5.5.3(j)-(o) - Big Bang evidence, age and composition

The Big Bang Model

The Big Bang theory says that the observable universe has evolved from a very hot, very dense early state. Since then, space-time has expanded and the universe has cooled.

That wording matters. The Big Bang is not best imagined as matter exploding from one point into already-empty space. In the model used at this level, space itself expands, so distant galaxies become farther apart because the scale of space-time changes. There is no special centre of expansion.

The previous split lesson taught that distant galaxies generally show redshift and that Hubble's law relates recession speed to distance. This lesson uses that as a starting point: if the universe is expanding now, then running the model backwards suggests a hotter, denser past.

Two pieces of language help avoid common mistakes:

• "early universe" is better than "an explosion at a point"
• "space-time expanded" is better than "galaxies flew through fixed space from the centre"

The theory is scientific because it makes testable claims. It predicts an expanding universe and a relic background of radiation from the hot early universe. The next part focuses on that radiation.

Microwave Background Radiation Evidence

The most important experimental evidence in this lesson is the cosmic microwave background radiation, usually shortened to CMB radiation.

In the early universe, matter and radiation were much hotter and more energetic. As the universe expanded and cooled, there came a stage when radiation could travel freely through space. Since then, the expansion of space-time has stretched the wavelengths of that radiation. Today it is detected mainly as microwaves with an equivalent temperature of about $2.7\,\mathrm{K}$.

This is strong evidence for the Big Bang theory because a hot, dense early universe naturally predicts leftover radiation. A universe that had always existed in roughly its present state would not obviously predict a near-uniform $2.7\,\mathrm{K}$ microwave glow across the sky.

Be precise about the "cooling" language. The photons are not little objects that have physically cooled like a cup of tea. Their wavelengths have increased because of the expansion of space-time, so their photon energies are lower and the radiation is now described by a lower temperature.

OCR questions often reward a chain like this:

1. Early universe was hot and dense.
2. Radiation from that early state should still be present.
3. Expansion stretches wavelengths/redshifts the radiation.
4. We now detect it as microwave background radiation at about $2.7\,\mathrm{K}$ from all directions.

Tiny variations in the CMB are also important in modern cosmology because they relate to the later formation of structure, such as galaxies. For this lesson, the assessable point is the CMB as experimental evidence for the Big Bang theory, not the detailed satellite analysis of those variations.

[DIAGRAM: asset_slug: 5_05_3c_big_bang_evidence_age_and_composition__diagram_01; description: A 2.7 K blackbody spectrum peaks at microwave wavelengths.; caption: A 2.7 K blackbody spectrum peaks at microwave wavelengths.]

Expansion Of Space-time And Age

The Big Bang model says that the Big Bang gave rise to the expansion of space-time. The age estimate in this specification uses the present expansion rate as a simple back-extrapolation.

From the previous split lesson, Hubble's law for receding galaxies is:

where $v$ is recession speed, $d$ is distance, and $H_0$ is the Hubble constant. If a galaxy has taken a time $t$ to reach distance $d$ while moving at speed $v$, then a simple estimate is:

Substitute $v \approx H_0 d$:

This is why the units of $H_0$ must be handled carefully. OCR may give $H_0$ in $\mathrm{km\,s^{-1}\,Mpc^{-1}}$, but $H_0^{-1}$ only gives a time directly if $H_0$ has been converted to $\mathrm{s^{-1}}$.

Worked example: estimating the age of the universe

Estimate the age of the universe using:

Use:

First convert $H_0$ into $\mathrm{s^{-1}}$:

Now invert it:

Convert seconds to years using $1\ \text{year} \approx 3.16 \times 10^7\ \text{s}$:

So this simple estimate gives an age of about 14 billion years.

This estimate is not exact. It back-extrapolates with the galaxy's present recession speed treated as approximately constant. It does not mean that the fractional rate $H_0$ was literally constant throughout history. The real expansion history is more complicated, but OCR expects you to understand the estimate and its units.