The Scale Factor, the Friedmann Equation and the Age of the Universe · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

One number stretches the whole universe

Science · Astronomy & Astrophysics · ages 21-22
Name ______________________   Date ____________

  1. Which component dominated first, second, and last in cosmic history?

    • Matter, then radiation, then dark energy
    • Dark energy, then matter, then radiation
    • Radiation, then matter, then dark energy

  2. What does the scale factor describe?

    • The temperature of one star
    • One function of time multiplying every cosmic distance
    • The speed of light through glass

  3. Cosmological redshift means galaxies fly apart through fixed space from one central point.

    Circle one:   True   False

  4. The scale factor doubles. By what factor does the matter density drop?

    • It drops eightfold
    • It stays exactly constant
    • It drops twofold

  5. Light left when the scale factor was half its present value. What is z?

    Answer: ______________

  6. What does the Friedmann equation link together?

    • The charge of an electron and its mass
    • The expansion rate and the densities of the contents
    • The age of stars and their colour

  7. Two theories share today's expansion rate, but one adds extra early matter. Which universe is older?

    • Both must be exactly the same age
    • The one with extra early matter
    • The one with less early matter

  8. A student quotes fourteen billion years from one over the Hubble rate as the exact age. What correction is missing?

    • Early matter braking and late dark energy pushing change the history
    • The speed of light has doubled since then
    • The universe has exactly one galaxy
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Answer key

For grown-ups. Fold this page away before handing over the rest.

One number stretches the whole universe W1-mt_v3VEzinvJe-s1

  1. Radiation, then matter, then dark energy · Radiation ruled the hot start, matter built galaxies, dark energy drives today.
  2. One function of time multiplying every cosmic distance · Expansion is a single time function stretching all distances together.
  3. False · Space itself stretches everywhere at once, with no centre.
  4. It drops eightfold · Matter thins with the volume, and doubling each side multiplies volume by eight.
  5. 1 · One plus z equals two, so z equals one.
  6. The expansion rate and the densities of the contents · It ties how fast space grows to how much of each component fills it.
  7. The one with less early matter · Stronger early braking means faster early growth, so less time is needed to reach today.
  8. Early matter braking and late dark energy pushing change the history · The simple estimate assumes a steady pace, but the pace changed.
Worksheet · LightMySky