The final set of notes on measuring dark matter and energy (Part 3 of 3):
- Why does everything in the universe look as if it is receeding from us? Are we at some ideal location in the universe? Pick any point on a sphere. As the sphere increases in size (think about blowing up a balloon) any other point on that sphere moves away from it. So we are not at some special point in the universe. Every point moves away from every other. The distance a point is away from another is proportional to the velocity at which it is receeding.
- Light is red shifted for the same reason as above. As space expands it stretches light making it redder (longer wavelenghts).
- Experimental evidence shows that this linearity of distance to velocity (determined via measuring the red shifts) breaks down with large distances. This implies that there is an acceleration.
- How are distances measured in cosmology?
- Standard Ruler uses the apparent angular separation compared to a known (actual) fixed separation. An exmaple of this technique is measuring how far a car is away from you by measuring the distance between the headlights (given that you know the actual distance between the headlights).
- Standard Candle uses apparent brightness compared to a known (actual) fixed luminosity. An example of this can be done by measuring the brightness of a car’s headlights at some distance away (given that the actual brightness of the headlights are known).
Various experiements to use the measuring techniques:
- The universe is spatially flat. This is not to be confused with being flat in space-time which would go against Einstein’s theories of relativity (equating curvature of space with mass providing for gravity). Spatially flat means that two parallel light beams will remain parallel (when ignoring the expansion of the universe). Coming back to the fact that space-time is not: since the expansion of the universe is subtracted to provide for the light remaining parallel, this shows that space-time is not flat.
- Since there is no direct way to measure parallel photons, the elongation of the cosmic microwave background (CMB) (the red shift) can be used to measure the expansion of the universe. That is, since the expansion of space causes a red shift (expanding space elongates the waves) and variance in the spectra from distant galaxies can be easily measured, the CMB can be used as a standard ruler.
- Supernovae are considered to be standard candles and are therefore used for measuring distances. Because supernovae are formed by drawing in mass from another object until a critcal mass (the Chandrashekar mass) is achieved and the mass explodes, the brightness of this explosion should be known. In practice, supernovae are known to not be standard candles but there are techniques to compensate for the fact that the luminosity does vary. These techniques involve measuring the time over which the explosion occurs and the brightness.
- The geometry of space-time and the expansion history is determined by the matter-energy content of the universe.
The power spectrum of the CMB has a very unique signature as seen in the graph. (The x-axis is the inverse of the spot size (measured as an angle) and the y-axis is the brightness.) The “bumps” or peaks in the graph on the right side can be explained by harmonics in the theory of sound.
The spectrum of sound has a fundamental frequency and harmonic overtones. The parallel in cosmology is that space (the distance over which the sound wave travels) is swapped for time. Very early in the big bang (
t ~ 10^-36s) the universe was much more dense (~1000x smaller than it is now) and composed of elementary particles and photons. As the universe expanded, recombination occurred which means that it cooled enough for the particles to form atoms (i.e. hydrogen). In comparison to sound waves, recombination is the maximum displacement for photons.
- The close correlation of the peaks in the power spectrum to that of the theory proves that only the initial conditions (i.e. the big bang) contributed to the signature as there are no other mechanisms that would produce that signature.
- One can use a standard ruler of the fundamental frequency to measure the curvature of space.
- The density of dark matter can be determined directly from the power spectrum as one of the harmonics can be directly attributed to dark matter. The first peak is the fundamental frequency. The second peak is attributed to baryons (“normal” matter). The thrid peak is attributed to dark matter.
- The heights of the peaks in the power spectrum indicates the contribution of each harmonic (component of matter). For example, a small second peak is indicative of baryon density comprable to the photon density. Also, without dark matter (matter that does not interact with light (photons)) the harmonic peaks would be much smaller.
- Dark energy could not have contributed at the time of recombination as it would be observed in the peaks (the relative heights of the peaks).
- Dark energy’s density decreases much more slowly than other matter as the universe expands. As the universe expands, the density of dark matter and normal matter decreases but the dark energy is constant (check the “constant” part). We are at a very unique time in which the density of dark matter and dark energy are comprable. This is relavant in the formation of large structures (see previous notes).
- As the density of dark and normal matter decreases (with the expansion of the universe), dark energy is much more prevalent. Dark energy has an effect that is opposite of gravity. This is believed to be the reason behind why the universe is currently accelerating.
- The discrepancy between particle theory and the measurements of dark energy is approximately 120 orders of magnitude. We need a new theory — enter string theory.
- These higher order theories (such as dark energy and string theory) may be due to a fundamental misunderstanding of the effects of gravity at very large distances.