Frequently Asked Questions in Cosmology

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What is the currently most accepted model for the Universe?

The current best fit model is a flat ΛCDM Big Bang model where the expansion of the Universe is accelerating, and the age of the Universe is 13.7 billion years.

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What is the evidence for the Big Bang?

The evidence for the Big Bang comes from many pieces of observational data that are consistent with the Big Bang. None of these prove the Big Bang, since scientific theories are not proven. Many of these facts are consistent with the Big Bang and some other cosmological models, but taken together these observations show that the Big Bang is the best current model for the Universe. These observations include:

The observations listed above are consistent with the Big Bang or with the Steady State model, but many observations support the Big Bang over the Steady State: Finally, the angular power spectrum of the CMB anisotropy that does exist at the several parts per million level is consistent with a dark matter dominated Big Bang model that went through the inflationary scenario.

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Why do we think that the expansion of the Universe is accelerating?

The evidence for an accelerating expansion comes from observations of the brightness of distant supernovae. We observe the redshift of a supernova which tells us by what the factor the Universe has expanded since the supernova exploded. This factor is (1+z), where z is the redshift. But in order to determine the expected brightness of the supernova, we need to know its distance now. If the expansion of the Universe is accelerating due to a cosmological constant, then the expansion was slower in the past, and thus the time required to expand by a given factor is longer, and the distance NOW is larger. But if the expansion is decelerating, it was faster in the past and the distance NOW is smaller. Thus for an accelerating expansion the supernovae at high redshifts will appear to be fainter than they would for a decelerating expansion because their current distances are larger. Note that these distances are all proportional to the age of the Universe [or 1/Ho], but this dependence cancels out when the brightness of a nearby supernova at z close to 0.1 is compared to a distant supernova with z close to 1.

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What is quintessence?

Quintessence, or the fifth essence, is a fifth element beyond the standard earth, air, fire and water of ancient chemistry. Steinhardt and colleagues have adopted quintessence as the name for a particular model for the vacuum energy which causes the accelerating expansion of the Universe. A search of astro-ph on the LANL preprint server arXiv for "quintessence" in the abstract hits over 600 articles of which the oldest dates from 1998.

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If the Universe is only 14 billion years old, why isn't the most distant object we can see 7 billion light years away?

This question makes some hidden assumptions about space and time which are not consistent with all definitions of distance and time. One assumes that all the galaxies left from a single point at the Big Bang, and the most distant one traveled away from us for half the age of the Universe at almost the speed of light, and then emitted light which came back to us at the speed of light. By assuming constant velocities, we must ignore gravity, so this would only happen in a nearly empty Universe. In the empty Universe, one of the many possible definitions of distance does agree with the assumptions in this question: the angular size distance, and it does reach a maximum value of the speed of light times one half the age of the Universe. See Part 2 of the cosmology tutorial for a discussion of the other kinds of distances which go to infinity in the empty Universe model since this gives an unbounded Universe.

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If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?

When talking about the distance of a moving object, we mean the spatial separation NOW, with the positions of both objects specified at the current time. In an expanding Universe this distance NOW is larger than the speed of light times the light travel time due to the increase of separations between objects as the Universe expands. This is not due to any change in the units of space and time, but just caused by things being farther apart now than they used to be.

What is the distance NOW to the most distant thing we can see? Let's take the age of the Universe to be 14 billion years. In that time light travels 14 billion light years, and some people stop here. But the distance has grown since the light traveled. The average time when the light was traveling was 7 billion years ago. For the critical density case, the scale factor for the Universe goes like the 2/3 power of the time since the Big Bang, so the Universe has grown by a factor of 22/3 = 1.59 since the midpoint of the light's trip. But the size of the Universe changes continuously, so we should divide the light's trip into short intervals. First take two intervals: 7 billion years at an average time 10.5 billion years after the Big Bang, which gives 7 billion light years that have grown by a factor of 1/(0.75)2/3 = 1.21, plus another 7 billion light years at an average time 3.5 billion years after the Big Bang, which has grown by a factor of 42/3 = 2.52. Thus with 1 interval we got 1.59*14 = 22.3 billion light years, while with two intervals we get 7*(1.21+2.52) = 26.1 billion light years. With 8192 intervals we get 41 billion light years. In the limit of very many time intervals we get 42 billion light years. With calculus this whole paragraph reduces to this.

Another way of seeing this is to consider a photon and a galaxy 42 billion light years away from us now, 14 billion years after the Big Bang. The distance of this photon satisfies D = 3ct. If we wait for 0.1 billion years, the Universe will grow by a factor of (14.1/14)2/3 = 1.0048, so the galaxy will be 1.0048*42 = 42.2 billion light years away. But the light will have traveled 0.1 billion light years further than the galaxy because it moves at the speed of light relative to the matter in its vicinity and will thus be at D = 42.3 billion light years, so D = 3ct is still satisfied.

If the Universe does not have the critical density then the distance is different, and for the low densities that are more likely the distance NOW to the most distant object we can see is bigger than 3 times the speed of light times the age of the Universe. The current best fit model which has an accelerating expansion gives a maximum distance we can see of 47 billion light years.

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Is the Universe really infinite or just really big?

We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.

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How can the oldest stars in the Universe be older than the Universe?

Of course the Universe has to be older than the oldest stars in it. So this question basically asks: which estimate is wrong -

The age of the Universe is determined from its expansion rate: the
Hubble constant, which is the ratio of the radial velocity of a distant galaxy to its distance. The radial velocity is easy to measure, but the distances are not. Thus there is currently a 11% uncertainty in the value of the Hubble constant measured directly by the Hubble Space Telescope. John Huchra gives a good discussion of the historical uncertainties in the Hubble constant since even before Hubble's work. There is now a more precise but more indirect determination from WMAP observations of the CMB anisotropy, and a more accurate direct measurement from Riess et al..

The estimated age of the Universe has been increased by the observations of an accelerated expansion of the Universe. The current best value is 13.74 +/- 0.11 billion years from a fit of 9 years of WMAP data to a flat Universe, or 13.750 +/- 0.088 billion years for a fit to WMAP+BAO+H0 data.

Determining the age of the oldest stars requires a knowledge of their luminosity, which depends on their distance. This leads to a 10% uncertainty in the ages of the oldest stars due to the difficulty in determining distances.

Thus the discrepancy between the age of the oldest things in the Universe and the age inferred from the expansion rate was always within the margin of error. In fact, in 1997 improved distances from the HIPPARCOS satellite suggested that the oldest stars were younger, and the WMAP results in 2003 suggest that the Universe is older, so the discrepancy has disappeared.

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Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. In the special case of the empty Universe, where one can show the model in both special relativistic and cosmological coordinates, the velocity defined by change in cosmological distance per unit cosmic time is given by v = c ln(1+z), where z is the redshift, which clearly goes to infinity as the redshift goes to infinity, and is larger than c for z > 1.718. For the critical density Universe, this velocity is given by v = 2c[1-(1+z)-0.5] which is larger than c for z > 3 .

For the concordance model based on CMB data and the acceleration of the expansion measured using supernovae, a flat Universe with OmegaM = 0.27, the velocity is greater than c for z > 1.407.

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What is the redshift?

The redshift of an object is the amount by which the spectral lines in the source are shifted to the red. That is, the wavelengths get longer. To be precise, the redshift is given by

z = [λobsem]/λem
where λem is the emitted wavelength of a line, which is known from laboratory measurements, and λobs is the observed wavelength of the line. In an expanding Universe, distant objects are redshifted, with z = Ho D/c for small distances. This law was discovered by Hubble and Ho is known as the Hubble constant.

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Are quasars really at the large distances indicated by their redshifts?

The short answer is


Stockton (1978, ApJ, 223, 747) observed faint galaxies near in the sky to bright quasars at moderate redshifts. He chose quasars with moderate redshifts so he would still be able to see galaxies at the redshift of the quasar. He found that a good fraction of the redshifts of the faint galaxies agreed with the redshifts of the quasars. In other words, quasars are associated with galaxies that have the same redshift as the quasar and have just the brightness expected if the quasars are at their cosmological distances. Thus at least some quasars are at the distance indicated by their redshifts, and this includes some of the most luminous quasars: for example 3C273. Thus the simple answer selected by Occam's razor is that all quasars are at the distances indicated by their redshifts.

A further argument in favor of cosmological redshifts for quasars is the essentially perfect rank ordering implied by the fact that quasar absorption line system always have redshifts less than or equal to the quasar emission line redshift. In gravitational lens systems, the redshift of the lens is always less than the redshift of the lensed object. Thus intervening systems like lensing galaxies or absorbing clouds, which obviously have smaller distances than the quasars, also have smaller redshifts.

The statistical arguments advanced by Arp and others in favor of anomalous quasar redshifts are often incorrect.

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What about objects with discordant redshifts, like Stephan's Quintet?

One famous example of objects with different redshifts appearing in the same part of the sky is Stephan's Quintet. But the low redshift galaxy (in the lower left) is obviously more resolved into stars and looks "bumpier". By the surface brightness fluctuation method of distance determination, this bumpiness means that the low redshift galaxy is indeed much closer to us than the other four members of the quintet.

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Has the time dilation of distant source light curves predicted by the Big Bang been observed?

This time dilation is a consequence of the standard interpretation of the redshift: a supernova that takes 20 days to decay will appear to take 40 days to decay when observed at redshift z=1. The time dilation has been observed, with 5 different published measurements of this effect in supernova light curves. These papers are:

These observations contradict tired light models of the redshift.

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Are galaxies really moving away from us or is space just expanding?

This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.

In the absence of the cosmological constant, an object released at rest with respect to us does not then fly away from us to join the Hubble flow. Instead, it falls toward us, and then joins the Hubble flow on the other side of the sky, as discussed by Davis, Lineweaver & Webb (2003, AJP, 71, 358). In what are arguably the most reasonable coordinates, the cosmic time t and the distance D(t) measured entirely at the cosmic time t, the acceleration is given by g = -GM(r<D)/D2 where M(r<D) is the mass contained within radius D. This gives g = -(4*pi/3)*G*(rho(t)+3P(t)/c2)*D(t). The 3P/c2 term is a general relativistic correction to the otherwise Newtonian dynamics. Galaxies all move under the influence of this acceleration and their initial position and velocity. In other words, F = ma and gravity provides the force. Nothing extra or weird is needed.

Also see the Relativity FAQ answer to this question.

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Why doesn't the Solar System expand if the whole Universe is expanding?

This question is best answered in the coordinate system where the galaxies change their positions. The galaxies are receding from us because they started out receding from us, and the force of gravity just causes an acceleration that causes them to slow down, or speed up in the case of an accelerating expansion. Planets are going around the Sun in fixed size orbits because they are bound to the Sun. Everything is just moving under the influence of Newton's laws (with very slight modifications due to relativity). [Illustration] For the technically minded, Cooperstock et al. computes that the influence of the cosmological expansion on the Earth's orbit around the Sun amounts to a growth by only one part in a septillion over the age of the Solar System. This effect is caused by the cosmological background density within the Solar System going down as the Universe expands, which may or may not happen depending on the nature of the dark matter. The mass loss of the Sun due to its luminosity and the Solar wind leads to a much larger [but still tiny] growth of the Earth's orbit which has nothing to do with the expansion of the Universe. Even on the much larger (million light year) scale of clusters of galaxies, the effect of the expansion of the Universe is 10 million times smaller than the gravitational binding of the cluster.

Also see the Relativity FAQ answer to this question.

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Is the Universe expanding or is it just that our definitions of length and time are changing?

The definitions of length and time are not changing in the standard model. The second is still 9192631770 cycles of a Cesium atomic clock and the meter is still the distance light travels in 9192631770/299792458 cycles of a Cesium atomic clock.

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What is meant by a flat Universe?

The Universe appears to be homogeneous and isotropic, and there are only three possible geometries that are homogeneous and isotropic as shown in Part 3. A flat space has Euclidean geometry, where the sum of the angles in a triangle is 180o. A curved space has non-Euclidean geometry. In a positively curved, or hyperspherical space, the sum of the angles in a triangle is bigger than 180o, and this angle excess gives the area of the triangle divided by the square of the radius of the surface. In a negatively curved or hyperbolic space, the sum of the angles in a triangle is less than 180o. When Gauss invented this non-Euclidean geometry he actually tried measuring a large triangle, but he got an angle sum of 180o because the radius of the Universe is very large (if not infinite) so the angle excess or deficit has to be tiny for any triangle we can measure. If the radius is infinite, then the Universe is flat.

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Bolyai developed this geometry and published it, whereupon Gauss wrote to Bolyai's father: "To praise it would amount to praising myself. For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." And Lobachevsky had published very similar work in the obscure Kazan Messenger.

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Is the Big Bang a Black Hole?

The Big Bang is really nothing like a black hole. The Big Bang is a singularity extending through all space at a single instant, while a black hole is a singularity extending through all time at a single point. For more, see the sci.physics FAQ.

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What is the Universe expanding into?

This question is based on the ever popular misconception that the Universe is some curved object embedded in a higher dimensional space, and that the Universe is expanding into this space. This misconception is probably fostered by the balloon analogy which shows a 2-D spherical model of the Universe expanding in a 3-D space. While it is possible to think of the Universe this way, it is not necessary, and there is nothing whatsoever that we have measured or can measure that will show us anything about the larger space. Everything that we measure is within the Universe, and we see no edge or boundary or center of expansion. Thus the Universe is not expanding into anything that we can see, and this is not a profitable thing to think about. Just as Dali's Corpus Hypercubicus is just a 2-D picture of a 3-D object that represents the surface of a 4-D cube, remember that the balloon analogy is just a 2-D picture of a 3-D situation that is supposed to help you think about a curved 3-D space, but it does not mean that there is really a 4-D space that the Universe is expanding into.

For objects in our ordinary experience, like the rising loaf of raisin bread dough also used as an analogy to the expanding Universe, there are two ways to see that the object is expanding:
  1. The distances between objects are all increasing, so the distance between any pair of raisins increases by an amount proportional to the distance.
  2. The edge of the loaf pushes out into previously unoccupied space. Note the distance between any pair of points on the edge increases by an amount proportional to the distance.
The first statement involves the internal geometry of the object, which can be measured by an observer sitting in the object. The second statement involves the external geometry of the object, which can only be measured by an observer outside the object. Since we are stuck within our spacetime, we need to study the internal geometry of space-time, and that is what general relativity does. In terms of internal geometry, any object with the first property above is expanding. Furthermore the Universe is homogeneous so it does not have any edge. Thus it can't have the second property above. But it does have the first property so we say the Universe is expanding.

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What came before the Big Bang?

The standard Big Bang model is singular at the time of the Big Bang, t = 0. This means that one cannot even define time, since spacetime is singular. In some models like the chaotic or perpetual inflation favored by Linde, the Big Bang is just one of many inflating bubbles in a spacetime foam. But there is no possibility of getting information from outside our own one bubble. Thus I conclude that: "Whereof one cannot speak, thereof one must be silent."

From Bruce Margon and Craig Hogan at the Univ. of Washington

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Why is the sky dark at night?

If the Universe were infinitely old, and infinite in extent, and stars could shine forever, then every direction you looked would eventually end on the surface of a star, and the whole sky would be as bright as the surface of the Sun. This is known as
Olbers' Paradox after Heinrich Wilhelm Olbers [1757-1840] who wrote about it in 1823-1826 but it was also discussed earlier. Absorption by interstellar dust does not circumvent this paradox, since dust reradiates whatever radiation it absorbs within a few minutes, which is much less than the age of the Universe. However, the Universe is not infinitely old, and the expansion of the Universe reduces the accumulated energy radiated by distant stars. Either one of these effects acting alone would solve Olbers' Paradox, but they both act at once. The radiation we do see after Olbers' Paradox is solved is the Cosmic Infrared Background Radiation (CIBR).

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Will the Universe expand forever or recollapse?

This depends on the ratio of the density of the Universe to the critical density. If the density is higher than the critical density the Universe will recollapse in a Big Crunch. But current data suggest that the density is less than or equal to the critical density so the Universe will expand forever. See
Part 3 of the tutorial for more information.

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Does entropy prevent a Big Crunch?

The issue of entropy in the Universe is subtle and not entirely settled. Theorists are still trying to work out what happens to the entropy of matter that falls into a black hole, a problem which involves both quantum mechanics and strong gravity. When a successful theory of quantum gravity is worked out, it should explain why the Universe came out of the Big Bang singularity with a very large entropy, and what happens to the entropy of the Universe if it recollapses.

Entropy is related to the number of ways a system can be in a given state or condition. Thus a shuffled deck of cards has a higher entropy than a new deck with all the suits in order. Adding energy to a system usually opens up more states, and increases the entropy. The temperature of a system is defined such that kT is the amount of energy needed to increase the number of available states by a factor of e = 2.71828... where k is Boltzmann's constant. Transferring heat from a hot piece of a system to a cold piece increases the number of ways to arrange the cold part by a larger factor than the decrease in the number of ways to arrange the hot piece. Thus the normal flow of heat from hot to cold causes an increase in the number of ways the whole system can be arranged which is then an increase in the total entropy of the whole system.

Entropy need not always increase in open systems. Energy could be used to make entropy decrease for a particular system. Your refrigerator does this by removing heat from the interior, if you consider the interior of your refrigerator to be a separate system. Of course, if you consider both the internal and external portions of the refrigerator then there is a net increase of entropy due to the inefficiency of the refrigerator.

Since entropy is a statistical concept, short term fluctuations in small systems can allow entropy to decrease.

Entropy remains constant in a system with a uniform temperature that has no heat added or subtracted from it. This is thought to be more or less the case for the Universe or for any representative piece of the Universe that expands or contracts in the same way the Universe does. Except for the contribution from black holes, the vast majority of the entropy of the Universe is in the cosmic microwave background radiation because the vast majority of particles in the Universe are the photons of the CMB. As the Universe expands, the temperature of the radiation drops to maintain constant entropy. If the Universe were to collapse at some point, the radiation would heat back up to maintain constant entropy. When the Universe expanded the radiation started out in thermal equilibrium with the matter and then de-coupled. In the collapse the radiation and the matter would once again come into thermal equilibrium. Whatever happened with the dynamics of the matter in the interim would be reflected in the final thermal equilibrium with the radiation. The final entropy of the Universe as it approaches the Big Crunch singularity would be larger than the initial entropy of the Universe because of the heat added by nuclear fusion in stars, so a recollapse does not involve a decrease in entropy.

Black holes probably contribute much more entropy than all the particles and photons put together. Egan & Lineweaver (2009) estimate S/k = 10104.5 in the observable Universe, primarily from the Bekenstein entropy of super massive black holes.

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What about the oscillating Universe?

If the Universe recollapses, then there is another singularity at the time of the Big Crunch. A singularity means that the laws of physics break down, so we have no way to predict whether the Big Crunch will connect to another cycle of expansion. Even if the density were high enough to cause a recollapse, there would be no guarantee that the Universe would oscillate. But the current evidence is strongly against any recollapse, which would rule out the oscillating Universe. See
PBS or Ask an Astronomer about this.

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What is the dark matter?

When astronomers add up the masses and luminosities of the stars near the Sun, they find that there are about 3 solar masses for every 1 solar luminosity. When they measure the total mass of clusters of galaxies and compare that to the total luminosity of the clusters, they find about 300 solar masses for every solar luminosity. Evidently most of the mass in the Universe is dark. If the Universe has the critical density then there are about 1000 solar masses for every solar luminosity, so an even greater fraction of the Universe is dark matter. But the theory of Big Bang nucleosynthesis says that the density of ordinary matter (anything made from atoms) can be at most 10% of the critical density, so the majority of the Universe does not emit light, does not scatter light, does not absorb light, and is not even made out of atoms. It can only be "seen" by its gravitational effects. This "non-baryonic" dark matter can be neutrinos, if they have small masses instead of being massless, or it can be WIMPs (Weakly Interacting Massive Particles), or it could be primordial black holes. My nominee for the "least likely to be caught" award goes to hypothetical stable Planck mass remnants of primordial black holes that have evaporated due to Hawking radiation. The Hawking radiation from the not-yet evaporated primordial black holes may be detectable by future gamma ray telescopes, but the 20 microgram remnants would be very hard to detect.

Also see the Relativity FAQ answer to this question, the Cryogenic Dark Matter Search (CDMS) home page, and Martin White on dark matter.


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What about MOND?

MOND, for Modification of Newtonian Dynamics, is an alternative theory that tries to explain away the need for dark matter. While some people are still trying to get it to work in cosmological models, it is not
widely accepted.

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What is the value of the Hubble constant?

This is the question that professional astronomers ask the most frequently. For many decades the Sandage [Ho = 50] and de Vaucouleurs [Ho = 100] camps battled in a long lasting distance scale controversy. Many outsiders thought that the geometric mean of these values, Ho = 71 km/sec/Mpc, was a good compromise. The Sunyaev-Zeldovich effect has been used to determine Ho = 77 +/- 10 km/sec/Mpc. The Hubble Space Telescope Key Project team came up with the answer Ho = 72 +/- 8 km/sec/Mpc, the Cepheids in the nuclear maser ring galaxy NGC 4258 gave 74 +/- 6 km/sec/Mpc, and the double-lined eclipsing binary in M33 gave 61 +/- 4 km/sec/Mpc. These average to 71 +/- 5 km/sec/Mpc. In 2011 Riess et al. reported a new value of 73.8 +/- 2.4 km/sec/Mpc based Cepheids and Type Ia supernovae. Finally the 9 year WMAP analysis came up with:

Ho = 70 +/- 2.2 km/sec/Mpc

based on a flat Lambda-CDM model fit to the CMB WMAP angular power spectrum but I would rather see
because it would be consistent with a simple Universe with dark matter but no dark energy. But the supernova evidence for an accelerating Universe makes this rather unlikely, even if the Hubble constant data were wrong.

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What can a layperson do in cosmology?

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When is the next WMAP data release?

The data release on 21 Dec 2012 included all 9 years of data. The hourglass has been retired. There will be no further releases.

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