By Bram Boroson
The “earliest picture of the Universe,” Figure 1, shows hot and cold spots on the sky from when time itself was as fresh compared to the present as a one-day old baby compared with a centenarian. The secrets of the Universe’s baby picture initiate us into the mysteries of the expansion of the Universe, the Dark Matter and Dark Energy that may outweigh the normal matter of atoms, how space itself is curved and shaped, the sounds that echoed through the early Universe, and gives credence to an ambitious attempt to reach staggeringly further back in time.
The Cosmic Microwave Background (CMB) radiation shown in this picture was crucial convincing evidence that our Universe has been expanding from a hot Big Bang for about 13.8 billion years. This radiation appears as if it came from a gas so thick it reveals only its temperature (the theoretical ideal of blackbody radiation). The temperature the radiation came from is about 2.73K (in the Kelvin scale, 0 is Absolute Zero, -273 Celsius, and each degree is the same size as a Celsius degree). This temperature is nearly the same in all directions, varying by only about 1 part in 105, and 1 part in 104 even for the largest fluctuation.(The colours in Figure 1, hotter spots in red and cooler spots in blue, are scaled to better show these tiny variations.) Scientists have observed the CMB radiation with more and more detail using better and better telescopes since it was discovered in 1964. The sharpest map of the CMB throughout the sky obtained as of 2018, using the Planck satellite, is shown in Figure 1.
Studying how the CMB radiation varies from one direction of the sky to another (called the “anisotropy” of the radiation) has allowed cosmology, the study of the Universe as a whole, to become a quantitative science. It has clarified and supported a model called ΛCDM because it finds that most energy in the Universe is in the form of Dark Energy (symbolized in Einstein’s equations of gravity by Λ, but otherwise undiscovered) and Cold Dark Matter, a hypothesized kind of matter that has gravitational pull but that otherwise interacts with known matter only weakly. Although ΛCDM is the standard model of cosmology, the dark matter and dark energy it relies on have resisted attempts to detect them directly.
Cosmology Before the Discovery of the CMB
Cosmologists often assume the “Cosmological Principle”:
Cosmological Principle: on larger scales, the Universe is found to be nearly homogeneous (uniform in density) and isotropic (different directions in space are not distinguished by the distribution of matter and its velocity).
In 1916 Einstein’s Theory of General Relativity (GR) supplanted Newton’s theory of the gravitational force. GR explained gravity as the curvature of space and time. Einstein added a term to his equations including the “cosmological constant,” or Λ, to keep the Universe static (not expanding or contracting).
Einstein’s equations were solved assuming the Cosmological Principle applied and that Λ=0. A solution to the equations describes how space and time are curved mathematically, affecting the motion of all matter under gravitational influence. This solution said everything in the Universe must expand while slowing as gravity pulls it back. The solution allowed three options for the “curvature” of space itself: that space is “positively” curved (closes in on itself like a sphere), “flat,” or “negatively” curved (spreads out like a horse saddle). If the average energy density of the Universe is too big, the curvature of space is positive; if the average energy density too low, then the curvature is negative, and if it is just right (has “the critical density”), then space is flat. These three possibilities for space go along with three possibilities for the ultimate fate of the Universe: that gravity will cause the Universe to decelerate enough to start contracting, expand eternally, or to expand forever on the cusp of these two possibilities.
Soon after these solutions were found (in 1929), Edwin Hubble and his assistant Milton Humason demonstrated Hubble’s Law, that the further away a galaxy is, the faster it tends to move away from us. The speed of each galaxy was measured through a shift in the wavelengths of its spectrum. (Wavelengths become longer, “redshifted,” when an object moves away from us, and “blueshifted” when it moves towards us).
Fig 3: An illustration of redshift and blueshift
Hubble’s Law showed that the solutions to Einstein’s equations were right: the Universe expands. Einstein gave in: the cosmological constant wasn’t needed.
Even though the Universe is not static, it may still require something that behaves like Einstein’s cosmological constant, an example of Dark Energy. Teams observing the catastrophic explosion of white dwarf stars (“supernovae”) to measure distances across the Universe, allowing the redshift-distance relation to be tested for galaxies far, far away. They found that instead of decelerating from gravity pulling it back together, the Universe is speeding up. Why? We don’t know but call the cause Dark Energy.
Not everyone was convinced by Hubble’s Law that the Universe arose in a Big Bang. The rival Steady State theory was built on a generalization of the Cosmological Principle: not only should all places in our Universe be on equal footing, but also all times. In the Big Bang scenario, matter in the distant past was packed more densely. In the Steady State theory, as the Universe expanded, new matter formed, keeping the average density constant.
The History of CMB Measurements
In 1948 researchers Gamow, Alpher, and Hermann realized that the early Universe would have been filled with radiation that we could still detect. Although the radiation would have arisen from very hot gas, it would be subject to cosmological redshift. The expansion of the Universe is an expansion of the scale of space itself. The radiation filling the hot (3,000 K) Universe originally had mostly short wavelengths, but as distances in the Universe expanded, so too did the wavelengths of this radiation.
The predicted CMB was discovered by accident in 1964. Penzias and Wilson tried to find radio waves reflecting off communications satellites using a horn antenna. They went through every effort to reduce any noise in their detector. When birds nested in (and littered with droppings) their antenna, the scientists cleaned up the mess and moved away the birds!
A mysterious static from all directions of the sky remained. They concluded it must be the CMB after consulting with Princeton researchers who were trying to observe the CMB themselves.
The Steady State model explained the CMB as originating in starlight scattered by dust. Later measurements of the CMB spectrum (its brightness at different frequencies) showed that it was nearly a perfect blackbody. The cause of a perfect blackbody has to be something all at the same temperature throughout. This showed the CMB could not come from dust reflecting a multitude of different stars, and the Steady State model lost popularity.
More accurate measurements of the CMB than those of Penzias and Wilson need to be taken from high altitude, especially dry places such as mountaintops or the South Pole, or space. Oxygen and water in the Earth’s atmosphere absorb and emit microwaves that can be confused with the CMB. The microwaves from the atmosphere vary from direction to direction, making it impossible to tell from Earth-based observations when the CMB is changing temperature across the sky and when it’s just the atmosphere. Earth-based observations have been very useful in getting sharp images the CMB but are limited to small patches of the sky.
Earth-based observations soon found a dipole in the CMB temperature map. In one direction of the sky, the wavelengths of the radiation are longer, while in the opposite direction they are shorter. We ourselves are moving through space, and at a velocity of 370 km/s. This includes all the ways the structures we are part of (solar system, Milky Way, Local Group of galaxies) are moving in relation to the CMB radiation itself.
The COsmic Background Explorer (COBE) satellite for the first time mapped the entire sky in microwaves from space, finding slight irregularities. The Universe around us now isn’t completely uniform. Maps of all the galaxies we can see (“redshift surveys” such as the CfA survey of Geller and Huchra, the 2DF, the Sloan Sky Survey), show there are “walls” and “voids” where galaxies are especially concentrated or nearly absent. These could only form if, tracing back to earlier eras, the Universe already was already slightly uneven.
The Wilkinson Microwave Anisotropy Project (WMAP) created a sharper sky map, turning the fluctuations seen with COBE into a precision tool that could measure properties of the Universe.
Our most sensitive map of the CMB (shown in Figure 1) comes from the Planck satellite operated by the European Space Agency (ESA). These three satellite observatories (COBE active from 1989-1993, WMAP from 2001-2010, Planck from 2009-2013) provided in their times the best maps of the CMB over the entire sky.
What Caused the CMB?
About 380,000 years after the Big Bang (this time can be measured using the temperature variations of the CMB radiation itself!), recombination occurred, the merging of electrons with nuclei to form atoms. (Don’t be confused by the name: there was no prior “combination”!) As the Universe cooled, more delicate structures like atoms could persist, free from destruction through the violent collisions that happen at high temperatures. The photons filling space stopped regularly bouncing off matter and could then reach us in uninterrupted straight lines. This is the furthest back in time that we can “see”.
When electrons roam free, they can scatter photons of any energy, but when locked in to atoms, they can only transit between certain allowed energy levels. With fewer free electrons that could scatter all energies of light, the Universe became transparent when it cooled to around 3,000K.
How to Measure the CMB
Our CMB telescopes don’t see images like Figure 1 without some correction first. We only see a combination of the CMB and foreground microwaves that must first first be removed to see the CMB itself.
A microwave foreground arises from our own Milky Way galaxy, which is mostly flat like a pancake and does not cover the whole sky. The most common causes of microwave radiation from the Milky Way are dust and electrons that are accelerated by magnetic fields or by encountering other charged particles. Multiple techniques can separate the CMB near the galactic plane from the foreground.
Instead of studying the image of the CMB as in Figure 1 pixel by pixel, scientists analyze a plot called a power spectrum that summarizes the statistical information in the picture. Figure 1 shows random overlapping splotches where the temperature is higher or lower than the average. Do those splotches tend to be around 1 degree in size? Half a degree? (All the way around the sky is 360 degrees.) A power spectrum, such as shown in Figure 7, is a summary of how much the image varies at each possible angle.
How the CMB reveals Secrets of the Universe
You can learn a lot about what’s inside something by listening to the sounds it makes. What’s in that box? Shake it and listen. You can often guess whether a person is large or small by the pitch of their voice (a deep bass indicates a larger size). Different musical instruments sound different even when they play the same note. If someone inhales helium, their voice temporarily becomes a high-pitched squeak.
We can also learn what’s in our Universe by the sounds that left an imprint on the CMB before recombination 380,000 years ago.
These sound waves, or baryon acoustic oscillations (BAO), grew from even earlier fluctuations are called primordial fluctuations. The CMB suggests that those were adiabatic, meaning that matter, dark matter, and photons all increased or decreased in density together. We’ll return to this subject!
These early fluctuations were made of overlapping waves with different wavelengths. Where a wave had extra density, there was extra pressure pushing out. The dark matter, because it feels forces other than gravity only weakly, did not feel this pressure push and stayed put. The photons and matter ended up moving away from the dark matter together. The photons scattered off electrons, and the negative electrons through the electric force pulled the positive nuclei with them so that photons, electrons, and nuclei all moved together. The end result was the extra density regions sent sound waves of photons and matter expanding out from the dark matter at 60% of light speed.
The waves of photons and matter sloshed back and forth until recombination. The pressure went down as the matter and photons expanded, and gravity of dark matter pulled them back again. At recombination (when the CMB formed), the photons streamed free and without them the matter stopped its sloshing.
How far the sound waves could get by recombination is called the sound horizon. If the sound horizon is a multiple of half the wavelength of the fluctuation, the primordial fluctuation with this wavelength imprints an especially clear signal on the power spectrum of the CMB. These are the acoustic peaks, the bumps in Figure 7.
Scientists use the placement and strengths of the peaks to measure aspects of the Universe, assuming ΛCDM, by using a method like this:
- Make a specific model. Describe the primordial density fluctuations, model how those are modified by baryon acoustic oscillations, how the later history of the Universe may slightly alter the CMB.
- Choose data to compare with the model. This could be a temperature power spectrum, or polarization power spectrum (see following discussion of polarization), both together, or a combination of CMB spectra with other astrophysical measurements, such as measurements from galaxy redshift surveys.
- Vary the parameters of the model until the model makes a prediction closest to the data.
You can try a simplified exercise like this yourself, if your computer uses Flash, at the WMAP science site: https://wmap.gsfc.nasa.gov/resources/camb_tool/index.html.
Here’s an example.The graph above shows on the left a pie chart of how much of the energy in the Universe is in the form of normal matter (atoms), dark matter, and dark energy. “Sliders” allow the user to control these and other inputs to the ΛCDM model. On the right the figure (ii) shows the power spectrum of CMB as observed with WMAP (red) and the current model (blue) with the inputs chosen. Below this is an image of how the CMB might appear on the sky if this model were true. On the top left, the age and flatness of the Universe in the chosen model are shown. A “flatness” of 1 means perfectly flat, <1 means an open Universe of negative curvature, and a flatness of >1 means a closed positive curvature Universe.
Based on the matter and energy ingredients selected, the flatness is 0.3 (an open Universe) and the first acoustic peak appears at too small an angle. Let’s try again, changing only one input: increase the dark energy to 100% of the critical density.
Now, with a flatness of 1.26 (a closed Universe), the first acoustic peak appears at a larger angle than the observed peak.
Just right! A flat geometry predicts the first acoustic peak should occur near 1 degree, where it actually does appear. Why is the first acoustic peak such a good way to measure the flatness of the Universe?
Peaks in the CMB radiation should be separated by the easy to calculate sound horizon size. How does distance translate into angle on the sky? By analogy, you can see in Figure 9, that in a closed geometry, the same angle spreads to a smaller physical size than in a flat geometry. In other words, to get the same physical size, you need a larger angle in a closed geometry. And as you can see from our models, a closed geometry predicts the first acoustic peak (at known physical size) appears closer to 2 degrees than the observed 1 degree (consistent with flatness).
The power spectrum allows us to measure more than the flatness. In very subtle ways the power spectrum is imprinted by:
- How common normal (baryonic) matter is,
- The expansion rate of the Universe,
- Properties of particles called neutrinos that have a tiny mass and interact with normal matter only weakly,
- And the rest of cosmic history. Times long after recombination could still (through scattering, gravitational lensing, etc.) affect the CMB photons.
Combined with other astrophysical knowledge, the CMB power spectrum has allowed us to:
- Conclude that Dark Energy has not undergone much change over time, indicating it DOES behave like Einstein’s cosmological constant
- Explain clustering of galaxies in redshift surveys like that shown in Figure 4.
That the Universe’s geometry is observed to be so near to perfectly flat was a major confirmation of the inflationary scenario, in which the Universe went through runaway rapid expansion VERY early in its history, for a period that lasted between 10-36 and 10-32 seconds to set up the hot Big Bang! Take 1 second compared with the entire 13.8 billion year history of the Universe. That’s a small fraction. Now imagine taking that fraction OF that fraction (for example, ½ of ½ is ¼). That is about as small as 10-36 seconds is compared with a single second!
Inflation was first proposed by Alan Guth and Andre Linde to explain why the Universe was already suspected of being nearly flat. The extreme expansion of inflation could have flattened out any curvature of space. Inflation could also explain why the CMB radiation is so uniform when otherwise there would not have been time for different regions to equalize their temperatures. Inflation also gives an explanation for the earliest fluctuations that the sound waves modified: our physical laws for tiny distances and times (quantum mechanics) allow for random results to emerge, and these were magnified to large scales through expansion.
Inflation gives a simple mathematical guess for how the density fluctuated throughout space prior to the baryon acoustic oscillations. How well does that fit the CMB data? It fits well, but not perfectly! The Planck satellite’s measurements actually rule out the simple prediction, but many scientists think inflation could have been more complex than our simplest model.
How else can we progress on inflation, this ambitious but controversial attempt to understand the tiniest fraction of a second after the Big Bang? One way is through polarization measurements.
Electromagnetic radiation, whether visible light or microwaves, carries electric and magnetic fields. That leaves different possible directions, called polarizations, for the fields. When particular directions of those fields are more common the radiation is said to be polarized.
There are two kinds of polarization, called E and B-mode. B-mode polarization can be caused by gravitational lensing, gravitational waves, or cosmic dust. Gravitational waves, a phenomenon detected directly for the first time in September of 2015 by the twin LIGO detectors in the U.S., and predicted from GR, are created whenever large masses undergo large acceleration.
In 2014 a team using the BICEP-2 detector at the South Pole announced they had found B-mode polarization imprinted on the CMB from gravitational waves, but it turned out to be possible to account for the apparent discovery entirely as the result of cosmic dust. B-mode polarizations from primordial gravitational waves would be an exciting discovery, adding to the successful predictions of inflation and giving clues to moving beyond our current state of the art picture of the Universe.
Perhaps BICEP-3 or NASA’s PIPER Balloon Observatory will soon discover B-mode polarization from gravitational waves.
The ΛCDM model, supported by a suite of evidence that includes the Cosmic Microwave Background, assumes the ingredients of our Universe are Dark Energy, Dark Matter, photons, neutrinos, and normal matter. It also assumes that General Relativity is the correct theory of gravity describing our Universe. This model is often called the concordance model because its results usually agree with what we’ve learned from studying completely different topics (the abundances of elements formed in the first three minutes following the Big Bang and the galaxies as seen in redshift surveys). The kind of analysis of the temperature fluctuations we’ve walked through above gives similar results when fluctuations in the E mode polarization is analyzed as well. This gives us confidence when we use the model and Planck CMB data to measure:
- the age of the Universe (13.797±0.023 billion years),
- the amount of normal matter (0.050±0.001, as a fraction of the critical density),
- the amount of dark matter (0.266±0.006),
- the amount of dark energy (0.6847±0.0073),
- the number of different kinds of neutrinos (consistent with what was expected, 3),
- the sum of the masses of each type of neutrino (<0.12 eV, electron Volts: for comparison the electron has a mass of 511 eV),
- the curvature of space (-0.0096±0.0061, or perfectly consistent with absolute flatness),
- the slope describing the power spectrum of primordial fluctuations (0.9649±0.0042, expected to be just a little bit less than 1 in the simplest inflation models),
- and the current expansion rate of the Universe (Hubble constant, slope of linear relation in Hubble’s Law, or 67.36±0.54 km/s/Mpc, where a Mpc is a megaparsec, about 3.26 million light years).
The last measurement was not exactly what scientists expected. When we use supernovae to measure Hubble’s constant we get a value of 73.5±2 km/s/Mpc. The measurements here are expressed together with “error bars” after the ± symbol, so for example, 67.36±0.54 means that given the known limitations of the measurement, 68% of the time the actual value would be between 66.82 (67.36-0.54) and 67.90 (67.36+0.54). (The ± for the curvature gives a 95% confidence interval.)
The error bars summarize only known uncertainties in the measurements, and there can be further unknown “systematic errors” that bias our results. We’ve measured different values for the Hubble constant from Planck and from supernovae, and this could be a sign that the model is limited in some way and that there is more to learn, or it could be the result of systematic errors that we don’t know about. In sum, studying the CMB has given scientists a generally agreed on picture of the Cosmos, complete with numerical measurements. We are confident in that picture but we’re faced with some puzzling surprises too.
The cliché is that “The sky is the limit,” and astronomers studying the microwave glow of the sky are now pushing through the limit from when a dense “fog” of matter became transparent, 380,000 years after the Big Bang.