- 2975 - COSMOLOGICAL CONSTANT - theory of the universe? One of the most mysterious components in the entire Universe is “dark energy“. It wasn’t supposed to exist. We had assumed that the Universe was a balancing act, with the expansion of the Universe and the gravitational effects of everything within it fighting against one another evenly. The Universe was supposed to be in balance?
-------------- 2975 - COSMOLOGICAL CONSTANT - theory of the universe?
- The Universe is supposed to be in balance? If gravity won, the Universe would re-collapse; if the expansion won, everything would fly away into oblivion. But, when we made the critical observations in the 1990s and beyond, we found that not only is the expansion winning, but the distant galaxies we see speed away from us at faster and faster rates as time goes on. The expansion is accelerating!
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- Is Einstein’s “cosmological constant” of expansion the same as the dark energy that is causing this? Why has, over time, the term “dark energy” replaced the original term “cosmological constant?” Are the two terms identical or not, and why?
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- We now know that a large fraction of galaxies beyond the Milky Way are spiral-shaped in nature, and that all of the spiral nebulae we were considering in the year 1920 are indeed galaxies beyond our own.
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- Back when the 1900’s when Einstein was working on a theory of gravity to replace to supersede Newton’s law of universal gravitation, we didn’t know very much about the Universe. We did not think about it expanding?
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- We did not know that the spirals and ellipticals nebulae were galaxies all unto themselves. In fact, that was only the second-most popular idea; the leading idea of the day was that they were entities perhaps proto-stars in the process of forming contained within the Milky Way, which itself comprised the entire Universe of the day.
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- Einstein was looking for a theory of gravity that could be applied to anything and everything that existed, and that included the known Universe as a whole.
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- The gravitational behavior of the Earth around the Sun is not due to an invisible gravitational pull, but is better described by the Earth falling freely through curved space dominated by the Sun. The shortest distance between two points isn’t a straight line, but rather a “geodesic“ which is a curved line that’s defined by the gravitational deformation of “spacetime“.
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- The problem became apparent when Einstein succeeded in formulating his theoretical equation for General Relativity. Instead of being based on masses exerting forces on one another infinitely fast across infinite distances, Einstein’s conception was vastly different.
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- First he said because space and time were relative for each and every observer, not absolute, the theory needed to give identical predictions for all observers. Physicists call this “relativistically invariant.” That meant instead of separate notions of space and time, they needed to be woven together into a four-dimensional fabric called spacetime.
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- And instead of propagating at infinite speeds, gravitational effects were limited by the speed of gravity, which in Einstein’s theory equals the speed of light, 186,282 miles per second.
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- The key advance that Einstein made was that, instead of masses pulling on each other, gravity worked by both matter and energy curving the fabric of spacetime. That curved spacetime, in turn, then dictated how matter and energy moved through it.
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- At each instant in time, the matter and energy in the Universe tells spacetime how to curve, the curved spacetime tells matter how to move, and when it does, the matter and energy moves a tiny bit and the spacetime curvature changes. And then, when the next instant arrives, the same equations of General Relativity tell both the matter and energy and the spacetime curvature how to evolve into the future.
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- On one side of the equation Einstein had all the matter and energy in the Universe, and, the other side of the equals sign in the equation he had the curvature of spacetime. Whatever the equations predict should tell you what happens next.
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- When Einstein solved these equations a large distance away from a small mass, he got Newton’s law of universal gravitation back. When he got closer to the mass, he started to get corrections, which both explained the orbit of Mercury and predicted that starlight passing near the Sun during a total solar eclipse would be deflected. This was how General Relativity was first validated when put to the test.
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- But there was another problem that arose in a different situation. If we assumed that the Universe was filled roughly evenly with matter, we could solve that scenario. What Einstein discovered was disconcerting, the Universe was unstable. If it began in a stationary spacetime, the Universe would collapse in on itself. So Einstein, to fix this, invented a “cosmological constant” to get the universe back into balance.
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- In a Universe that isn’t expanding, you can fill it with stationary matter in any configuration you like, but it will always collapse down to a blackhole. Such a Universe is unstable in the context of Einstein’s gravity, and must be expanding to be stable.
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- To understand where the idea of a cosmological constant comes from there’s a very powerful mathematical tool that we use all the time in physics, it is called a differential equation.
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- Something as simple as Newton’s “F = ma” is a differential equation. Force equals mass times acceleration. All it means is that this differential equation tells you how something we will have in the next moment, and then, once that moment has elapsed, you can put those new figures back into the same equation, and it will go on to tell you what happens in the next moment. This is the basis of Calculus.
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- For example, a differential equation can tell you what happens to a ball rolling down a hill on the Earth. It tells you what path it will take, how it will accelerate, and how its position will change at every moment in time. Just by solving the differential equation describing the ball rolling down the hill, you can know precisely what trajectory it will take.
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- The differential equation tells you almost everything you’d want to know about the ball rolling down the hill, but there’s one thing it can’t tell you: how high the base level of the ground is. You have no way of knowing whether you’re on a hill atop a plateau, on a hill that ends at sea level, or on a hill that ends in a hollowed-out volcanic crater. An identical hill at all three elevations will be described by the exact same differential equation.
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- When we see something like a ball balanced precariously atop a hill, this appears to be what we call a finely-tuned state, or a state of “unstable equilibrium“. A much more stable position is for the ball to be down somewhere at the bottom of the valley. But is the valley at zero, or some non-zero positive or negative value? The mathematics of a ball rolling down the hill is identical up to this additive “constant” to reach equilibrium.
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- That same problem shows up in calculus when you first learn how to do an indefinite integral; anyone who’s taken calculus will remember the infamous “plus C” that you have to add at the end. You always have to add the constant “c” because when you integrate it disappears.
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- Well, Einstein’s General Relativity isn’t just one differential equation, but a matrix of 16 differential equations, related in such a way that 10 of them are independent of one another.
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- But to each of those differential equations, you can add a “constant” in a particular way. This became known as the “cosmological constant“. It is the only thing you can add to General Relativity that won’t fundamentally alter the nature of Einstein’s theory.
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- Einstein put a cosmological constant into his theory not because it was allowed, but because, for him, it was preferred. Without adding a cosmological constant in, his equations predicted that the Universe should either be expanding or contracting, something he thought clearly wasn’t happening.
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- Instead of going with what the equations said, Einstein threw the cosmological constant in there in order to “fix” what appeared to be an otherwise broken situation. If he had listened to the equations, he could have predicted the expanding Universe, not the stationary one.
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- Instead, the work of others would have to overturn Einstein’s prejudicial choices, with Einstein himself only abandoning the cosmological constant in the 1930s, well after the expanding Universe had been observationally established using the Hubble telescope.
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- While matter (both normal and dark) and radiation become less dense as the Universe expands owing to its increasing volume, dark energy, and also the field energy during inflation, is a form of energy inherent to space itself. As new space gets created in the expanding Universe, the dark energy “density’ remains constant.
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- The cosmological constant is unlike the types of energy we know of otherwise. When you have matter in the Universe, you have a fixed number of particles. As the Universe expands, the number of particles stays the same, so the density goes down over time.
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- With radiation, not only are the number of particles fixed, but as the radiation travels through the expanding Universe, its wavelength stretches relative to an observer that will someday receive it: its density goes down, and each individual quantum also loses energy with time.
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- But for a cosmological constant, it’s a constant form of energy that’s intrinsic to space.
Various components of and contributors to the Universe’s energy density, and when they might dominate. Note that radiation is dominant over matter for roughly the first 9,000 years, then matter dominates, and finally, a cosmological constant emerges.
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- However, dark energy may not be a cosmological constant, exactly. If we extrapolate back in time to when the Universe was younger, hotter, denser, and smaller the cosmological constant wouldn’t have been noticeable. It would have been swamped by the much larger effects of matter and radiation early on.
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- Only after the Universe has expanded and cooled so that the matter and radiation density drops to a low enough value can the cosmological constant finally appear.
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- Dark energy, might turn out to be a cosmological constant. when we take all of the observations we have so far, it appears that dark energy is consistent with being a cosmological constant, as the way the expansion rate changes over time agrees, within the uncertainties, with what a cosmological constant would be responsible for.
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- But there are uncertainties, and dark energy could be:
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------------------------ increasing or decreasing in strength over time,
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------------------------ changing in energy density, unlike a cosmological constant,
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------------------------ evolving in a novel, complicated fashion we do not understand
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- Although we have constraints on how much dark energy could be evolving by over the past 6 billion years or so, we cannot definitively say it’s a ‘constant‘.
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- While the energy densities of matter, radiation, and dark energy are very well known, there is still plenty of wiggle room in the equation of state of dark energy. It could be a constant, but it could increase or decrease in strength over time as well.
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- Large data sets are the key, as is sampling the Universe at a wide variety of distances, as it’s the way the light evolves as it travels through the expanding Universe that allows us to determine how the expansion rate has changed over time.
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- By the end of the 2020s, we’ll have an enormous and comprehensive ground-based survey of the Universe thanks to the “Vera C. Rubin observatory“, which will supersede everything that surveys like “Pan-STARRS” and the “Sloan Digital Sky Survey” have done.
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- We’ll have an enormous suite of space-based data thanks to the “ESA’s Euclid observatory” and NASA’s “Nancy Roman telescope“, which will see more than 50 times as much Universe as Hubble presently sees.
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- With all of this novel data, we should be able to determine whether dark energy is truly identical to what the very specific “cosmological constant” predicts, or whether it varies in any way at all.
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- We don’t know how to calculate the zero-point energy of empty space in quantum field theory, and that contributes to the Universe in exactly the same fashion as a cosmological constant would as well. When we make our observations, they’re all consistent with dark energy being a cosmological constant, with no need for anything more complicated.
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- But that underscores exactly why it’s so vitally important to make these novel measurements. If we didn’t bother to measure the Universe in a careful, precise, intricate fashion, we’d never have discovered the need for Einstein’s relativity in the first place.
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- We never would have discovered quantum physics, nor would we have conducted most of the Nobel-winning research that’s driven society forward over the 20th and 21st centuries. 10 years from now, we’ll have the data to know whether dark energy differs from a cosmological constant by as little as 1%.
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- The viewing area of Hubble telescope as compared to the area that the “Nancy Roman telescope” (formerly WFIRST) will be able to view, at the same depth, in the same amount of time. Its wide-field view will allow us to capture a greater number of distant supernovae than ever before, and will enable us to perform deep, wide surveys of galaxies on cosmic scales never probed before.
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- If dark energy varies by more than 1% from a cosmological constant, we’ll know in under a decade. Stay tuned, you still have a lot more to learn.
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--------------------------------- Other reviews available:
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- 2799 - - COSMOLOGICAL PRINCIPLE - a homogeneous universe? Astronomers “ assume” the Universe is homogeneous. That means on the grandest scales the universe is the same everywhere. From the dictionary something homogeneous is composed of parts or elements that are all the same, having a common property throughout.
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- 2797 - COSMOLOGICAL CONSTANT - expanding the Universe? The Universe is not only expanding its expansion is accelerating at an ever faster rate. Now, science is resurrecting the cosmological constant in order to use Einstein’s equations to explain an accelerating expansion that began 5 billion years ago.
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- 2428 - COSMLOGICAL CONSTANT - - The Cosmological Constant was invented by Albert Einstein. When he was thinking about gravity and the birth of the Universe, he could not see how , if gravity were the only force working over long distances, the Universe would not stop expanding and begin contracting into a “ Big Crunch.
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- 1006 “ Is Time Slowing Down?” for more analysis on this assumption. It gets even weirder.
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January 12, 2021 COSMOLOGICAL CONSTANT 2975
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