(2009-09-21) In an infinite and unchanging Universe, the night sky would be white!
Since the night sky isn't brightly lit, the obvious logical conclusion is that theUniverse is not infinite and unchanging. We now know that it's finite and expanding. Historically, the argument presented by Olbers helped clarify that viewpoint. Arguably, the night sky is neither bright nor dark, it's just darker thanit used to and it's dimming steadily...
Nowadays, Heinrich Olbers (1758-1840) is often presented as an amateurmathematician because he earned a living as a physician. However, he must be credited with several important contributions to astronomy,including an efficient method for computing cometary orbits (1779) and thediscovery of two of the three largest asteroids, 2 Pallas (28 March 1802) and 4 Vesta (29 March 1807).
Olbers' Paradox did not originate with Olbers but heused his considerable reputation to popularize the argument. In the cosmological view where outer space consists only of stars and emptyspace, ... / ...
(2020-09-06) Local physics is determined by the whole Universe.
(2009-09-21) A short history of a mind-boggling idea.
Thefamous catalog of 110nebulae (including spiral nebulae) which Charles Messier (1730-1817)andPierre Méchain(1744-1804)published in 1777 was arguably little more than a list of nuisances which might hinder the glamorized hunt for fleeting comets, traveling through the solar system
The nature of those nebulae kept puzzling astronomers. Because they have no measurable parallax, it was clear early on that they are located at great distances from the Solar system. In spite of that, they don't look pointlike like stars do. So, they must be much larger than stars.
Pierre-Simon Laplace(1749-1827) advocated the dominant (misguided) opinion that the spiral nebulae were rotating clouds forming new stars, according to thenebular hypothesiswhich had been formulated in 1734 byEmanuelSwedenborg (1688-1772) to explain the formation of the Sun itself.
Curiously, Swedenborg had also put forth another unrelated seminal idea which would ultimately lead to the correct understandingof the true nature of the spiral nebulae (and the downfall of Laplace's views): Swedenborg envisioned a definite order among visible stars, within a huge local "starry sphere". Although the details of his description are ambiguous and incompatible with modern views (it's unclear whether he thought of the Via Lactea as a polar axis or an equatorial ring for that sphere). Swedenborg broke fantastic new groundswhen he suggested the mind-boggling possibility that there could be manyother such "starry spheres" at very large distances...
Around 1731, similar speculations were being made independentlyby the gifted son ofa well-to-do carpenter and land owner from the hamlet of Byers Green (6 milesto the south ofDurham City)... In 1750, having fulfilled hisunlikely destinyof becoming an astronomer,Thomas Wright(1711-1786) published his proposalthat the distant starry formations envisioned by Swedenborg (henceforth called galaxies ) might actually be visible to us in the form of nebulae. Wright also explained the appearance of the Milky Way as"an optical effect due to our immersion inwhat locally approximates to a flat layer of stars."
Both ideas were enthusiastically embraced by the philosopherImmanuel Kant (1724-1804)who credited Wright (but not Swedenborg) for them, although he candidly admitted(in print)that he had never read Wright's book ! Kant coined the popular term of Island Universes, which he (correctly) envisioned as fairly thin rotating disks of very many stars (thus discarding, possibly involuntarily, Wright's misconceptions abouthollow spherical distributions of stars). Kant dubiously conjectured Sirius (the brighteststar in our Sky) to be located at the center of the Milky way and he still called the Milky Way, the main plane of all motion. When he published his UniversalNatural History and the Theory of Heavens (1755) Kant had no university degree yet, but he had this to sayagainst the views of Maupertuis onnebulae in general and spiral nebulae in particular:
In 1910, VestoMelvin Slipher (1875-1969) tried to argue Laplace's case but ended upshowing that the other view was probably correct!
The mystery was finally solved when it was confirmed that the nebulaewere extremely large objects at huge distances. The proof came in 1923 when Edwin Hubble turned his attention to the largest of them, the Andromeda Nebula, which is visible to the naked eye and was first described as a nebulous smear in AD 964 by Azophi (AD 903-986).
Using the 100-inch Hooker telescope on Mount Wilson, (in Los Angeles County) Hubble managed to identify a Cepheid variable star (now called V1) in the Andromeda nebula. He measured the period of V1 to be 31.4 days from which its absolute luminositycan be deduced. The faintness of V1 meant that it was more than a million light-years away. So are the other stars of the nebula which is actually composed of nearly a trillion stars. Andromeda was thus revealed to be one of the island universes, envisioned by Kant and our view of the cosmos was forever changed!
The work of Hubble was a bit flawed because of the existence of two classes of Cepheid variables, depending on which population they belong to, a distinction which Walter Baade (1893-1960) introduced in 1944.
Working at the Mount Wilson Observatory (MWO), from 1931 to 1958, Baade took advantage of the low light pollution in 1944 (resulting from the blackout of Los Angeles during WWII) and could resolve individual stars in thecenter of the Andromeda Galaxy, which helped with the aforementioned distinction. As a result, Baade rescaled the results of Hubble by a factor of two in 1952. The most recent estimate of our distance to the center of the Andromeda Galaxy is 2.537 million light-years.
The Cosmological Principle says that, when viewed on a large enough scale, our physical Universe is mostly homogeneous and isotropic.
In other words, the distant Universe looks roughly the samein any broad direction from any typical point (technically, such pointsare comoving points in free fall). Thus, the reason why the Earth isn't at the center of the Universe, as once thought, is that there's no such center (alternately, the center isanywhere). In that respect, the Universe resembles the surface of a perfect sphere: All points are equivalent and no direction is special.
The idea that the Earth isnot at the center of the Universe is ancient, but it was suppressed for a long time and its current prevalence is fairly recent...
In his Sand Reckoner masterpiece (c.213 BC), Archimedes of Syracuse (287 BC-212 BC) reports that Aristarchus of Samos (310 BC-c.230 BC) was alreadyarguing that the Earth revolves around the Sun. However, the opposite viewpoint advocated by Aristotle (384-322 BC) and Ptolemy of Alexandria (c. AD 87-165) remained official Church dogma for centuries.
The heliocentric idea was thus considered a dangerous heretical view when it was finallyrevived privately, in 1514, by a Pole named Copernicus (1473-1543). In spite of the courageous support ofKepler (1571-1630) andGalileo (1564-1642), Church coercion would not allow the "new" perspective to prevail easily (to say the least).
However, once this viewpoint is adopted, it's only natural to think that the Earth shouldn'toccupy any special place whatsoever in the Universe as a whole. After the discovery that the Milky Way (which harbors our ownSolar System) is onlyone of many similar galaxies, it seemed fairly obvious to assume that all such galaxiesare essentially placed on an equal footing. At a sufficiently large scale, the distant Universe should look essentially the samein any direction from any typical galaxy.
That statement was first called theCosmological Principle by the British astrophysicist EdwardArthur Milne (1896-1950). Before the Cosmological Principle was even known by that name,it had been used by the Russian cosmologist Alexander Aleksandrovich Friedmann (1888-1925),who should be given credit for theidea of an expanding Universe.
(which Albert Einstein had introduced mostly to accommodatethe [then] prevalent idea of a static Universe). In 1929, the American astronomer Edwin Hubble (1889-1953) independently discovered the first observational evidence of the expansion of the Universe...
There is now overwhelming observational evidence for the validity of theCosmological Principle, from careful measurements of the so-calledCosmic Microwave Background (CMB) which was discovered in 1964-65 by Arno A. Penzias and Robert W. Wilson (Nobel 1978). The CMB has been found to be isotropic to a precision of about one part in 100 000.
(2020-09-06) Filaments, walls, voids and supervoids. The foamy distribution of galaxies.
Ordinary foam only seem homogeneous if you observe it at a scale much larger than that of a single bubble.
(2007-09-09) The term "Big Bang" was coined in jest byFred Hoyle in 1956.
The idea that the entire Universe could have originated froma single pointlike "primeval atom" was first formulated in 1927by the Belgian mathematician,AbbéGeorgesLemaître (1894-1966) in a momentous article:
Un Univers homogène de masse constante et de rayon croissant rendant comptede la vitesse radiale des nébuleuses extragalactiques Annales de la Société scientifique de BruxellesA47, pp.49-59 (1927)
A homogeneous universe of constant mass and increasing radius accounting for theradial velocity of extra-galactic nebulae Notices of the Royal Astronomical Society 91, pp.483-490 (1931)
Lemaître had been ordained a catholic priest in 1923. He then studiedGeneral Relativity at Cambridge under Arthur Eddington and went on to MIT. In 1925, he started lecturing at theUniversité catholique de Louvain (UCL) and accepteda full-time position there in 1927, as he was obtaining his Ph.D. from MIT.
Georges Lemaîtrepresented his hypothesis of the primeval atom as describinga day withoutyesterday. This idea is now universally called the Big Bang theory.
Curiously, the name "Big Bang" was originally a derogatory termcoined by Fred Hoyle in 1956 to mock the concept... Hoyle was then a leading proponent of a rival theory which is now all but forgotten.
The theory became universally accepted once the theoretical investigationsof Stephen Hawking and othersproved thatGeneral Relativity and the observedexpansion of the Universe do imply such a pointlike origin. The viewpoint has even become part of the official Catholic doctrine (Msgr. Lemaître was made an honorary prelate in 1960,by Pope John XXIII).
Although Georges Lemaître himselfwas not an official participant in the 1927 Solvay conference in Brussels (on the foundations ofQuantum Mechanics) he was residing nearby and met with Einstein on that occasion. Einstein was not impressed at the time; he was quoted as saying: "Your calculations are correct, but your grasp of physics is abominable." However, several years later (c.1935) Einstein would reportedly applaud Lemaître'sideas as "the most beautiful and satisfactory explanation of creation to which I have ever listened".
What prompted that enthusiastic reaction from Einstein seems to have beenLemaître's description of cosmic rays as possible left-overs fromtheprimeval explosion. It turns out that this early insight does not really apply to high-energy cosmic rays (as described by Robert Millikan) but to the low-energyphotons of the cosmic microwavebackground, discovered by Penzias & Wilson in 1965, a few months beforeLemaître passed away...
(2003-07-14) What's the energy density of the Cosmic Microwave Background today?
The Cosmic Microwave Background is a gas of photons with a blackbody spectrum, whose estimated temperature was recently consolidated as:
Using the variable x = h / kT ,the energy density ofall photons is thus:
0
u d =
0
8 k4 T 4x3 dx
h3 c3 (e x 1 )
=
85 k4T 4
15 h3 c3
In the above, the definite integral of x3/(e x 1 )was obtained as thesum (for n = 1 to ) of all definite integrals of x3e -nx : As the n-th one is 6/n4 the whole sum is 4/15 (the reciprocals of fourth powers add up to4/90).
) the above is equal to (4/c) T 4.
Well before Planck, that fact was known as the Stefan-Boltzmann law, which was discoveredexperimentally by Jozef Stefan (1835-1893) the year Einstein was born (1879). It was established theoretically five years later (1884) by his star studentLudwig Boltzmann (1844-1906).
Planck used the bold new idea of quantization to justify his radiation formula, which unifies asymptotically two different regimes: The classical Rayleigh-Jeanslaw (1900,1905) for low frequencies and the Wien distribution (1896) which fails for low frequencies.
Incidentally, Planck expressed the Stefan constant in term of the new constant h he introduced for the occasion:
To a temperature T = 2.72548 K corresponds an energy density of:
7.565723-16 T4 = 4.1747-14 Pa ( 1 Pa = 1 J/ m3 )
That's about 261 electronvolts per liter; 261 eV/L or 0.26056 eV/cc.
Number of Photons in Blackbody Radiation:
Since each photon has energy h, the density of photons per unit volume is the following integral (whose value involves Apéry's constant (3), defined asthe sum of the reciprocals of all perfect cubes ) :
0
u
h
d =
16(3) k3T 3
h3 c3
= ( 20.2868266) T3
For the CMB, that's 0.410729 photons per m3 (411 photons per cc).
Average Energy of a Thermal Photon:
It's the ratio of the total energy density to the density of photons, namely:
4
30 (3)
kT = ( 2.70117803291906389613472623...) kT
Median Energy of a Thermal Photon:
m kT 2.35676305705 kT (where m is given by the relation at right)
m 0
x2 dx
(e x 1 )
=
(3)
Thermal Photon at the Peak of the Frequency Spectrum:
When the spectral density of the blackbody energy is plotted against frequency (as above) it's proportional to x3 / (exp(x)-1) and reaches a maximum when exp(-x) = 1-x/3. That's to say that, in the most energetic interval of frequencies,a thermal photon has the following energy:
h = ( 2.82143937212...) kT
Thermal Photon at the Peak of the Wavelength Spectrum:
In the nineteenth century, the spectral energy per wavelength interval (instead of frequency interval) was commonly plotted. The maximum of that diagram is reached at a totally different point, corresponding to the solution of exp(-x) = 1-x/5. Namely:
(2018-05-20) Mostly hydrogen and helium. Some deuterium and a little lithium.
In the very first second of the Universe, the overabundance of neutrinos and thermalphotons helped maintain an equilibrium with roughly the same number of neutrons and protons. The intense radiation overwhelmed any nuclear bonds which might otherwise have formed.
At a slightly lower temperature, protons become significantly more abundant thanneutrons, on account of their slightly lower mass. An equilibrium was established well before nuclear fusion started for good (when the Universe was about 10 seconds old) with roughly only one neutron to six protons. During the next 20 minutes or so, some lone neutrons did decay before they fused into atomicnuclei, which lowered the neutrons-to-protons ratio from 1:6 to 1:7. However, most of them formed stable deuterium nuclei by fusing with protons. Most of those deuterium nuclei fused with each other to form Helium-4 (alpha particles). Some fused with protons to form stable Helium-3 directly orwith remaining neutrons to form radioactive tritium which would be completely transformed to Helium-3 by beta-decay in a few short centuries (the half-life of tritium is 12.3 years ).
The 1:7 ratio of neutrons to protons at the end of the so-called BBN (Big-Bang nucleosynthesis) doesn't depend much on reaction details. It matches the often-quoted primordial abundance of helium (25% by mass). In the main, with 14 protons and 2 neutrons we form 12 hydrogen nuclei andone helium-4 nucleus. The latter thus accounts for a quarter of the total mass.
On the other hand, the relatively low abundance of unfused deuterium nuclei (deuterons) at that time depends very much on the dynamics of the primordial reactionsand is therefore a good test of any model thereof.
Abundance of Primorial Deuterium :
As the Universe evolved into galaxies harboring several generations of stars, primordial deuterium has been steadily depleted in all stellar cores faster than regular hydrogen. It's the only form of nuclear fuel available to brown dwarfs which are, by definition, too small for gravitational collapse to produce the temperatures requiredto ignite hydrogen fusion.
Estimates for the abundance of primordial deuterium must be derivedfrom measurements of various present-day environments. Our best estimates are that the early Universe had 27 atoms ofdeuterium per million of hydrogen atoms. Although it was thought that about a third of the primordial deuteriumhad been destroyed over time, some hydrogen clouds in the Milky Waystill show a deuterium concentration as high as 23 ppm (just 15% below the estimated primordial abundance).
The abundance of Deuterium currently observed in the Earth's oceansis higher: About 156 ppm or, more precisely, one atomof deuterium (D) for about 6420 atoms of protium (H). Most is in the form of semi-heavy water molecules (HDO) which are about 3210 times more common in seawater than "pure" heavy water molecules (deuterium oxide, D2O).
When some signal [sound, light, etc.] emitted at a frequency is observed at frequency / (1+z) , the quantity z is called theredshift of the source for the observer. In the case of visible light, a positive redshift makes the source appear redder(anegative redshift makes it look bluer and theopposite of a redshiftis thus sometimes called ablueshift).
Redshift may have a number of combined causes, including theclassical Doppler effect(which depends only on theradial velocity of the source),and the time dilation at the source due to its speed (Special Relativity)and/or surrounding gravity (General Relativity). Finally, for very distant sources, there is also acosmological redshift dueto the fact that the wavelength of a traveling signal increases in the same proportion as theUniverse expands. In other words, light which was emitted from cosmic distances, whenthe Universe was (1+z) times smaller than now, is currently observedwith acosmic redshift equal to z.
The quantity 1+z is the ratio of the observed wavelength to the emitted one andmay be expressed as a simple product of several factors. Each of these correspond to one of the four causes of redshift listed above (some authors quote only three such causes by viewingboth types of Doppler shifts as a single aspect of the same phenomenon;I beg to differ):
1 + z =
(1 + v/u)
1
12
1
1 GM / Rc2
T
T
Classical (Radial)
Relativistic (Isotropic)
Gravitational
Cosmic
Doppler Effect
General Relativity
Rarely, if ever, are the quantified effects of the four causes of redshiftexplicitly unified in this way. Almost always, that grand formula is reduced down to only one or two dominantredshift factors.
The symbols have the following meanings:
v is theradial speed of the source. For cosmological distances and/or curved signal propagation,this is defined in terms of the velocities of the observer and the sourcewith respect to localcomoving points at rest in the CMB: The "radial" speed v is actually thedifferencebetween the projections of thesevelocities on the local tangents to the signal's "path".
u is thecelerity of the signal [itsphase speed]. For light in a vacuum, u = c = 299792458 m/s. For sound in dry air (20°C), u 343.37 m/s.
is the ratio of thespeed of the sourceto c (thespeed of light). (There may be a nonzero transverse velocity, in which case > v/c.)
G is thegravitational constant. M is the mass of some dominant nonrotating spherical body at a distance R from the source. (Thegravitational redshift factor given here as an example would, of course,be different for other mass distributions, but it's usually a good enough approximationwhenever there's no rapidly rotating black holeorneutron starin the immediate vicinity...)
The cosmic redshift factor T/T is the ratioof the "old" temperature T of theCosmic Background at the source to the "newer"value seen by the observer( T is currently about 2.728 K). This factor is actually equal to D / D,where D is any distance characterizing the whole Universe,like the average distance between major galaxies,or the wavelength of a typical background photon (which is indeed inverselyproportional to T ).
Astronomers observe theredshift (z) directly by measuring the wavelengths of knownlines in the atomic spectra of the light emitted by a distant source. However, there is adubious tradition to quote also theapparentrecession speed of such distant sources(defined as the purelyradial velocity of a nearby source with the same redshift,in the absence ofGeneral Relativistic effects). This is obtained by retaining the first two factors of the above formula,(letting u = c and = v/c),so that (1+z) 2is and we have:
For example, aredshift z = 1 corresponds toexactly 60% of the speed of light,whereas z = 2 is 80% of the speed of light,and z = 6 is (exactly) 96% of the speed of light... (Again, in a cosmological context,it's best to quote only z and ignore this dubious "translation".)
In April 2009, a cosmological redshift of 8.2 was observed for the gamma-ray burst identified asGRB 090423(which lasted for a few seconds, during the violent implosion of a short-livedmassive star into a black hole). At the time,that object was the oldest and most distant ever seen. The light we saw from it had been emitted when the Universe was 9.2 times smaller thantoday (the temperature of the CMB was then about 25 K).
In October 2010, one galaxy with a redshift of 8.55 (HUDF.YD3) was found among the 10000 galaxies of theHubbleUltra Deep Field.
The oldest light we can observe is that of the CMB itself. It was emitted when the Universe became transparent to electromagneticradiation, at a temperature of about 3000 K. This corresponds to a redshift of about 1100.
Botched inYahoo! Answers (2010-11-18) In Einstein'sGeneral Theory of Relativity,the redshift of galaxies in the Universe is correctly interpreted as:
Clueless students who systematically pick the longest answers wouldenjoy an unfair advantage here: The only correct answer is (c).
Answer (a) was once used by Edwin Hubble and others outside of the framework of General Relativity (it still appears occasionally in misguided essays). However, this is not acceptable in the proper context of General Relativitywhere typical galaxies occupy locations that are as motionless asthe expansion of the Universe can possibly allow (i.e.,comoving points with fixed coordinates). As discussedabove,theDoppler effectis another cause of redshiftwhich is unrelated to the cosmological redshift.
Answer (b) conjures up other deprecated viewpoints which arenot compatible with General Relativity, unless you redefine "aging" of light as the matching of thewavelength of traveling photons to the changing scale ofthe Universe described by the correct answer (c)
Answer (d) is wrong but barely so. It would be correct if we could interpret "temperature of agalaxy" as the temperature of the Cosmic Background around that galaxy at the time when the light we see was emittedfrom it.
(2002-12-09) What is Hubble's "constant"?
Arguably, modern cosmology originated in 1917 at theLowell Observatory,whenVestoMelvin Slipher (1875-1969)observed thatdistant galaxies are all receding from our own Milky Way.
In 1929,EdwinP. Hubble (1889-1953) took Vesto Slipher's velocity data (incidentally, witout giving Slipher proper credit) andtried to correlate them with his own distance measurements (obtained with the method inaugurated by Henrietta Leavitt(1868-1921) in 1908). What Hubble discovered (from sketchy data)is that the recession speed (v) of a galaxy is roughly proportional to its distance from us (d). The nonrelativistic coefficient of proportionality is now called Hubble's constant (H or Ho ):
v = H d
Hubble's constant (H) actually describes the rate of expansionof the Universe and its value evolves as the Universe ages. Various modelsof the Universe make the product of H into the Age of the Universe equal to a dimensionless number which depends on specific assumptions: This product would be equal to 1 in a Universe of very low density[H would be the reciprocal of the Universe's age]. It would be 2/3 in aflat Universe ( = 1) dominated by ordinary matter, and only 1/2 in a radiation-driven expansion phase (the fireball conditions which prevailed for less than 56 000 years).
However, if some form of exotic stuff and/or a nonzero cosmological constant dominates the large-scale structure of the Universe(as modern dataindicates), the above product could be equal to or larger than one,so the Universe might beolder than 1/H.
The actual value of H is difficult to determine experimentally, mostly because it's difficult to determine precisely the distance to an object that'sfar enough to make its [unknown] proper motion a negligiblefactor in its observedredshift. The latest estimates place H somewhere between 68 km/s/Mpc and 75 km/s/Mpc.
The reciprocal of H is sometimes called theHubble time, and theAge of the Universe is commensuratewith it. One "s-Mpc/km" is 977 792 221 400 years, and theHubble time corresponding to the above values of H is thus 75 or 68 times smallerthan this, namely between 13 and 14.4billion years...
(2002-07-24) What is meant by "critical density"? What's the omega () constant?
Following Steven Weinberg (The First Three Minutes, 1977)we'll introduce the notion ofcritical density in theframework ofNewtonian mechanics. It turns out that therelativistic computation that we'lloutline next gives the same final result, provided the density "" is understood toinclude the density of energy divided by cand a corrective term for what's now called dark energy. First things first, here's the simple Newtonian argument:
Consider a sphere of radius Rmuch smaller than the whole universe,but large enough to apply theCosmological Principle. If is the average mass density of the Universe,such a sphere is roughly homogeneous and its total mass M is equal to times its volume, namely:
M = 4R3/3
The (Newtonian) potential energy of a galaxy of mass m near the surface of the sphereis negative (it's a binding energy). It's equal to:
On the other hand, this galaxy has a (purely radial) speedV = HR given byHubble's Law(H = H(t) being the value of Hubble's constant at the present time t)and its kinetic energy is therefore:
½ m V2 = ½ m H2 R2
The total mechanical energy of the galaxy is the sum of the above two terms andremains constantas the Universe expands:
m R2 [ H2/2 4G/3 ]
If this total energy is positive, the galaxy will eventually escape to infinitywith some kinetic energy left over. If it's negative, this won't happen and, in fact,the Universe's expansion will eventually stop and reverse(the Universe will then collapse). Between these two alternatives is thecritical case where the bracket in the aboveexpression is precisely zero, whereby the Universe keeps on expanding forever,but just barely so (the relative speed of two typical galaxies eventually approaches zero but their distancestill keeps growing to infinity). The above expression shows that this happens precisely when the density of the Universe is equal to the following quantityo,which is called thecritical density :
o = 3 H2 / 8G = /o
The ratio () of the actual density to thecritical densityis the famousomega "constant", which determines the ultimatefate of the Universe: If is less than or equal to 1, the Universe will expand forever,otherwise it will eventually collapse.
is notreally constant but the sign of -1 is (in this model at least).
As advertised, the results of the previous section remain valid within General Relativity, whereby an homogeneous andisotropic universe (as envisioned byFriedmann in 1922) is characterized by two parameters; an increasing scale factora(t) (which is a length) and a dimensionless constant K (the spatial Gaussian curvature being K/a). Under those assumptions, the temporal (00) component of Einstein's field equations yield the following relation:
First Friedmann Equation (1922)
H2 (a'/a)2 = (8G) / 3 K c2/a2
Solving for when =0 and K=0 gives the aforementioned value of o .
Our previous Newtonian interpretation remains valid only if Einstein's field equations holdwith a vanishing cosmological constant (=0). Otherwise, a positive cosmological constant can even entail an accelerating expansion of the Universe, which is compatible with the big picture that emerged fromobservational data in 1998. There's simply no Newtonian explanation for that !
More precisely, according to the First Friedmann equation, a positive cosmological constant can be tallied as a supplemental density / 8G attributed to dark energy (this is just a name) which is added to the combined total from ordinary matter and energyas well as dark matter.
If the overall geometry of our universe wasn't very nearly flat (like a Friedmann universe with K=0) then it would either have collapsed or thinned out beyond recognition a long time ago. Thecurrent prevalent view is thus that dark energy is due to a positive cosmological constantthat accounts for whatever is needed to balance the above Friedmann equation (assuming vanishing Gaussian curvature). This would mean that empty space accounts for about 70% of the total tally (i.e, space itself and all itsmatter-energy content, including dark matter). Mind-boggling, isn't it?
As the Universe expands, its density (>0) and pressure (p>0) decrease steadily. So does the above negative bracket. If the cosmological constant () is positive, the right-hand-side becomes positive after a while, which means that the expansion of the Universe accelerates after a certain point.
Since 1998, it's known that we passed that point about 5 billion years ago. This shows that is positive (which Einstein's equations don't require).
(2003-07-16) How is the "look-back time" of distant objects determined?
Theredshift of a very remote object is observed directly. All other indicators of its distance depend on some cosmological model of the Universe.
In particular, thelook-back time of a distant source is defined asthe time elapsed since the light reaching us was emitted. Because of the Universe's expansion, such a distant source isalways farther awaythan what would be naively estimated by multiplying itslook-back time by the speed of light.
Our estimate oflook-back time depends on which model of the Universewe rely on. Currently, the most popular such model is the Lambda-CDM_model which allows for the existence of dark matter and a positive Cosmological Constant which accelerates the expansion of the Universe. The table below presents two (obsolete) versions of the semi-Newtonian model. The first one is utterly incompatible with modern observations. The second one (represented by the last two columns) is surprisingly good for a rough estimate. It assumes that the Universe behaves gravitatonally as if it was effectivelyempty.
Look-Back Times (Millions of Years)for 2 Cosmic Models & 2 Values of H
Cosmic Redshift ( z )
"Apparent" Recession ( )
Matter-Dominated ( = 1 )
Zero Total Energy ( Effectively, = 0 )
z 0
z
z / H
z
(1+z) 2 1
(1+z) 2 + 1
2
1
1
3H
(1+z)3/2
t =
1
z
H
1+z
1
60%
5619
6197
6518
7190
2
80%
7019
7741
8691
9586
6
96%
8222
9069
11175
12325
100%
8691
9586
13037
14379
(2002-12-09) What isdistance in a cosmological context?
Astronomers estimate distance inmany different ways. It's not at all obvious that all such methods end up measuring the same thing. In fact, they don't.
In anobservational cosmological context, the distance to a distant objectis [probably] bestdefinedas the distance its light hastraveled before reaching the observer. This definition would mean distance andlook-back time aresimply proportional (the coefficient of proportionality beingEinstein's constant). Thus the relation between distance and redshift would depend, as discussed above,on how the Universe has expanded between the emission and the reception of light.
Thisobserved cosmological distance is thus not a simple concept and it'sfairly useless in theoretical speculations, where the distance of an object to the[arbitrary] origin is best defined as the value of aspace-coordinatewhen the time-coordinate is the same [we're talking curvilinear coordinates in curvedspace, here]. In an expanding universe, this latterflavor of distance is greater than the former one. [The source has "moved away" after emitting its light.]
The straightforwardparallax method, based on Euclidean trigonometry,may not be valid for very large distances and/or when strong gravity is present;the three angles of a large physical triangle may not quite add up to 180°. Although the parallax angles of galaxies are actuallyfar too small to be measured,we may wonder how trigonometry could be usedin principleto measure intergalactic distances... The very concept of distance is worth questioning under at least three types ofextreme conditions:
Extremely small scales: ThePlanck length(1.6 m)is the characteristic unit of a scale at which physical space itselfis thought to lack any kind of smoothness. Geometry breaks down when we "look" this close. This is the not-yet-understood domain ofquantum gravity.
Extreme curvature: Around black holes, our Euclidean intuition fails. It's best to avoid considering the "distance to the center of a black hole",because this distance would turn out to be infinite under most definitions.
Extremely large scales: As the Universe expands,so does the distance between two objects sufficiently far apart. The expansion of the Universe may thus introduce a significant delayin the light signals that go from one object to the other. It becomes important to state precisely what is meant by "distance" in such a context,as discussed above.
(2002-07-24) What are "comoving points" ?
In the Euclidean space of classical geometry,motion is actually considered relative to some immobile framework of fixed points. This viewpoint is not a practical proposition within our expanding physical Universeconsidered as a whole. Instead, the cosmological approach is to introduce reference points whose relative motionsare entirely due to the general expansion of space itself, whatever that may be. By definition, such points are said to becomoving.
The relative motions of galaxies are not entirely due to the expansion of the Universe(nearby galaxies attract each other) and their centers of mass are thusnotstrictlycomoving. However, descriptions of our expanding Universe will often discardthe distinction for the sake of simplifying the presentation. The centers of fairly large clusters of galaxies could seem to be slightly betterembodiments of comoving points, but such attempted refinements are vastly inferior tothe better characterization we shall now give...
The mostpractical viewpoint is to characterizeacomoving point as a point which is at rest with respect to theCosmic Microwave Background (CMB). The Sun isnot comoving(relative to the CMB, its speed is about 370 km/s ). Neither is the center of mass of ourLocal Group of galaxies,which moves at about 600 km/s with respect to the CMB(three dozen galaxies are thus not a large enoughchunk of matterto estimate the value of our localHubble flow).
The dipolar anisotropy of the CMB from our local viewpoint (which indicates that the Earth and the Sun are notcomoving) was first precisely determined in 1977 by the so-calledU2 Anisotropy Experimentwhich was flown aboard the NASA Ames U2 jet aircraft by a UC Berkeley group. The results were later confirmed from outer space,by the "Cosmic Background Explorer" (COBE) launched on November 18, 1989. George Smootmasterminded both projects.
Knowing our own speed in the CMB is just the beginning. The tiny irregularities in the CMB offer a baby picture of the Universeat the age of about 379 000 years, when it first becametransparent. (A COBE picture made headlines in April 1992.)
On June 30, 2001, NASA launched its Microwave Anisotropy Probe (MAP) at a cost of $145 000 000. It is 45 times more sensitive than COBE and its angular resolution is 33 times better. On Oct. 1, 2001, It arrived at the secondLagrange point L2 (a semi-stable orbital position on the Earth-Sun line, 1.5 million kmfurther from the Sun than the Earth). A firstsky scan was completed in April 2002.
MAP was renamed in honor of David T. Wilkinson, who died on September 2, 2002 (it's now called WMAP =Wilkinson Microwave Anisotropy Probe) and the firstWMAP resultswere released on February 11, 2003.
(2021-01-18) Even a slow worm will eventually reach the end of a fast-stretching band.
(2002-07-30)
TheAnthropic Principle is the statement that the Universeweobserve must allow intelligent life to evolve, or elsewe wouldn'tbe here to observe it.
In any universe with features that rule out intelligent life, there would notbe anybody around to wonder why such features exist... Yet, there is a general feeling that theAnthropic Principle by itselfprovides a poor sort of explanation. Indeed, if we were to assume that there's onlyone possible universe,it seems that thereshould always be a reasonfor what we observe, other than our own existence. Thus, cosmologists often find theAnthropic Principle somewhat repugnantand will invoke it only as a last resort...
The alternative, however, is that there could very well be (in some obscure sense) many universes. Some have intelligent observers in them and some don't. The Anthropic Principle simply states that our own Universecan only be of the former type. In fact, Andrei Linde's chaotic inflation theories do predict that the creation of a universe likeours is best explained as part of a process which creates a large multiplicity of universesin which the fundamental constants of nature may have different values. If that viewpoint is correct, there would not be any ultimate explanation forthe values of the fundamental physical constants, except that their rangeshould be compatible with the Anthropic Principle...
Now, the tricky part is that the dubious existence of other universes isentirely irrelevant, by definition, to the physics of our own Universe. As an irrelevant assumption does not change anything, we may conclude that the Anthropic Principle (which may or may not be ultimatelyneeded )is fully justified even if we leave open the "existence" of anything outside ofour own Universe.
(2002-10-28)
I would like to learn that Newton's laws must be modifiedin order to correctly describe gravitational interactions at large distances. That's more appealing than a universe filled with a new kind ofparticle. Vera Rubin (1928-2016)
Dark Matter & the Pull of Galaxies:
The Sun and other stars have an orbital speed around the Galaxy which is muchlarger than what it would be if gravitational forces were only due to all the ordinary matter we can tally (stars and interstellar gas). The same observation can be made in other galaxies as well. Galaxies have massivedark halos which consist of somestrange stuff, calleddark matter.
Although the early evidence for the existence of dark matter came fromgalacticrotation curves, the relative speeds of galaxies in some clusters alsoimply the existence of intergalactic dark matter to hold clusters together(at the large speeds observed, the galaxies would otherwise haveflown apart a long time ago). More localizedevidence has also been found recently.
Although most ordinary matteractually resides outside of galaxies,all the evidence that has been gathered since 1998seems to indicate that there's about five times more dark matterthan ordinary matter in the Universe.
Dark Energy & the Accelerating Expansion of the Universe:
In 1998, the study of distant Type-1A supernovae (Nobel 2011) indicatedthat the expansion of the Universe is accelerating. Such an acceleration can be accounted for by a small positive cosmological constant () in Einstein'sfield equations.
This would mean that empty space itself has a nonzero energy densityof about 0.5 nPa or 3 keV/cc (that's roughly equivalent to therest energyof one helium atom per cubic meter of empty space).
This type of energy is called dark energy and it accounts for most (70%) of the followingcomposition of our Universe [courtesy of NASA]:
(2024-06-01) Dark matter probably consists of at least one kind right-handed neutrino.
Ryan Landfield (2009-04-10;UA931) A residual (decaying) sunward acceleration of 8.74(45) 10 -10 m/s2
This is commensurate with the Hubble acceleration (i.e., the product of the Hubble constant H by the speed of light c).
H c = 6.9 10 -10 m/s2
In July 2012, Slava G. Turyshev et al. apparently nailedthat coffin with a full quantitative explanation ofthe "anomalous" acceleration in term of the recoil of infrared photonsemitted by the onboard nuclear power and bouncingoff the back of the parabolic communication antenna. This would explain not only the magnitude of the observed effectbut also its exponential decrease with time at arate similar to the decay of the plutonium which powers the Pioneer probe (behind its own antenna).
(2018-08-01)
(2018-08-01)
(2019-06-25) The end of inflation is a phase transition. It propagates like one.
(2020-04-01) A promising experiment has failed to detect evidence for inflation.
(2002-07-24) 
