the formula to solve for \(v\): \(v = c \times \frac{\Delta \lambda}{\lambda_0}\)
3. Step 3: Substitute values (units for \(\Delta \lambda\) and \(\lambda_0\) match so no conversion is needed): \(v = 3 \times 10^8 \times \frac{33}{656}\)
4. Step 4: Calculate the result: \(v \approx 1.51 \times 10^7 \text{ m/s}\) (3 significant figures, matching given values)

> **Exam tip:** Always show your rearrangement of the formula, check units are consistent for \(\Delta \lambda\) and \(\lambda_0\), and use standard form for large velocities to avoid arithmetic errors.

*Calculator:* allowed

## Key Concept Summary and Check

**Summary**

- Red-shift of all distant galaxies shows they are receding from Earth
- Larger red-shift in more distant galaxies means they recede faster, proving the universe is expanding
- CMB radiation is the leftover heat from the early hot universe, directly supporting the Big Bang model
- The red-shift formula \(\frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}\) must be recalled for calculation questions

**Check your understanding**

1. Which of the following is NOT evidence for the Big Bang theory?

   - A: Red-shift of distant galaxies
   - B: Cosmic microwave background radiation
   - C: The existence of black holes
   - D: Uniform temperature of CMB across the sky

   *Why:* Black holes are a prediction of general relativity but are not direct evidence for the Big Bang. The other three options all support the model.

2. A galaxy shows a \(\Delta \lambda\) of 12 nm for a rest wavelength of 480 nm. What is its recessional velocity? Use \(c = 3 \times 10^8 \text{ m/s}\)

   - A: 7.5 × 10⁶ m/s
   - B: 1.2 × 10⁷ m/s
   - C: 3 × 10⁸ m/s
   - D: 4 × 10⁷ m/s

   *Why:* \(v = c \times \Delta \lambda/\lambda_0 = 3 \times 10^8 \times 12/480 = 7.5 \times 10^6 \text{ m/s}\)

## Common pitfalls

- **Wrong:** Confusing red-shift as galaxies moving towards Earth
  - Why it fails: Red-shift is an increase in wavelength, which only occurs when a wave source moves away from an observer, not towards them.
  - Correct: Remember red = longer wavelength, so stretched light waves = the galaxy is receding from Earth.
- **Wrong:** Using different units for \(\Delta \lambda\) and \(\lambda_0\) in calculations
  - Why it fails: The ratio of wavelengths is dimensionless, so mismatched units will produce an incorrect value for recessional velocity.
  - Correct: Convert both wavelengths to the same unit (e.g. nm or m) before substituting values into the red-shift formula.
- **Wrong:** Only naming one piece of evidence for the Big Bang in 6-mark extended response questions
  - Why it fails: Full marks require you to explain both red-shift and CMB radiation, not just one evidence type.
  - Correct: Structure answers to cover both evidence types, with clear explanations of how each supports the Big Bang model.
- **Wrong:** Expecting the red-shift formula to be provided on the exam formula sheet
  - Why it fails: The \(\Delta \lambda/\lambda_0 = v/c\) formula is not included on the formula sheet for 4PH1 exams.
  - Correct: Memorize the formula and its rearrangement for \(v\) as part of your Paper 2 revision.
- **Wrong:** Stating red-shift directly proves the Big Bang without linking to expansion
  - Why it fails: Red-shift first proves the universe is expanding, which is a core prediction of the Big Bang model.
  - Correct: Explicitly follow the logical chain: red-shift → recessional motion → universal expansion → supports Big Bang in explanation questions.

## Cheatsheet

| Concept | Key Details | Exam Reminder |
| --- | --- | --- |
| Big Bang Theory | Universe began as hot dense point ~13.8bn years ago, expanded ever since | Name both evidence types for 6-mark questions |
| CMB Radiation | Uniform microwave 'afterglow' from early hot universe | Links directly to the hot origin of the universe |
| Red-shift | Increase in observed wavelength of light from receding galaxies | Larger red-shift = more distant = faster recession |
| Red-shift Formula | \(\frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}\), \(c = 3 \times 10^8 \text{ m/s}\) | Must recall this formula, not provided on formula sheet |
| Calculation Rules | \(\Delta \lambda\) and \(\lambda_0\) must have matching units, \(v\) in m/s | Use standard form for large values to avoid errors |

## What's next

Now that you have mastered cosmology content, you are ready to tackle full Paper 2 Astrophysics practice questions, which often combine this topic with content on galaxies, orbital motion, and stellar evolution. This topic is consistently tested in Higher Paper 2, so make sure you practice red-shift calculations and 6-mark extended response questions on Big Bang evidence to maximize your marks. You can also review wave basics to reinforce your understanding of wavelength and frequency, which underpins the Doppler effect and red-shift calculations.

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