This column is about the beginning of a new era of what is being called precision cosmology. It used to be a joke in the physics community that astrophysicists put the error bars in the exponent. In other words, they used numbers so poorly determined that they were unknown by several orders of magnitude. Well, as I predicted in a column eight years ago (Analog, August-1995), those days in astrophysics have definitely come to an end. As we will describe below, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, a joint initiative of Princeton University and NASA’s Goddard Spaceflight Center, in its first year of operation has nailed down most of the constants of our universe to an accuracy of a few percent.
Let me start by summarizing the inflationary Big Bang model, today’s standard paradigm for the history and future of the universe. According to this scenario, the universe began as a state of near-infinite temperature and energy density, a “singularity” in which the laws of physics are unknown. It almost immediately began a process of accelerated superluminal expansion that cosmologists call “inflation”. Inflation smoothed out any energy lumpiness and flattened any curvature or space warping, leaving the universe with only tiny variations in the energy density. These variations ultimately became the complex structures, stars, galaxies, galactic clusters, great voids, etc., that we see today. To form these structures, the gravitational pull of “dark matter” as well as ordinary matter was absolutely essential. But in addition to the normal and dark matter, a sizable part of the initial energy in the universe ended up in another form that we call “dark energy”. This is the energy contained in space itself, and, as we have discussed in previous columns (Analog, May-1999), it creates a negative “anti-gravity” pressure that pushes the universe to expand at an ever-increasing rate.
After the initial Big Bang, after inflation was over and had been replaced by continued but slower expansion, the universe was cooling down, so that the amorphous mass-energy of the early universe resolved itself into particles, mainly photons, protons, electrons, and neutrinos. By some process that remains obscure, a slight excess of protons and electrons over their antimatter equivalents (antiprotons and positrons) had earlier been created. In the high-density early stages of the universe, essentially all of the antimatter had paired off with its matter counterpart and annihilated, leaving behind the slight surplus of matter particles as “the only game in town”.
About 400,000 years later, when the temperature had dropped to a few thousand degrees K, the negative electrons and positive protons began pairing off to form neutral hydrogen atoms. Free charged particles, which easily absorb photons, were being replaced by light-transparent neutral atoms, so that the “fluid” of the universe was changing from murky black to crystal clear. The photons of light then present in the universe, characteristic of a black object with a temperature of about 2,900 K, were released from their trap in the “ping-pong match” of repeated emission and re-absorption by the growing transparency. They became free photons, and ever since they have been traveling through the universe. However, as the universe expanded and space itself stretched, the wavelengths of these visible-light photons produced by the hot matter in the universe at a temperature of about 2,900 K, were also stretched until they became microwave photons characteristic of a very cold object with a temperature of 2.7 K. The tiny energy variations left over by inflation show up as variations in the intensities of these microwaves, revealing “the sound of the Big Bang” (see Analog, January -2001) at 400,000 years of age. These photons, which have not interacted with matter since the early youth of the universe, form the cosmic microwave background (CMB) radiation that WMAP was designed to detect and measure.
WMAP was launched into a high orbit on June 30, 2001 aboard a Delta II 7425-10 rocket from Cape Canaveral. It used lunar gravity-assist to put it in orbit at the L2 point of the Sun-Earth system, 940,000 miles behind the Earth, with the Sun on the other side. WMAP detects the CMB in five frequency windows between 23 and 94 GHz in two linear polarization channels. The square root of the observation solid angles of the five frequency windows are 0.88°, 0.66°, 0.51°, 0.35°, and 0.22°, respectively, for the lowest to highest frequency windows. As these small-angle detectors of CMB scan over the sky, they map the power of the CMB at a very small angular scale, where the “ringing” of the early universe shows up and provides very tight constraints on the various numerical constants that characterize our universe.
Broadly speaking, the WMAP data shows (mostly with few-percent errors) that our universe is “flat”, that it has an age of 13.7 billion years, that it became transparent and the CMB decoupled 379,000 years after the Big Bang, and that the CMB has stretched in wavelength by a factor of 1089 since that time and presently has a characteristic temperature of 2.725 K. The data also shows that the mass-energy content of the universe is 73.0% dark energy, 22.6% dark matter, 4.4% normal matter, and that less than 1.5% is in the form of light neutrinos.
Now let’s talk in more detail about the parameters that describe our universe: W_{0}, W_{B}, W_{M}, W_{L}, T_{cmb}, n_{g}, h, H_{0}, t_{0}, t_{d}, and t_{r}. Here the "0" subscript indicates the present value of a time-dependent parameter. The density parameter W_{0} describes the ratio of the present mass-energy-density of the universe to the "critical" mass density r_{c} that would exactly "close" the universe (about 10^{-29 }gm/cm^{3}). If there were no dark energy, the value of W_{0} by itself would imply the ultimate fate of the universe, whether it will expand forever or will re-contract to a Big Crunch singularity. However, with sufficient dark energy, the universe accelerates in its expansion for a wide range of W_{0} values. The baryon density parameter W_{B} describes the fraction of W_{0} that is provided by ordinary matter (galaxies, stars, planets, gas clouds, atoms, protons, electrons, etc). Similarly, matter density parameter W_{M} describes the fraction of W_{0} that is provided by normal matter and dark matter, the two taken together because they affect gravitational attraction in the same way. The dark energy density parameter W_{L} describes the fraction of W_{0} that is provided by dark energy, which we now know accounts for more than ^{2}/_{3} of the mass-energy of the universe.
The present characteristic temperature of the cosmic microwave background radiation T_{cmb}_{ } temperature at which an object of this temperature would emit radiation with the same distribution of wavelengths. The photon density of the CMB n_{g} is the number of photons per cubic centimeter. It is very large because CMB photons are the most abundant particles in the universe. The baryon-to-photon ratio h, essentially the number of protons per photon, is very small for the same reason. The baryon-to-matter ratio W_{B}/W_{M} represents the fraction of all matter that is in the form of normal matter, and tells us that normal matter represents only about ^{1}/_{6} of the total.
The Hubble constant H_{0} describes the present expansion rate of the universe. In other words, with H_{0} = 71 km/sec/Mpc a galaxy 100 million parsecs away should presently be receding from us at a speed of 7,100 kilometers per second due to the expansion of the universe. The age of the universe t_{0} is the elapsed time since the Big Bang, and is a bit larger than the “extrapolated age” given by 1/H_{0} (about 1.1 × 10^{10} years) because of the accelerated expansion caused by dark energy. The time at which neutral atoms formed and photons became free particles is t_{d}. The time duration over which the decoupling process occurred is Dt_{d} and is about 20% of the decoupling time.
The final parameter that we will consider is the re-ionization time t_{r}. Here the WMAP data tells an interesting story. Many of the CMB photons did not pass unscathed from decoupling to detection by WMAP. About 180 million years after the Big Bang, the first stars formed. There was lots of hydrogen around, so the stars that formed first were very massive, became very hot, burned up their fuel fast, and made supernovas and black holes. The abundant ultraviolet radiation produced by these first stars re-ionized some fraction of the interstellar hydrogen, producing a plasma of electrons and protons that interacted with the CMB radiation in a significant way, altering the distribution and changing the polarization of the radiation. These effects are visible to WMAP, and so some of the parameters describing the re-ionization era can be extracted from the data.
The table below gives the parameters of the universe provided by the fit to WMAP data with the best present cosmological model.
Cosmological Parameters from WMAP Data
Description |
Symbol |
Value ± uncertainty |
Units |
Total density |
W_{0} |
1.02 ± 0.02 |
number |
Baryon density |
W_{B} |
0.044± 0.004 |
number |
Matter density |
W_{M} |
0.135 ± 0.008 |
number |
Dark energy density |
W_{L} |
0.73± 0.04 |
number |
Neutrino density |
W_{n} |
<0.015 @ 95% CL |
number |
CMB Temperature |
T_{cmb} |
2.725 ± 0.002 |
K |
CMB photon density |
n_{g} |
410.4 ± 0.9 |
photons/cm^{3} |
Baryon-to-photon ratio |
h |
(6.1 ± 0.3) ´ 10^{-10} |
baryons/photon |
Baryon-to-matter ratio |
W_{B}/W_{M} |
0.17 ± 0.01 |
number |
Hubble constant |
H_{0} |
71 ± 4 |
km/sec/Mpc |
Age of universe |
t_{0} |
13.7 ± 0.2 |
billion years |
Age at decoupling |
t_{d} |
379 ± 8 |
thousand years |
Decoupling duration |
Dt_{d} |
118 ± 3 |
thousand years |
Age at re-ionization |
t_{r} |
180 + 220 - 80 |
million years |
With such excellent data, we can ask whether the standard inflationary Big Bang model is completely and uniquely consistent with the data. Interestingly, the answer is “not quite”. There remains room for alternatives like the ekpyrotic cyclic universe model of Steinhart and Turock (see Analog, April-2002 and January-2003), in which two extra-dimensional “branes” clap together to produce a later-stage Big Bang with no inflation or initial singularity. The issue between that model and the standard scenario will not be resolved until the polarization effects of primordial gravity waves are observed (or not observed).
The standard model also leaves in the dark (so to speak) about the nature of the gravitationally self-repulsive dark energy. Is the amount of dark energy per unit volume of space inert, uniform, and unchanging (Einstein’s cosmological constant)? Or is it produced by some dynamic cosmic field that changes as the universe expands and evolves (quintessence)? The model fit to the WMAP data gives a parameter (not listed above) that relates cosmological negative pressure to the energy density. The value extracted is not well determined, but it is more consistent with constant vacuum energy than with quintessence. However, examination of WMAP data at large angular scales shows that the enhanced fluctuations expected there from constant vacuum energy are missing. This gives the proponents of quintessence some hope that their model may receive some experimental support when better data becomes available.
There is also an ambiguity in the WMAP data because the product of W_{M} and a quantity called s_{8} , which quantifies density fluctuations inside an 11 megaparsec sphere, is constrained very well, but the individual values of W_{M} and s_{8} are not very well determined. By relaxing constraints on s_{8}, the matter density W_{M} can have any value between 0.1 and 0.5. Thus, the parameters of the universe may not be as well determined as the WMAP table would imply. However, in no case can one reach a condition where W_{M} = W_{B}, so that the dark matter problem goes away.
Dark matter is definitely there, we’re stuck with it, and we really need to find out what it is. Does it signal the presence of one or more parallel and mutually gravitating universes? Is it in the form of some unknown particles that might have interesting technical or science-fictional uses? Is it something else? Perhaps we’ll find out soon.
John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402.
SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at https://www.amazon.com/Twistor-John-Cramer/dp/048680450X and https://www.amazon.com/EINSTEINS-BRIDGE-H-John-Cramer/dp/0380975106. His new novel, Fermi's Question may be coming soon.
Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: http://www.npl.washington.edu/av .
References:
WMAP Data:
“First Year Wilkinson Anisotropy Probe (WMAP) Observations: Preliminary Maps and
Basic Results”, C. L. Bennett, et al, submitted to Astrophysics
Journal,
preprint astro-ph/0302207 available at
http://arxiv.org .
WMAP and
Cosmology:
“Precision Cosmology? Not Just Yet …”, S. J. Biddle, O. Lahav, J. P. Ostricker,
and P. J. Steinhart, preprint astro-ph/0303180 available at
http://arxiv.org .