Expanding Universe
Section: Space Physics | Syllabus: Cambridge AS Level Physics 9702
Cosmic Microwave Background Radiation (CMBR) Cosmic Microwave Background Radiation (CMBR) Microwave radiation of a specific frequency that is observed at all points in space around us, arriving from every direction with nearly equal intensity.
It fills the entire Universe. CMBR was produced shortly after the Universe was formed (the Big Bang), when the Universe was extremely hot and dense The original radiation was very high-energy (gamma rays / X-rays) As the Universe expanded and cooled, the wavelength of this radiation was stretched (redshifted) into the microwave region of the electromagnetic spectrum CMBR is detected at all points in space - it is the "afterglow" of the Big Bang The existence of CMBR is further strong evidence for the Big Bang Theory Why Microwaves?
The Big Bang produced extremely high-energy radiation. Over billions of years, as the Universe expanded enormously, the wavelength of this radiation was stretched by the same factor. What started as gamma rays has been stretched to microwave wavelengths - much longer and lower in energy.
This matches exactly what we observe as CMBR. Hubble's Law Edwin Hubble found that the speed at which galaxies move away from us is proportional to their distance . This relationship is known as Hubble's Law .
Hubble Constant (H₀) The ratio of the speed at which a galaxy is moving away from the Earth to its distance from the Earth. H₀ = v / d v = speed at which the galaxy moves away (m/s) d = distance of the galaxy from Earth (m) H₀ = Hubble constant ≈ 2.2 × 10 −18 s −1 How Speed and Distance Are Measured Speed (v): found from the redshift of the galaxy's starlight - the greater the redshift (longer wavelength shift), the faster the galaxy is moving away Distance (d): determined using the brightness of a supernova in that galaxy - Type Ia supernovae always have the same intrinsic brightness, so comparing apparent brightness to known brightness gives the distance Worked Example: Finding a Galaxy's Speed Given: A galaxy is 1.4 × 10 25 m away.
H₀ = 2.2 × 10 −18 s −1 Rearrange: v = H₀ × d v = 2.2 × 10 −18 × 1.4 × 10 25 = 3.1 × 10 7 m/s Figure: Hubble's Law Graph (recession speed vs. distance) A scatter graph with "Distance from Earth, d (×10 22 m)" on the horizontal axis and "Recession speed, v (×10 6 m/s)" on the vertical axis.
Several data points (representing different galaxies) are plotted and show a clear positive linear correlation - the further the galaxy, the faster it recedes. A straight best-fit line is drawn through the origin.
The gradient of the line equals the Hubble constant H₀. A dashed construction triangle on the line shows rise/run = Δv/Δd = H₀. The graph title reads "Hubble's Law: v = H₀d". A note states that galaxies closer to Earth cluster near the origin with low recession speeds, while distant galaxies plot far right with high speeds.
Age of the Universe Hubble's Law allows us to estimate the age of the Universe . If all matter was once at the same point and has been moving apart ever since the Big Bang, then: Age of Universe Estimate Age ≈ d / v = 1 / H₀ Using H₀ = 2.2 × 10 −18 s −1 : Age ≈ 1 / (2.2 × 10 −18 ) ≈ 4.5 × 10 17 s ≈ 14 billion years What This Means The equation d/v = 1/H₀ gives an estimate for the time since the Big Bang.
It is evidence that all matter in the Universe was once present at a single point. The current best estimate for the age of the Universe is about 13.8 billion years . Summary: Evidence for the Big Bang Evidence Observation What it tells us Redshift Light from distant galaxies has longer wavelengths than expected Galaxies are moving away → Universe is expanding Hubble's Law More distant galaxies move away faster (v = H₀d) Consistent with all matter expanding from a single point CMBR Uniform microwave radiation observed in all directions Afterglow of the Big Bang, stretched to microwaves as Universe expanded Exam Tip For the Hubble constant: know the equation H₀ = v/d , the value H₀ ≈ 2.2 × 10 −18 s −1 , and that 1/H₀ ≈ age of Universe .
Also know that CMBR is in the microwave region because the Universe's expansion has stretched the original Big Bang radiation to longer wavelengths.
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