Stephen Hawking
by Leonard Mlodinow · 8 Sep 2020 · 209pp · 68,587 words
it keeps the universe from collapsing upon itself. They were unsuccessful. Even Einstein joined the game. He added an extra “anti-gravity” term, called the cosmological constant, to the equations of general relativity to supply the repulsive force needed to keep the cosmos from contracting.*2 The realization that all these eminent
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“unchanging” they meant on the cosmic scale. Obviously, small-scale change is part of nature—planets orbit, rocks fall, people live and die. *2 The cosmological constant acts only on very large scales. It introduced no effects that could be measured with the technology available at the time, and so whether or
A Grand and Bold Thing: An Extraordinary New Map of the Universe Ushering
by Ann K. Finkbeiner · 16 Aug 2010 · 225pp · 65,922 words
hadn’t known about. Maybe gravity doesn’t work the way Albert Einstein’s theory of general relativity says it does. Maybe Einstein’s famous cosmological constant—which he put into the equations of general relativity to fudge the universe’s expansion and which he later took back out—was right after
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Sky Survey Congress, U.S., 39, 78 Connolly, Andy, 155, 169 Copernicus (space telescope), 33 cosmic microwave background, 143, 146, 175, 195 cosmic rays, 64 cosmological constant, 148 Crafoord Prizes, 42, 195 critical path, 83–84 Crocker, Jim, 82–85, 86, 90–91, 105, 118 Leger appointed telescope engineer by, 110 monitor
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, 125, 162 Dusty (software), 197 dwarf galaxies, 163–65 Early Data Release, 138, 158 East Tennessee State University, 165–66 Einstein, Albert, 11, 43, 148 cosmological constant of, 148 Eisenstein, Daniel, 145, 147, 178, 180 electrons, 137, 187–90 elements, formation of, 188, 190 elliptical galaxies, 173, 182–83, 185, 191, 192
First Light: Switching on Stars at the Dawn of Time
by Emma Chapman · 23 Feb 2021 · 265pp · 79,944 words
with the idea that our Universe might be anything other than static. He famously changed his general relativity equations to include an extra term, a ‘cosmological constant’, to arrest the expansion that naturally fell out of his equations, and keep everything still.13 Don’t feel bad if the idea of a
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, London, UK. 12 The Big Bang’s echo. NPR News. May 2005. www.npr.org/templates/transcript/transcript.php?storyId=4655517. 13 What is a Cosmological Constant? https://wmap.gsfc.nasa.gov/universe/uni_accel.html. 14 Van der Marel, R. et al. 2012. The M31 velocity vector. III. Future Milky Way
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here, here, here constraint on Epoch of Reionisation here discovery here, here spin temperature and here, here, here, here Cosmic Spectrum, The (Paterson) here, here cosmological constant here cyanobacteria here, here, here, here, here Dark Ages here, here, here, here, here, here, here, here, here, here, here, here Dark Energy Survey here
The Fabric of the Cosmos
by Brian Greene · 1 Jan 2003 · 695pp · 219,110 words
redefining the meaning of “empty,” envisioning that space is unavoidably suffused with what are called quantum fields and possibly a diffuse uniform energy called a cosmological constant—modern echoes of the old and discredited notion of a space-filling aether. What’s more, we then describe how upcoming space-based experiments
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prejudice. It didn’t take him long. In 1917 he achieved the goal by introducing a new term into the equations of general relativity: the cosmological constant.4 Einstein’s strategy in introducing this modification is not hard to grasp. The gravitational force between any two objects, whether they’re baseballs,
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t be static—space can’t hover at a fixed overall size—without there also being some kind of balancing repulsive force. Einstein introduced the cosmological constant because he found that with this new term included in the equations, gravity could provide just such a repulsive force. But what physics does
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this mathematical term represent? What is the cosmological constant, from what is it made, and how does it manage to go against the grain of usual attractive gravity and exert a repulsive outward push
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? Well, the modern reading of Einstein’s work—one that goes back to Lemaître—interprets the cosmological constant as an exotic form of energy that uniformly and homogeneously fills all of space. I say “exotic” because Einstein’s analysis didn’t specify
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electrons, or photons. Physicists today invoke phrases like “the energy of space itself” or “dark energy” when discussing the meaning of Einstein’s cosmological constant, because if there were a cosmological constant, space would be filled with a transparent, amorphous presence that you wouldn’t be able to see directly; space filled with a
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as heat), but also on any pressures that may be exerted. And this is the essential physics we need if we are to understand the cosmological constant. Here’s why. Outward-directed pressure, like that exerted by a compressed spring, is called positive pressure. Naturally enough, positive pressure makes a positive
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pressure is negligible) and, in particular, when pressure is negative (for ordinary matter like protons and electrons, pressure is positive, which is why the cosmological constant can’t be composed of anything familiar) there is a contribution to gravity that would have shocked Newton. It’s repulsive. This result is central
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in a region is negative enough, repulsive gravity will dominate; gravity will push things apart rather than draw them together. Here is where the cosmological constant comes into the story. The cosmological term Einstein added to the equations of general relativity would mean that space is uniformly suffused with energy but
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it might have been the greatest discovery—of all time. After learning of Hubble’s results, Einstein rued the day he had thought of the cosmological constant, and he carefully erased it from the equations of general relativity. He wanted everyone to forget the whole sorry episode, and for many decades
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everyone did. In the 1980s, however, the cosmological constant resurfaced in a surprising new form and ushered in one of the most dramatic upheavals in cosmological thinking since our species first engaged in cosmological
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All right, it’s nice that Guth found a specific physical mechanism for realizing Einstein’s idea of a cosmological constant, but so what? What’s the big deal? The concept of a cosmological constant had long been abandoned. Its introduction into physics was nothing but an embarrassment for Einstein. Why get excited
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that had been discredited more than six decades earlier? Inflation Well, here’s why. Although a supercooled Higgs field shares certain features with a cosmological constant, Guth realized that they are not completely identical. Instead, there are two key differences—differences that make all the difference. First, whereas a
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cosmological constant is constant—it does not vary with time, so it provides a constant, unchanging outward push—a supercooled Higgs field need not be constant.
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quickly roll down to the valley, much like a ball rolling down a hill. The upshot is that if a Higgs field acted like a cosmological constant, it did so only for a brief moment. Figure 10.1 (a) A supercooled Higgs field is one whose value gets trapped on the
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energy, like the frog’s jumping off the bump. The second difference is that whereas Einstein carefully and arbitrarily chose the value of the cosmological constant—the amount of energy and negative pressure it contributed to each volume of space—so that its outward repulsive force would precisely balance the inward
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, obviously, and so the outward push supplied by the Higgs field’s repulsive gravity is monumental compared with what Einstein envisioned originally with the cosmological constant. Figure 10.2 A smoother and more gradually sloping bump allows the Higgs field value to roll down to the zero-energy valley more easily
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mass/energy that physicists had been seeking. The Missing 70 Percent If you cast your mind back to 1917 and Einstein’s introduction of a cosmological constant, you have enough information to suggest how it might be that the universe is accelerating. Ordinary matter and energy give rise to ordinary attractive
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acting to slow the expansion, gets weaker. And this sets us up for the new and unexpected twist. If the universe should have a cosmological constant—and if its magnitude should have just the right, small value—up until about 7 billion years ATB its gravitational repulsion would have been overwhelmed
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of expansion, in keeping with the data. But then, as ordinary matter spread out and its gravitational pull diminished, the repulsive push of the cosmological constant (whose strength does not change as matter spreads out) would have gradually gained the upper hand, and the era of decelerated spatial expansion would have
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the Schmidt group to suggest that Einstein had not been wrong some eight decades earlier when he introduced a cosmological constant into the gravitational equations. The universe, they suggested, does have a cosmological constant.23 Its magnitude is not what Einstein proposed, since he was chasing a static universe in which gravitational attraction
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of a supernova depends on the difference between the gravitational pull of ordinary matter and the gravitational push of the “dark energy” supplied by the cosmological constant. Taking the amount of matter, both visible and dark, to be about 30 percent of the critical density, the supernova researchers concluded that the
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accelerated expansion they had observed required an outward push of a cosmological constant whose dark energy contributes about 70 percent of the critical density. This is a remarkable number. If it’s correct, then not only does
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of the universe would hardly have been diminished. But there is a second, equally important reason why 70 percent is a remarkable number. A cosmological constant that contributes 70 percent of the critical density would, together with the 30 percent coming from ordinary matter and dark matter, bring the total mass
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thinned out, the gravitational pull diminished. About 7 billion years ago, ordinary gravitational attraction became weak enough for the gravitational repulsion of the universe’s cosmological constant to become dominant, and since then the rate of spatial expansion has been continually increasing. About 100 billion years from now, all but the
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dark matter, there would still be a significant plot twist in need of experimental vetting: the supernova observations that give evidence of an outward-pushing cosmological constant accounting for 70 percent of the total energy in the universe. As the most exciting and unexpected discovery of the last decade, the evidence
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for a cosmological constant—an energy that suffuses space—needs vigorous, airtight confirmation. A number of approaches are planned or already under way. The microwave background experiments play
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determine the nature of the dark energy more precisely. You see, although I have described the dark energy as being a version of Einstein’s cosmological constant—a constant, unchanging energy that pushes space to expand—there is a closely related but alternative possibility. Remember from our discussion of inflationary cosmology (
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and the jumping frog) that a field whose value is perched above its lowest energy configuration can act like a cosmological constant, driving an accelerated expansion of space, but will typically do so only for a short time. Sooner or later, the field will find its
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be experiencing an extremely gentle version of the inflationary burst believed to have happened during the universe’s earliest moments. The difference between a true cosmological constant and the latter possibility, known as quintessence, is of minimal importance today, but has a profound effect on the long-term future of the
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universe. A cosmological constant is constant—it provides a never-ending accelerated expansion, so the universe will expand ever more quickly and become ever more spread out, diluted, and
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at various times in the past), SNAP may be able to distinguish between the two possibilities. By determining whether the dark energy truly is a cosmological constant, SNAP will give insight into the long-term fate of the universe. Space, Time, and Speculation The journey to discover the nature of space
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an outward push on its walls, then it might be possible to keep the wormhole open and stable. Although similar in its effect to a cosmological constant, exotic matter would generate outward-pushing repulsive gravity by virtue of having negative energy (not just the negative pressure characteristic of a cosmological constant13).
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expands or inflates? A Lambda does the job! Another answer cannot be given.” (Translation by Koenraad Schalm.) Lambda refers to something known as the cosmological constant, an idea we will encounter in Chapter 10. 8. To avoid confusion, let me note that one drawback of the penny model is that every
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mathematically inclined reader: Einstein replaced the original equation Gμv = 8πTμv by Gμv + Λgμv = 8πTμv where Λ is a number denoting the size of the cosmological constant. 5. When I refer to an object’s mass in this context, I am referring to the sum total mass of its particulate constituents. If
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negative rather than positive pressure. In such a situation, negative pressure will contribute a repulsive gravitational field acting within the region. 7. Mathematically, the cosmological constant is represented by a number, usually denoted by Λ (see note 4). Einstein found that his equations made perfect sense regardless of whether Λ was
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rise to negative pressure and repulsive gravity. A negative value for Λ yields ordinary attractive gravity. Note, too, that since the pressure exerted by the cosmological constant is uniform, this pressure does not directly exert any force: only pressure differences, like what your ears feel when you’re underwater, result in
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a pressure force. Instead, the force exerted by the cosmological constant is purely a gravitational force. 8. Familiar magnets always have both a north and a south pole. By contrast, grand unified theories suggest that there
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on standard big bang cosmology. They have never been observed. 9. Guth and Tye recognized that a supercooled Higgs field would act like a cosmological constant, a realization that had been made earlier by Martinus Veltman and others. In fact, Tye has told me that were it not for a
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Higgs field perched on a plateau, its pressure density turns out to equal the negative of its energy density (the same is true for a cosmological constant), and so the righthand side is indeed positive. 10. The physics underlying these quantum jumps is the uncertainty principle, covered in Chapter 4. I
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Western and Michael Turner of the University of Chicago, and Gary Steigman of Ohio State, had suggested that the universe might have a small nonzero cosmological constant. At the time, most physicists did not take this suggestion too seriously, but now, with the supernova data, the attitude has changed significantly. Also
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note that earlier in the chapter we saw that the outward push of a cosmological constant can be mimicked by a Higgs field that, like the frog on the plateau, is perched above its minimum energy configuration. So, while a
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early moments of inflationary cosmology. We will discuss this in Chapter 14, when we consider the question of whether the data do indeed require a cosmological constant, or whether some other entity with similar gravitational consequences can fit the bill.) Researchers often use the term “dark energy” as a catchall phrase
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major challenge facing theoretical physics is to show that the combined contribution of all field jitters yields a total energy in empty space—a total cosmological constant—that is within the observational limit currently determined by the supernova observations discussed in Chapter 10. So far, no one has been able to
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approximate calculations have gotten answers wildly larger than observations allow, strongly suggesting that the approximations are way off. Many view explaining the value of the cosmological constant (whether it is zero, as long thought, or small and nonzero as suggested by the inflation and the supernova data) as one of the
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which permeates space. cosmic horizon, horizon: Locations in space beyond which light has not had time to reach us, since the beginning of the universe. cosmological constant: A hypothetical energy and pressure, uniformly filling space; origin and composition unknown. cosmology: Study of origin and evolution of the universe. critical density: Amount
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a p-brane to which open string endpoints are attached. dark energy: A hypothetical energy and pressure, uniformly filling space; more general notion than a cosmological constant as its energy/pressure can vary with time. dark matter: Matter suffused through space, exerting gravity but not emitting light. electromagnetic field: The field which
Coming of Age in the Milky Way
by Timothy Ferris · 30 Jun 1988 · 661pp · 169,298 words
, Einstein reluctantly concluded that there must be something wrong with the theory, and he modified its equations by adding a term that he called the cosmological constant. Symbolized by the Greek letter lambda, the new term was intended to make the radius of the universe hold steady with the passing of time
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. Einstein never liked the cosmological constant. He called it “gravely detrimental to the formal beauty of the theory,” pointing out that it was nothing more than a mathematical fiction, without any
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the lambda term. (Fumed Einstein, “If Hubble’s expansion had been discovered at the time of the creation of the general theory of relativity, the [cosmological constant] would never have been introduced.”)2 Yet Hubble, like Slipher, was isolated by the gulf that still separated the world of the American observational astronomers
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the universe as a whole. Combines astronomy, astrophysics, particle physics, and a variety of mathematical approaches including geometry and topology. (2) A particular cosmological theory. Cosmological constant. A term sometimes employed in cosmology to express a force of “cosmic repulsion,” such as the energy released by the false vacuum thought to power
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largely untouched by other biographies. —————. Hans Bethe: Prophet of Energy. New York: Basic Books, 1980. Anecdotal profile of the pathfinding physicist. —————, and Gerald Feinberg, eds. Cosmological Constants. New York: Columbia University Press, 1986. Berry, Michael. Principles of Cosmology and Gravitation. London: Cambridge University Press, 1981. Berry, W.B.N. Growth of a
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inflationary universe hypothesis, 345, 356–360, 362 prescientific creation myths, 349–350 quantum genesis hypothesis, 351, 362–365 vacuum genesis hypothesis, 351–356, 361, 362 Cosmological constant, 205–206, 208 Coulomb barrier, 260, 262–263, 274, 352 penetration by protons of, 262, 264–265 quantum indeterminacy and, 288 Council of Nicaea (A
Average Is Over: Powering America Beyond the Age of the Great Stagnation
by Tyler Cowen · 11 Sep 2013 · 291pp · 81,703 words
. String theory is known to contain configurations that describe all the observed fundamental forces and matter but with a zero cosmological constant and some new fields. Other configurations have different values of the cosmological constant, and are metastable but long-lived. This leads many to believe that there is at least one metastable solution
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that is quantitatively identical with the standard model, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. It is not yet known whether string theory has such a solution, nor how much
Day We Found the Universe
by Marcia Bartusiak · 6 Apr 2009 · 412pp · 122,952 words
-accepted astronomical observations, Einstein altered his famous equation, adding the term λ (the Greek letter lambda), a fudge factor that came to be called the “cosmological constant.” This new ingredient was an added energy that permeated empty space and exerted an outward “pressure” on it. This repulsive field—a kind of antigravity
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hammer blow,” swiftly swinging down his hand to illustrate the point to his audience. Einstein at this stage recognized that he no longer needed his cosmological constant to describe this dynamic universe. His original equations could handle the cosmic expansion just fine, which pleased him immensely. From the start, he had had
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surveyor of stellar parallaxes. Georges Lemaître made few notable contributions to cosmology after 1934 but continued to publish reviews and discussions. Although Einstein abandoned the cosmological constant λ in 1931, Lemaître continued to champion it. They had friendly arguments about this issue whenever they met, which led to the joke that “everywhere
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quantum or cosmological theory and primarily tried, unsuccessfully, linking the forces of nature in one grand unified theory. He died in 1955, still thinking the cosmological constant was his biggest blunder. Ironically, astronomers have recently brought back the constant to help explain a universe that is not only expanding but accelerating, a
Is God a Mathematician?
by Mario Livio · 6 Jan 2009 · 315pp · 93,628 words
Genius Discovered the Language of Symmetry The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos Simon & Schuster 1230 Avenue of the Americas New York, NY 10020 Copyright © 2009 by Mario Livio All rights reserved
Life Is Simple: How Occam's Razor Set Science Free and Shapes the Universe
by Johnjoe McFadden · 27 Sep 2021
in the 1990s to revive a form of Lamarckian inheritance known today as epigenetics.14 In the twentieth century Einstein invented a factor called the cosmological constant to make his theory of general relativity consistent with a static universe. He abandoned it when the universe was seen to be expanding. Yet in
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the twenty-first century, the cosmological constant has been revived to account for the dark energy of space itself. Similarly, as we discussed in the last chapter, nobody has ever disproven geocentricity
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the universe it predicted was not stable: it must either contract or expand. To counter this instability and generate a static universe, Einstein added a cosmological constant, which is a kind of energy of space providing a kind of pressure against contraction. However, in 1929 the astronomer Edwin Hubble measured the velocities
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of galaxies and discovered, to his astonishment, that they are nearly all moving away from us as the universe is expanding. Einstein abandoned his cosmological constant, calling it the ‘biggest blunder’ of his life. If the universe is expanding into the future then it must have been much smaller in the
Big Bang
by Simon Singh · 1 Jan 2004 · 492pp · 149,259 words
saw that his formula for gravity could be adapted to include a new feature known as the cosmological constant. This imbued empty space with an inherent pressure that pushed the universe apart. In other words, the cosmological constant gave rise to a new repulsive force throughout the universe which effectively worked against the gravitational
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on the value given to the constant (which in theory could adopt any arbitrary value). Einstein realised that by carefully selecting the value of the cosmological constant he could exactly counteract conventional gravitational attraction and stop the universe from collapsing. Crucially, this anti-gravity was significant over huge cosmic distances, but negligible
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successes in low gravity (e.g. Earth), 3. succeed where Newton failed in high gravity (e.g. Mercury). Many cosmologists were happy with Einstein’s cosmological constant, because it seemed to do the trick of making general relativity compatible with a static eternal universe. But no one had much of a clue
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about what the cosmological constant actually represented. In some ways it was on a par with Ptolemy’s epicycles, inasmuch as it was an ad hoc tweak that allowed Einstein
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to get the right result. Even Einstein sheepishly admitted that this was the case when he confessed that the cosmological constant was ‘necessary only for the purpose of making a quasi-static distribution of matter’. In other words, it was a fudge that Einstein used to
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get the result that was expected, namely a stable and eternal universe. Einstein also admitted that he found the cosmological constant ugly. Talking of its role in general relativity, he once said that it was ‘gravely detrimental to the formal beauty of the theory’. This was
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are false. Beauty in any context is hard to define, but we all know it when we see it, and when Einstein looked at his cosmological constant he had to admit that it was not very pretty. Nevertheless, he was prepared to sacrifice a degree of beauty in his formula because it
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orthodoxy in a radically different vision of the universe. Having read Einstein’s cosmological paper with relish, Alexander Friedmann would question the role of the cosmological constant and defy the scientific establishment. Born in St Petersburg in 1888, Friedmann grew up amid great political turmoil, and learned to challenge the establishment from
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to cosmology and forge his own model of the universe. While Einstein had started with the assumption of an eternal universe and then added the cosmological constant to make his theory fit expectation, Friedmann adopted the opposite stance. He started with the theory of general relativity in its simplest and most aesthetically
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appealing form—without the cosmological constant—which gave him the freedom to see what sort of universe logically emerged from the theory. This was a typically mathematical approach, for Friedmann was
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came to a climax in 1922, when he published an article in the journal Zeitschrift für Physik. Whereas Einstein had argued for a finely tuned cosmological constant and a finely balanced universe, Friedmann now described how different models of the universe could be created with various values of the
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cosmological constant. Most importantly, he outlined a model of the universe in which the cosmological constant was set to zero. Such a model was effectively based on Einstein’s original formula for gravity, without any
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cosmological constant. With no cosmological constant to counteract gravitational attraction, Friedmann’s model was vulnerable to gravity’s relentless pull. This gave rise to a dynamic and evolving model of the
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it is time to take stock. Einstein had offered two versions of general relativity, one with the cosmological constant and one without. He then created a static model of the universe based on his theory with the cosmological constant, whereas Friedmann had created a model (with three variations) based on a theory without the
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cosmological constant. Of course, there might be many models, but there is only one reality. The question was this—which
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academic post and began to develop his own cosmological models based on Einstein’s equations of general relativity, but largely ignoring the role of the cosmological constant. Over the next two years he rediscovered the models that described an expanding universe, oblivious to the fact that Friedmann had been through the same
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that everybody else considered foolish. Meanwhile, the world focused on Einstein’s static universe—which was also a perfectly legitimate model, although the finely tuned cosmological constant was somewhat contrived. In any case, the static universe was consistent with the prevailing belief in an eternal universe, so any scientific blemishes were overlooked
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, but this attractive force would eventually cause the entire universe to collapse. Because the universe was supposed to be eternal and static, he added the cosmological constant—in effect, a fudge—to his equation in order to simulate a repulsive force that acted over large distances, thereby preventing collapse. Now that the
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universe no longer appeared to be static, Einstein ditched the cosmological constant and returned to his original equation for general relativity. Einstein had always felt uncomfortable about the cosmological constant, having inserted it into his equation only to comply with the establishment view of a static and
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ignored authority. On the single occasion on which he had bowed to peer pressure, he was proved to be wrong. Later he would call the cosmological constant the greatest blunder of his entire life. As he wrote in a letter to Lemaître: ‘Since I have introduced this term I had always a
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in nature.’ Although Einstein was keen to abandon his cosmic fudge factor, cosmologists who still believed in an eternal, static universe were convinced that the cosmological constant was an essential and valid part of general relativity. Even some Big Bang cosmologists had become quite fond of it and were reluctant to lose
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it. By retaining the cosmological constant and varying its value, they could tweak their theoretical models of the Big Bang and modify the universe’s expansion. The cosmological constant represented an anti-gravity effect, so it made the universe expand faster. The value
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and validity of the cosmological constant generated some conflict among the supporters of the Big Bang theory, but Lemaître and Einstein showed
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, it has since been stretched from infrared to microwave wavelengths by the expansion of the universe. The COBE satellite measured variations in the CMB radiation. cosmological constant An extra parameter incorporated by Einstein into the equations of his general theory of relativity when it became clear that his equations implied either a
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430-8; predicted 333-4,336, 430; satellites 453-63, 458, 461,471, 481, 482; variations in 446-62, 452, 461 cosmic-ray physics 158 cosmological constant 148-9, 151-2, 153, 161, 273-4 cosmological principle 146,345; perfect 347 Coulson, Charles 484 creation 180, 261,276,284, 489-90, Table
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,191, 198; and bending of light 130-3, 140-2; and Big Bang 161,273-4,372; constancy of speed of light 103—5, 107; cosmological constant 148—9, 151-3,161,273-4; cosmology 145-9, 167,272-3; E = mc2 formula 298-9, 301; eternal, static model of universe 146
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