The joint analysis of CMB data by BICEP2 and Planck was posted to the arXiv a few days ago. You can find it here.
Last year, the BICEP2 experiment announced – to great fanfare – that they had found evidence of primordial gravitational waves, as would be expected to be left over from inflation, in their measurements of the polarization of the Cosmic Microwave Background. It’s being reported that a new joint analysis of BICEP2 and Planck data has been submitted to PRL. The paper, which isn’t out yet, apparently says that in the joint analysis the significance of the BICEP2 result goes away. The new result, which should be more powerful, is consistent with no signal.
This shows the dangers of releasing data – and especially possibly controversial data – before it’s ready. It also shows the dangers of trumpeting results to the media before there’s been time for the scientific community to fully vet a result.
I haven’t had a physics post in a few weeks, so here’s another one on dark matter.
When trying to find evidence for dark matter or trying to understand its effects on the universe, it is often necessary to have some sort of estimate of its density. The most directly measurable form of the density is the mass density (or energy density, but these are the same if the dark matter is nonrelativistic). The number density is important in understanding things like even rates for interactions of particle dark matter, but typically we use a mass density estimate and then report measurements as a function of particle mass.
There are also two types of relevant density measurements: the average density throughout the whole universe and the local density in some region of interest.
The Average Dark Matter Density
The average dark matter density throughout the whole universe can be determined from cosmological measurements, such as studies of the CMB. This density is most important in trying to understand the evolution of the universe. The presence of dark matter changes the gravitational forces felt by the photon-baryon fluid making up the universe prior to the epoch of recombination. This changes the properties of oscillations of that fluid, allowing the effects of dark matter to be seen in the shape of the CMB power spectrum. These measurements tell us that the overall dark matter density is around 1/4 of the critical density (where the universe is flat). The critical density is incredibly tiny compared to what we’re used to: of order 10 GeV per cubic meter.
The Local Dark Matter Density
Much of the evidence for dark matter comes from different ways to try to measure the local dark matter density in some region of space. The motion of objects in a gravitationally bound system lets us estimate the gravitation potential as a function of position, which in turn lets us map out the energy density of the system. Gravitational lensing lets us measure the strength of gravity acting on photons, which also lets us do the same. One density of particular interest to us is the local dark matter density at the position of Earth. Knowledge of this is necessary if we wish to measure dark matter interactions in detectors. Careful measurements of the motion of star systems within the Milky Way tell us that the local density at Earth should be around 0.3 GeV/cm3. This is orders of magnitude higher than the average density of dark matter in the whole universe but is still a very small number. This is only a fraction of an atom per cubic centimeter.
The Planck collaboration has released a new measurement of the power spectrum of polarized light from dust. It’s been getting a lot of press because the measurement seems to present a challenge to the earlier (and much-touted) BICEP2 result that claimed to see evidence of primordial gravitational waves in polarized light from the Cosmic Microwave Background (CMB).
Sean Carroll has a summary here. It seems that there is a good chance that BICEP’s measurement was good but their interpretation of it as gravitational waves was not correct. However, a member of the Planck collaboration shows up in the comments to say that Carroll is probably overstating the case that the BICEP2 result was spurious. The two groups are apparently working on a combined result that will hopefully clear up the current confusion over what was actually seen.
I’ve already gone over some of the main pieces of evidence for the existence of dark matter. There are also a lot of more indirect reasons why we think dark matter should exist. I’ve already mentioned these in earlier posts, but here are some of the other measurements and models supporting the dark matter hypothesis.
Big Bang Nucleosynthesis
Using a model of the universe assuming the universe started in a very hot and dense state that expanded adiabatically, we can estimate the relic abundances of the lightest few isotopes, which are mostly produced here rather than in the centers of stars.
The abundances (typically ratios rather than absolute abundances) of objects thought to have compositions close to what’s left after BBN have been measured and have been found to match predictions quite well. There is some disagreement on lithium-7 but the lighter isotopes match predictions from BBN models.
While this doesn’t necessarily tell us that dark matter exists, it does help validate our model of the early universe. It also helps to further challenge models where the “dark matter” is really just some regular matter that we aren’t measuring for some reason.
Large structures in the universe are believed to have coalesced out of small primordial density fluctuations. Matter is pulled into regions that start with a slight overdensity, leading that overdensity to keep increasing in magnitude. This eventually leads to dense (compared to the average density of the universe) objects like galaxies, clusters, etc.
It turns out that simulations suggest that a universe containing only regular matter will not lead to the structures we see in the universe. The clumps of matter will not form quickly enough. However, if the mass overdensities are made of dark matter, large gravitationally bound objects will form properly. The dark matter provides mass to increase the gravitational forces in these overdense regions but does not clump into compact objects. The compact objects are made of baryonic matter trapped by the dark matter’s gravitational forces.
Cosmic Microwave Background
The CMB is the result of the photon-baryon fluid in the early universe (at a redshift around 1100) becoming transparent to photons. When the universe cools sufficiently, the baryonic atomic nuclei start capturing electrons, changing from charged ions to neutral atoms. This means that there are no (or at least few) charged particles left, so photons, which couple to electric charge, have trouble interacting with anything. The photons then are able to continue on without interacting with anything until we measure them billions of years later. The photons follow the standard blackbody spectrum, which is then redshifted until today where the spectrum corresponds to a temperature of 2.7 K (a few degrees above absolute 0) and peaks at microwave wavelengths.
The CMB is not uniform in the sky. It’s temperature is seen to feature tiny fluctuations in space. These can be seen as relics of oscillations in the photon-baryon fluid (to lowest order the different oscillatory modes do not interact with one another). The power spectrum tells us the strengths of these different modes. The properties of the modes (basically the size of the temperature fluctuations on different spatial scales) are related to the properties of the photon baryon fluid. So, we can extrapolate the composition of the early universe from the CMB power spectrum. Fits of a generic early universe model to the measured power spectrum show that a large fraction of the energy content of the early universe (and the current universe) appears to be from non-relativistic, non-baryonic dark matter. Measurements of other things such as Type Ia supernovae (a popular standard candle) help us refine our model, and everything points to the existence of dark matter.
In this last part of this set of posts, I will discuss the thermal history of the universe. Also, note that if you find this subject interesting, this site has a nice poster on cosmology, as well as more posters on particle physics, nuclear physics, and plasma physics/fusion. The posters were designed by LBL (Lawrence Berkeley National Lab) and would make nice classroom decorations if you’re a physics teacher.
Anyway, when I say “thermal history of the universe” what I really mean is the evolution of smaller scale structures from subatomic physics to galactic clusters rather than the evolution of the global properties of the universe.
Conditions of the Early Universe
Cosmological measurements tell us that the early universe must have been very dense and very hot. It would be so dense and hot in fact, that all the various particles of the Standard Model would exist at thermal equilibrium. The temperature would be high enough (i.e. the kinetic energy of individual particles is high enough) that any known particle could be created in collisions between other particles, as long as that interaction is allowed. The high density means that each type of particle is readily created and destroyed in collisions, so the overall density reaches some equilibrium value.
The universe is assumed to expand in an adiabatic manner. That is, no energy (heat) is introduced into the system. So, if we consider a typical volume and follow it as it expands (this is a comoving volume: it expands along with the expansion of the universe), the average energy in the expanded volume does not change (other than small fluctuations since the universe is not completely uniform). If this expansion occurs in a reversible manner (a reasonable assumption), then the expansion is also isentropic.
In order to maintain equilibrium during this adiabatic expansion, the temperature must decrease and the number density of particles must also fall as the universe expands. So, the universe cools and gets less dense. At some point, the temperature gets low enough that very few particles will have enough energy to create the heaviest particles in interactions. Without any ability to generate new particles, these heavy particles must fall out of thermal equilibrium. From here, two things can happen:
- Heavy particle is unstable: The particles may continue annihilating, but even if they don’t they will eventually all decay away.
- Heavy particle is stable: At some point, the density of these particles gets so low that the probability of annihilating is basically zero. In other words, the mean free path of annihilation becomes larger than the observable universe. At this point, the particles can no longer be created in significant numbers (no production) but can also no longer annihilate in noticeable amounts. The density can only change due to the expansion of the universe. Thus, the comoving density (number of particles in a “unit” volume that expands with the universe) remains constant for the rest of time. We say that such particles have frozen out.
Particles don’t necessarily need to be heavy to undergo some sort of freeze out problem. As long as the density and cross sections are low enough for production and annihilation of a stable particle to cease, there should be some primordial signal from the early universe.
Evolution of Particles and Nuclei
- We start with all the particles of the Standard Model at equilibrium in a radiation-dominated expanding universe.
- As the temperature falls well below the electroweak scale (100 GeV – 1015 Kelvin!), production of top quarks, Higgs bosons, and W and Z bosons ceases and these unstable particles disappear except for briefly appearing in rare high-energy interactions.
- The universe cools even further, leading to the disappearance of tau mesons, bottom quarks and charm quarks (T around 1 GeV), muons and strange quarks, as well as all mesons and baryons except for protons and neutrons (T below 100 MeV). At all these scales, there is slightly more matter than antimatter, so even after annihilation of all antimatter, there is some remaining matter.
- At a temperature of a few MeV, the density drops enough that neutrinos can no longer be created in large numbers from electron-positron annihilation. The neutrinos then freeze out since they don’t annihilate very easily and don’t decay, leading to the theorized Cosmic Neutrino Background of “relic neutrinos.” Th
- The MeV scale is also interesting because it is also where nuclei first appear. The typical binding energy of a nucleus is a few MeV per nucleon, so nuclei would immediately be torn apart at higher energies. In the process of Big Bang Nucleosynthesis (BBN), the lightest few isotopes are created as the temperature falls enough for them to freeze out. The amounts of the lightest stable isotopes (hydrogen, helium, lithium) are set by BBN. The model explains observational data very well, giving us strong evidence for our model of the early universe.
- Below the MeV scale, the universe contains nuclei, electrons, neutrinos (noninteracting) and photons. At eV (12,000 Kelvin) to keV temperatures, the nuclei can start capturing electrons. This is the epoch of recombination, where neutral atoms are formed. The universe then contains mostly neutral particles, so photons freeze out as well. The universe goes from opaque to transparent. The photons left over from this form the Cosmic Microwave Background (CMB). The CMB is one of the most important tools for studying the early universe and actually reportedly contributes some of the static seen in broadcast TV (that is how it was discovered by Penzias and Wilson).
- At this point, the universe is around 400,000 years old and basically everything has frozen out. The universe is a pretty uniform fluid of noninteracting atoms, neutrinos, and photons.
After the epoch of recombination, not much seems to be happening. There is very little to measure from this era, so it is called the “Dark Ages”. One possible way to see what is happening is to look at the hydrogen 21 cm hyperfine transition line (something a number of people I know are working on). This is due to a spin transition of the electron in neutral hydrogen relative to the proton spin.
In general, what’s happening is that fluctuations in the density create gravitational potentials that attract even more matter. At some point in the first billion years or so, enough gas collects in a small enough area to start nuclear fusion, creating the first stars and heating up most gas enough to reionize it. This is the epoch of reionization. Larger and larger clumps of matter form and eventually they get big enough to start collapsing due to gravitational forces, creating the earliest galaxies and then galactic clusters as larger structures form. From here, galaxies and stars continue to form and evolve leading to the creation of the Milky Way and then our own solar system as well as countless other stars and galaxies.
There is one important thing I didn’t mention yet. It turns out that normal matter (i.e. atoms) is not sufficient to explain the structure formation we actually see. We need something else to provide the large gravitational potential wells in which galaxies and clusters formed in the early universe. This matter can’t interact much outside gravity (hence “dark matter:” it doesn’t interact with light). So, the matter component of the universe is actually composed of interacting matter (the Standard Model particles) and noninteracting matter (dark matter). Dark matter is the dominant form of matter in the universe and drives the formation of large scale structures. The “Standard Model of Cosmology” consisting of a universe composed primarily of dark energy, dark matter, and regular matter is typically called the ΛCDM (Λ(dark energy) Cold Dark Matter) model.
And that’s the end of my brief discussion of cosmology. Again, there will probably be more on this subject later. I plan to start discussing dark matter in much more detail in the near future.