Baryon Acoustic Oscilliations

Baryon acoustic oscillations and dark energy
There are now several independent ways to show that the expansion of the Universe is accelerating.
This indicates that:

  1. Our theory of gravity is wrong, or
  2. The universe is dominated by a material which violates the strong energy condition.

If (2) then it cannot be any classical fluid, but some weird quantum stuff which dominates the energy density of the Universe (today). We refer to it as dark energy. We see the dark energy through its effects on the expansion rate of the Universe. Indeed dark energy was first found by measurements of cosmic expansion, although models containing it had been around for several years. To constrain the nature of dark energy we need to be able to measure the expansion rate of the Universe and there are three main approaches:

  1. Standard candles: which measure the luminosity distance as a function of redshift.
  2. Standard rulers: which measure the angular diameter distance and expansion rate as a function of redshift.
  3. Growth of fluctuations.

Consider (2) further. Suppose we had an object whose length (e.g. in meters) we knew as a function of cosmic epoch. By measuring the angle subtended by this ruler as a function of redshift we map out the angular diameter distance, d(z). By measuring the redshift interval associated with this distance we map out the Hubble parameter, H(z).

Cosmological objects can probably never be uniform enough so we use statistics of the large-scale distribution of matter and radiation.

In cosmology, baryon acoustic oscillations (BAO) refers to regular, periodic fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic waves which existed in the early universe.

In the same way that supernova experiments provide a “standard candle” for astronomical observations, BAO matter clustering provides a “standard ruler” for length scale in cosmology. The length of this standard ruler (cica 490 million light years) is measured by looking at the large scale structure of matter using astronomical surveys. The measurements help cosmologists understand more about the nature of dark energy (which causes the apparent slight acceleration of the expansion of the universe) by constraining cosmological parameters.
 
Let us consider the early universe, which was composed of a coupled plasma of energetic photons (light particles) and ionized hydrogen (protons and electrons) plus other trace elements and the mysterious dark matter. Photons interact to a much lesser degree with neutral matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to decouple from the matter and free-stream through the universe. The cosmic microwave background (CMB) radiation is light emitted after recombination which is only now reaching our telescopes. Therefore when we look at Wilkinson Microwave Anisotropy Probe (WMAP) data, we are looking back in time to see an image of the universe when it was only 379,000 years old.

When we observe the universe today we find large structure and density fluctuations. Galaxies, for instance, are a million times more dense than the universe’s mean density. The current belief is that the universe was built in a bottom-up fashion, meaning that the small anisotropies of the early universe acted as gravitational seeds for the structure we see today. Overdense regions attract more matter, while underdense regions attract less, and thus these small anisotropies we see in the CMB become the large scale structures we observe in the universe today.

Imagine an overdense region of the primordial plasma. While this overdensity gravitationally attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward pressure. These counteracting forces of gravity and pressure create oscillations, analogous to sound waves created in air by pressure differences.

Consider a single wave originating from this overdense region in the center of the plasma. This region contains dark matter, baryons and photons. The pressure results in a spherical sound wave of both baryons and photons moving with a speed slightly over half the speed of light outwards from the overdensity. The dark matter only interacts gravitationally and so it stays at the center of the sound wave, the origin of the overdensity. Before decoupling, the photons and baryons move outwards together. After decoupling the photons are no longer interacting with the baryonic matter so they diffuse away. This relieves the pressure on the system, leaving a shell of baryonic matter at a fixed radius. This radius is often referred to as the sound horizon. Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons is gravitational. Therefore, the baryons and dark matter (still at the center of the perturbation) form a configuration which includes overdensities of matter both at the original site of the anisotropy and in a shell at the sound horizon.

The ripples in the density of space continue to attract matter and eventually galaxies formed in a similar pattern, therefore one would expect to see a greater number of galaxies separated by the sound horizon than by nearby length scales. This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of one sound ripple, but many overlapping ripples. As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water. It is not possible to observe this preferred separation of galaxies on the sound horizon scale by eye, but one can measure this signal statistically by looking at the separations of large numbers of galaxies.

The physics of the propagation of the baryon waves in the early universe is fairly simple, so cosmologists can predict the size of the sound horizon at recombination. In addition the CMB provides a measurement of this scale to high accuracy. However in the time between recombination and present day, the universe has been expanding. This expansion is well supported by observations and is one of the foundations of the Big Bang Model. In the late 90’s, observations of supernova determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the acceleration of the universe, or dark energy, has become one of the most important questions in cosmology today. In order to understand the nature of the dark energy, it is important to have a variety of ways of measuring this acceleration. BAO can add to the body of knowledge about this acceleration by comparing observations of the sound horizon today (using clustering of galaxies) to the sound horizon at the time of recombination (using the CMB). Thus BAO provides a measuring stick with which to better understand the nature of the acceleration, completely independent from the supernova technique.

The problem is that the ruler we are using is inconveniently large. It is only with the latest generation of large galaxy redshift surveys that we are able to probe the giga-parsec volumes required to make a precision measurement of the BAO signal.

In order to turn this idea into a workable measurement there are number of higher order effects which need to be taken into account. These involve the details of how the statistics are measured on the galaxy redshift survey and the corrections for non-linearity, galaxy bias and redshift space distortions.

Sources: http://astro.berkeley.edu/~mwhite/bao/,
https://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

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