Understandings: The accelerating universe and redshift (z); The cosmic scale factor (R)
Applications and skills: Solving problems involving z, R and Hubble’s law; Estimating the age of the universe by assuming a constant expansion rate
Guidance: CMB radiation will be considered to be isotropic with T ≈ 2.76K; For CMB radiation a simple explanation in terms of the universe cooling down or distances (and hence wavelengths) being stretched out is all that is required; A qualitative description of the role of type Ia supernovae as providing evidence for an accelerating universe is required
We have previously seen how cosmic redshift provides evidence for an expanding universe. When we look at distant objects in space we are looking at them as they were in the distant past when the universe was a smaller place. We can describe the amount of redshift that we observe with a particular object using the variable z. This is simply the ratio of the wavelength or frequency shift compared to the un-redshifted wavelength or frequency values. The different sizes of the universe are described using the cosmic scale factor (R). Redshift (z) describes how much the universe has stretched (∆R). Mathematically we can use this to calculate the ratio of the current scale factor to the scale factor at the time a distant object emitted its radiation to find out how much smaller the distances between objects were at that point in the universe's life.
Note that we need to be careful with our terminology. Our current best evidence is that the universe is infinite ... and it was born infinite. It was just less stretched in the past. This is a very difficult concept to grasp!
As we have also previously seen, one possible fate for a star after it has exhausted its available helium is a white dwarf. We have also seen that many stars are part of stellar systems that include multiple stars, sometime close to each other. Sometimes a white dwarf and a companion star orbit each other closely enough, that when the companion star becomes a red giant material falls onto the white dwarf and adds to its mass. If the mass of the white dwarf becomes greater than the Chandrasekhar limit (about 1.4 solar masses) then the self-attraction / gravity of the white dwarf is enough to overcome electron repulsion ... and the white dwarf collapses. It doesn't, however, now form a neutron star. Enough energy is released by this process in a short enough time to destroy the star entirely, and the resulting explosion is known as a Type 1s supernova. Since the progenitor stars of these supernovae are all exactly the same mass (at the Chandrasekhar limit) these supernovae make good standard candles. They all have exactly the same luminosity and we can find them to calculate distance. Not only that they are very bright so we can see them from very far away.
By measuring the distance and acceleration of Type 1a supernovae in distant galaxies (and therefore galaxies that we are seeing as they were very long ago) we can plot the expansion history of the universe.
Until relatively recently (1998) we thought that the acceleration rate was more or less constant or slowing down as the gravity of the universe acts against the expansion, but the data seems to show that the rate is accelerating. We do not know why - the only idea is that there is some force or energy pushing the universe apart. We can call this 'dark energy' but just naming something doesn't actually help explain what it is.
Oxford Physics: pages 664 - 665
Hamper HL (2014): pages 560 - 562, but with a lot of HL Cosmology mixed in.
None really - for questions use the resources in the textbooks and provided in class