Sunday, December 8, 2013

Dark Energy Part 14

The Universe Is Not Intuitive

I had a lot of trouble visualizing how the universe is evolving and even where we are within it. There are several online sources that tell us something like "It has taken 13.8 billion years for the radiation from the Big Bang to reach us here on Earth." That statement, though true, led me to think of us as out here away from the Big Bang. Sometimes I imagined that we could trace back to a single point somewhere in space where the Big Bang originated. I also thought of the Big Bang as being long over. We are seeing a mere ghost of it in the CMB (cosmic microwave background). All those imaginings turn out to be totally wrong.

When a pinpoint of unimaginably dense energy burst into existence 13.8 billion years ago, there was nothing outside of it - no space, no kind of theoretical framework, no time and no physics (according to most cosmologists and excepting the multiverse theory). 13.8 billion years later, that Big Bang is still occurring and we are inside it. Thermodynamically, we live inside this nearly perfect blackbody that is our universe. When photons decoupled from matter, they moved at light speed in every possible direction, rather than all shooting away from some point source. The universe was filled with dense gamma radiation at first. As the universe expanded it cooled according to thermodynamic laws, and the radiation stretched into X-rays and then eventually into visible light and beyond. I imagine some period of time when the universe glowed violet, then blue and eventually orange and then red. Over time, photons, going in all directions occasionally struck matter, reflecting off it or being absorbed and readmitted. Photon trajectories bent as they passed through the gravity wells of massive objects. Many of them have been travelling through space never interacting with matter at all.

Now the universe is bathed in microwaves - that is why the CMB fills the entire sky and comes to Earth from all directions not just one. The universe, from 380,000 years old until its very end, if it has one, will always be bathed in CMB radiation, although the radiation is many factors less dense than it once was and that density will continue to decrease. The wavelength of the CMB will eventually stretch into ultra-long radio waves.

As CMB photons traveled, their wavelengths were stretched as space itself stretched, and right now space is stretching faster then the speed of light, and that expansion is ever increasing. As space expands, all matter comes along for the ride. The scaffolding for large-scale structures such as super clusters formed when the universe was very young, within pockets of slightly denser energy that were once as tiny as Planck-scale. Now these super clusters are many billions of light years across. Even with all this clustering, matter, overall, is distributed extremely evenly throughout the universe.

Stars and galaxies are moving away from each other and from us at increasing velocity. If the universe were not expanding, we would eventually be able to observe even the most distant stars as their photons eventually reached us, but instead there exists a spherical boundary beyond which we can never observe any event. This boundary corresponds to the outer horizon of the CMB, 93 billion light years across. Imagine viewing a faint star near this horizon. You may be viewing a star that shone almost 13 billion years ago. It is almost certain that it exploded long ago and many new crops of stars have been born and died since, but you will never be able to see those stars. They are likely in a new location altogether thanks to the curved expansion of space and they are red-shifted out of our view, a cosmic red shift that continues to increase. In the distant future our night skies will be darker as distant stars move away from us at increasing speed and their light will not have time to reach us.

An intelligent creature on some distant planet is looking up at its night sky and realizing the same thing, as the stars in its view move away from it at increasing speed just like ours do. That creature is inside the center of the universe just as we are, because there is no center to the universe. The center is everywhere because we are inside the Big Bang. We are the Big Bang.

Saturday, December 7, 2013

Dark Energy Part 13

How To Prove Which Theory for Dark Energy Is Correct?

The existence of this mysterious energy is fairly well established in the scientific world. However, is the constant nature of vacuum energy or a dynamically changing scalar field behind the wheel (or both or neither)? The ultimate fate of the universe hinges on which theory is correct. The cosmological constant suggests that the universe will continue to expand at an ever-increasing rate until it basically freezes to death. The universe will continue to cool as it expands and, eventually, gas clouds will be too diffuse to ignite star formation. Stars will eventually burn out, and black holes will slowly evaporate through Hawking radiation. Even stellar remnants may disappear if the proton itself is unstable. Temperatures will approach a uniform quantum minimal value and no thermodynamic work will be possible.

In the quintessence theory, the rate of expansion of the universe might either slow down or even stop at which point it will begin to collapse as the scalar field dissipates and gravity takes over as the dominant force. Or, it may continue to expand at a rate that may vary with time. Different categories of quintessence theory offer different scalar field dynamics, and therefore, a wide range of possible fates.

In the cosmological constant theory, the energy density of dark energy remains constant throughout time. In quintessence, the energy density of dark energy not only changes with time but it might vary spatially as well. The quintessence scalar field couples to a trace of the energy-momentum tensor, which means it couples gravitationally with matter, so you might expect spatial perturbations to grow in the scalar field because of its interaction with matter as it clusters into galaxies and super clusters, etc. Would these spatial perturbations leave an imprint on the CMB (cosmic microwave background) and on the large-scale structures themselves, one that could be measured and attributed to quintessence? Physical computer models for the different categories of quintessence are being separated into different scenarios for the evolving universe. These tests will rule out some less likely versions of quintessence and they might even rule out the cosmological constant theory as well.

A third and fascinating possibility is that the scalar field of quintessence might simply be a scalar addition to the rank-2 tensor description of general relativity laid out by Einstein, meaning that it is not a new energy field in itself but instead a refinement of the theory of gravity.

To figure out which of these possibilities might be true, NASA planned to launch a future investigation into the nature of dark energy, called the Joint Dark Energy Mission (JDEM), in partnership with the U.S. Department of Energy. This idea was scrapped and rolled into a new project called Wide Field Infrared Survey Telescope (WFIRST), which has top priority. Wikipedia lists its possible launch date at around 2023. The design is based on the JDEM proposal. It will not only attempt to detect the nature of dark energy but it will also search for extra-solar planets (a new field of cosmology that is absolutely exploding right now). A telescope in deep space orbit, shown below as a digital rendering, should be able to measure thousands of Type 1a supernovae every year it operates, as well as very distant galaxies, many of which are far too distant to measure accurately from closer to Earth.

Image courtesy NASA/Goddard Space Flight Center WFIRST Project
WFIRST will use three techniques to try to answer questions about the nature of dark energy - many more Type 1a supernova distances (and with greater precision), more precise measurements of baryon acoustic oscillations, and measurements of weak gravitational lensing. These sets of data will help to paint a picture of what dark energy is doing to the evolution of the universe, and that will help physicists figure out what it is.

Type 1a supernova distances and baryon acoustic oscillations are two lines of evidence that dark energy exists. These were explored in detail in Dark Energy Parts 8, 9 and 10. I didn't mention weak gravitational lensing as evidence because it is not evidence so much as a way to probe the expansion history of the universe, and the way it will do it is very cool.

Gravitational lensing happens when the trajectory of photons bends as it passes near a mass. Spacetime around a mass is curved, so light, propagating through spacetime is bent as it follows that curvature. Many cases of gravitational lensing have been observed, and they offer proof for Einstein's theory of general relativity. Observations of multiple images of a single galaxy, for example, demonstrate gravitational lensing, as shown below in this NASA diagram.

This diagram shows how light from a distant galaxy bends around a massive object in the foreground, perhaps a neutron star or a black hole. The orange arrows show the apparent position of the background galaxy. A duplicate or multiple image can be observed from Earth. The white arrows show the path of light from the true position of the source.

Less often the lens alignment produces a ring-shaped mirage, shown in the NASA image below.

The gravity of a luminous red galaxy is bending the light from a more distant blue galaxy, distorting the image of the blue galaxy into a horseshoe. This image was taken by Hubble's Wide Field Camera 3. WFIRST might use two telescopes similar in design to the Hubble Space Telescope, but with an even wider (and much deeper) field of view. The WFIRST telescope rendering shown far above looks very much like the Hubble telescope, which is still functioning.

Most gravitational lensing is so subtle that it is impossible to detect in a single background source. These cases are called weak gravitational lenses, and this is what the new telescope will focus on. Multiple wide arrays of galaxies will be imaged and statistics will be used to measure two kinds of transformation due to gravitational lensing - convergence and cosmic shear. Convergence increases or decreases the objects image size and shear stretches the object image tangentially around the mass in the foreground that is doing the lensing. Examples are shown in the diagram below right. The solid green circles are the true shape and size of the object while the black outlines show the effects of convergence (top; K) and shear (Re[γ] and Im[γ].

Many galaxies must be observed in order to get statistical results. Galaxies tend to be naturally elliptical so their true shape is difficult to separate from shear effects. Instrumental effects can also smear images slightly. This telescope will be far from Earth's atmosphere so noise that can look like shear and convergence will be eliminated. To observe the effects of dark energy, these observations will be separated into groups of different redshifts. Low redshift groups will only be lensed by relatively close objects and high redshift groups will be lensed by by a wide range of objects. This technique, called cosmic tomography (taking consecutive slices of space), makes it possible to make a 3-dimensional map of the mass distribution in the universe that not only tells researchers how it's distributed today but also how that distribution evolved over time, offering a detailed expansion history of the universe.

This much larger set of very precise observational data will hopefully hint at which kind of dark energy scenario the universe is actually playing out. What will happen in the end? Explore the possibilities in the final article in this series,  Dark Energy Part 14.

Friday, December 6, 2013

Dark Energy Part 12


This name, deriving from ancient Greek, meaning "fifth element" after the four medieval elements of air, water, earth, and fire, is a theory for a new kind of energy field that creates negative pressure. This theory was first proposed in 1998 by R.R. Caldwell, R. Dave and P.J. Steinhardt. Here, quintessence is treated as the fifth factor influencing the universe's evolution, along with baryons, leptons, photons and dark matter.

Like the cosmological constant, this theory must be able to describe the relatively recent shift from slowing expansion to the accelerating expansion of the universe. Unlike the cosmological constant, quintessence is an evolving form of energy with negative pressure derived from the potential and kinetic energy of a quantum field. How these two kinds of energy interact, and the pressure that results from that interaction, may be behind the relatively recent effects of dark energy. The equation of state of quintessence compares its dynamic nature to the constant nature of the cosmological constant. For quintessence, the equation of state (the relationship between variables), w, is equivalent to p/p where p is pressure and p, again, is energy density. For most quintessence models, w is somewhere between 0 and -1. In the cosmological constant, w is always precisely -1.

In most mathematical models, quintessence is the energy density of a scalar field (points in scalar fields have magnitude but no direction) that is slowly rolling downward toward a specific potential energy. Rolling scalar fields, as the CERN (European Organization for Nuclear Research) paper's link tells us, are a central concept in cosmology. "Their dynamics are governed by two main ingredients: the steepness of the potential [] and the equation of state of the background fluid []." Equation of state is a set of values for all the variables of a system, and they all relate to one another. Here, physicists treat space as a perfect fluid. Measurements such as the ratio of pressure to density are often used. In this case, radiation energy density and matter energy density are incorporated into the formulas. In this model, both total energy density and equation of state evolve over time. There are currently several categories of quintessence models in which the dynamics of the scalar field differ. The following description is a general one.

The energy is negative as long as the change is slow enough that the kinetic energy remains less than the potential energy. As the universe evolves, the energy density of radiation (photons) decreases more quickly than matter energy density does, as mentioned in previous articles in this series. The quintessence field has a density that closely tracks, but is less than, the radiation density of the universe until the energy densities of radiation and matter meet up and become temporarily equal to each other. The mathematical expression of this theory has something called an attractor solution built into it and this is key to how its behaviour changes once matter begins to dominate in the universe. An attractor is any set of points toward which a variable (moving according to the rules of the dynamical system it is in) evolves over time. The scalar field slowly rolls downward until an attractor solution is reached. At this point, the field becomes frozen in a sense.

The graph below adapted from a paper called A Quintessential Introduction to Dark Energy from Princeton University helps us to visualize what this means. (this paper is a great introduction to the mathematics behind this theory, and, also, I like the pun in the title). This graph compares the energy densities of matter, radiation and quintessence from the very young universe to almost present time. Notice that the universe starts with a greater radiation energy density than matter energy density, but that picture changes as the universe evolves. This means that both the kinetic energy and potential energy evolve too, and that, in turn,  changes the overall dynamics of the universe. The rolling scalar field describes this dynamical change over time and it has a unique feature in that it becomes frozen at a certain point and from then on begins to have a growing effect on how the universe behaves - it leads to runaway expansion. The mathematics of this theory provides a mechanism in which the dynamics of quintessence can change, becoming a force that dominates and drives the accelerated expansion of the universe.

(Redshift is defined as z + 1 = wavelength observed/wavelength at rest, where redshift is always a positive value and blueshift is a negative value. Stars very close to us, such as the Sun have no redshift so z +1 = 1 (here t = 0 and z = 0) just right of the graph above).

The graph below, redrawn from a CERN paper called Scalar Fields and Cosmological Attractor Solutions offers an explanation for how the dynamics of quintessence changes through the utilization of attractor solutions. For a rolling scalar potential you can pick out up to 5 attractor solutions when you build a mathematical framework of it. This graph is a generic set of solutions. The red line represents a unit circle, x2 + y2 = 1.

You can think of the five regions above as something like physical phase transitions of space. All regions describe what kind of energy state the scalar field is in as it evolves over time. Region 1 represents the very early universe - a situation in which the potential energy is quickly changing into kinetic energy. In region 2, kinetic energy dominates the energy density of the scalar field. In region 3, the field stays fairly constant until the attractor solution is reached. In region 4, the field evolves along the attractor solution (showing the "attraction" aspect of an attractor solution). Here the ratio of kinetic to potential energy remains fairly stable. In region 5, potential energy in the scalar field becomes important to the dynamics of the universe. The field approaches the unit circle (red line above). As the field evolves toward the end, y approaches 1 and x approaches zero. This is where the scalar potential is overtaking the energy density of matter in the universe and the potential evolves into a basically flat, or frozen field. At this point, the scalar field of quintessence is driving the dynamics of the universe. It is expanding at an ever-increasing rate.

Quintessence is like the cosmological constant in that both theories evoke a kind of energy interwoven into space itself. Quintessence differs in that its energy is an evolving energy that is tied very closely to the universe's changing potential and kinetic energy states, whereas the cosmological constant vacuum energy is a constant amount of energy per unit space. As space increases, its energy increases. The following brief 3-minute video by the Science Channel describes where physicists are at in terms of understanding this mysterious phenomenon.

Quintessence theory is a very new one. No one knows if there really is a scalar field driving the runaway expansion of the universe, or whether there is some kind of scalar boson perhaps that mediates it. The idea is mathematically quite elegant at least to me but then again the mathematics behind string theory are wonderfully sewn together too. Neither have observational evidence to back them up. There is going to have to be much more work done (and more precise observation of how objects behave in our universe) before anyone can say with confidence quintessence is real. And if it is, how does it interact with the cosmological constant. Physicists are very confident that there is indeed a non-zero vacuum energy in the universe, but how that energy might play with this kind of scalar field is another question to ponder.

It's possible that dark energy isn't dark energy at all. It might not be about mysterious energy fields in space. The accelerating universe could instead signal something about gravity that general relativity has overlooked. In this case, both dark matter and dark energy could be sign posts to a new frontier in gravity theory. The way to figure out what dark energy really is is to look more closely at how dark energy is affecting the expansion of the universe over time. More precise data about how stars are moving in expanding space is exactly what researchers need to help solve the puzzle of what dark energy is, next in Dark Energy Part 13.

Thursday, December 5, 2013

Dark Energy Part 11

Cosmological Constant Theory

The simplest explanation for dark energy is that it is the cosmological constant. This means that any volume of space, whether it is a perfect vacuum or filled with matter, has an intrinsic fundamental energy associated with it. As the volume increases so does this vacuum energy. It is the energy density of an empty vacuum. This energy has negative pressure, meaning that this force results in expansion, against what you might intuitively think - positive pressure in fluid mechanics makes gases expand. Surprisingly, general relativity can describe both attractive gravity and this repulsive type of force. In fact, Einstein thought that the universe was static and he called upon this repulsive force to counteract gravity, which wants to collapse matter in on itself. He called this force the cosmological constant and latter, upon learning that the universe is expanding, threw the notion out, a rare blunder for an amazing genius, but then not quite. It's back in vogue but for an entirely new reason - to explain why the expansion rate is increasing!

Let's briefly compare the workings of gravity with vacuum energy. Gravity in general relativity doesn't depend just on the distribution of matter in space. It depends on both mass and energy (recall their equivalence). This means that all kinds of energy including photons as well as the momentum of objects and particles determine the gravitational force, in addition to rest mass. And it means both the energy density and the momentum density of space must be calculated. The gravitational force at any point in space can be described in detail using an energy-momentum tensor. I describe what tensors are in the article Gauge Theory, if you are curious about them. This is a rank-2 tensor that encodes the energy density in matter, the energy flux, the momentum density and the momentum flow (pressure) at any point in space. It is a force that is proportional to energy density plus 3 times pressure (G is the gravitational constant and c is the speed of light), shown below to give you a basic idea what the formula looks like.

General relativity tells us that, in the case of vacuum energy, its negative gravitational (repulsive) force at any point is proportional to the sum of the energy density (p) plus three times the pressure (p; pressure measures momentum's flow, and it is in 3 dimensions of space) just like how the gravitational force works. The WMAP data measures dark energy as a positive energy density of about 6 x 10-10 J/m3 (it is this positive energy density that allows for accelerating expansion) WITH negative pressure, and this is where the two forces differ.

Quantum theory tells us that the pressure of dark energy is equal and opposite the energy density at any given point in space. This is sometimes explained by treating space like a gas of particles. In the quantum world, virtual particles and their antiparticles pop in and out of existence all the time. This imparts a certain amount of energy into the system - vacuum energy. Vacuum energy increases as the volume increases, so work must be done to expand the universe's inventory of vacuum energy. Work must go in, in other words. This expenditure of work makes the force repulsive rather than attractive, in contrast with gravity, which can do work - work comes out. Going back to the gas laws, this is what lends vacuum energy its negative pressure.

Now we can describe vacuum energy by using the following simplified equation, which becomes p + 3p = p - 3p.  Pressure (p) is equal and opposite energy density(p)) so we can swap those therms out. This leaves us  -2p, a negative pressure. An analogy is a rubber ball that is inflated past its normal pressure. It will want to explode.

These equations are efforts to try to understand how dark energy works in spacetime. Dark energy does not fit well into our current theoretical framework. Trying to calculate the energy density of dark energy using quantum field theory or general relativity give you either zero or infinity for answers, respectively. Trying to reconcile these theoretical answers with the (very well established) observational measurement of about 6 x 10-10 J/m is a problem that points yet again to the fact that general relativity and quantum mechanics don't yet fit together (and almost every physicist thinks they should - logically, there should be a single unified theoretical framework that describes all behaviours in the universe).

Intense negative pressure was also created very early in the universe's evolution, during cosmic inflation. However, the mechanism there, according to most physicists, seems to be attributed to the fact that the particle field, which was created at that moment, was initially way out of equilibrium.

Quantum vacuum fluctuations (virtual particles popping in and out of existence) suggest that even a perfect vacuum is teaming with energy fluctuations at the quantum level. Normally we would think that this kind of quantum effect would be smoothed out or erased at the macroscopic level, and vacuum energy would even out to zero on large scales, but because vacuum energy is quantized it cannot diminish down to zero - it must have some non-zero lowest possible energy, called zero-point energy.

Is Vacuum Energy Useable?

Gravitational energy is usable so why not vacuum energy? There seems to be a vary large and continuously growing supply of it, right? There is a very real and measurable energy associated with a vacuum, as evidenced by the well-verified Casmir effect illustrated in the diagram below right.

Even a perfect vacuum is filled with various quantum fields, for example, with electromagnetic (EM) waves that cannot be completely eliminated, and they come in all possible wavelengths.

Physicists can measure a tiny suction force created between two very close metal plates in a perfect vacuum where the longest of these quantum waves do not have the physical space required to form. Because some EM waves are eliminated between the plates, that space between them contains less vacuum energy than the space outside them. This (very tiny) unbalanced force pushes (or sucks if you want) the plates closer together. Sometimes people extrapolate from this example to the idea that dark energy is directly creating the suction force. It is not - the force is better described as an imbalance of forces. However, it does prove that even vacuums contain energy fields and  energy fields contain energy, which can be manipulated to do work on a system.

This is also direct evidence of a physical force arising from a quantized field. In this sense, we must think of a vacuum as having an underlying complex structure of some sort that supplies these fields. Many physicists use the analogy that the underlying quantum fields in a vacuum act like a kind of web made up of interconnected vibrating balls. You can think of these balls as the various boson force particles in quantum field theory. The strong, weak and electromagnetic forces can all be described this way. Not gravity - a quantum framework for general relativity doesn't yet exist.

This ball-string arrangement makes each point in space a kind of harmonic oscillator. Each field is quantized so it must also have a lowest possible energy or ground state. It must retain at least a tiny bit of "jiggle" to it. The uncertainty principle requires that this zero-point energy be greater than the minimum of its classical potential energy (which can go down to zero). A fascinating analogy can be drawn for matter. Even at absolute zero, where there is no useable energy in a system (this means that it cannot do any work), there must still be some tiny minimal jiggle of atoms and this is why liquid helium will not freeze, ever (but it will solidify under tremendous pressure). This is one example where you can actually "see" what is usually a sub-microscopic quantum effect.

The Casimir effect is another example. It has only been measured for photons because only that force is measurable at this experimental scale, but in theory, all bosons, including photons, produce an attractive Casimir-type force while fermions (particles of matter) produce a negative or repulsive force (arising from the Pauli exclusion principle).

The Casmir effect has led many people to wonder whether we could harness vacuum energy to do work. DARPA (a U.S. defense research department), for example, launched a $10 million project in 2009 to attempt to harness the energy behind the Casmir effect.

Let's examine the thermodynamics of the Casimir effect a little closer. Potential energy in the form of vacuum energy is converted into kinetic energy - the plates move together if they are free to do so, and heat energy can be created as well if the plates then collide. This line of reasoning is analogous to what happens in free fall. An object's gravitational potential energy is converted into kinetic energy, and then heat is created through friction when the object hits the ground. A problem arises right at the beginning with this potential energy. Is the Casimir effect potential energy coming from the EM field or from vacuum energy? I mentioned previously that work is required to expand the universe's inventory. Is there energy, therefore, available to do work? The majority of physicists consider the idea of harnessing dark energy a non-starter, analogous to the classic perpetual motion machine.

Thermodynamic problems also arise when we think about the expanding universe and the ever-increasing supply of vacuum energy that comes with it. If the universe is an isolated system, it's total energy should be conserved; it should stay the same (this assumes there is no interaction with other universes if they exist).

It might be interesting here to investigate the idea of energy conservation further by revisiting the CMB photons traveling through space in the expanding universe: Imagine this finite number of photons shooting around in all directions. As the volume of space expands, the photons redshift. This means that the energy of each photon (and therefore, the total EM radiation energy) decreases, resulting in a loss in total photon energy over time. Assuming that few of the photons lost energy through interactions with other particles, where did that energy go? I've read some online claims that the energy goes into some unknown quantum field or perhaps into the gravitational field. Perhaps this is a trick question. We observe the photon energy as decreasing because we are looking at the photons from our reference point. If we were moving alongside the photons, they would appear to maintain exactly the same energy they started out with. In fact, it seems to me that neither us nor nor the photons would have experienced any time passing at all, according to special relativity. Could dark energy be an example of a relativistic situation as well? The Casimir experiment would seem to claim otherwise. Nothing there is traveling at relativistic speeds. But then is the Casimir effect showcasing not dark energy but the quantized nature of EM energy?

One last question: Is that unknown field, that some online sources suggest, the vacuum energy field? Or, is it better to simply think of the photon energy as conserved in the sense that a much larger space now heated to 2.73 K (current CMB temperature) is thermodynamically equivalent to a much tinier space that was once heated to 4000 K (recombination epoch temperature)? This is simply the gas pressure-temperature law at work, and it means that no energy is lost when volume is taken into account.

Physicists maintain that the total energy of the universe is conserved, even though it seems that the expansion of space, with its ever-increasing supply of dark energy, messes with the rules a bit. Perhaps it is more accurate to say that quantum mechanics messes with essentially classical thermodynamics laws? Dark energy as the cosmological constant probes the non-zero energy requirement of the quantum uncertainty principle. None-the-less, most physicists claim that vacuum energy does not violate the laws of thermodynamics because it is energy that is not available to do work. However, if you do a quick Google search, you will find many recent published papers online that suggest ways that we could harness vacuum energy. Wikipedia deals with this conundrum briefly. I had fun examining some of them but I too am not convinced (a least as far as I can understand the problem).

Still, does the question for you remain - if dark energy draws from a seemingly inexhaustible reservoir of vacuum energy, does this break the second law of thermodynamics? Does the requirement of not being able to do work hold for you or not? Was my earlier statement that the two pie charts represent identical total mass-energy correct? Is the universe truly an isolated system? Or, do thermodynamic conservation laws fall short of explaining the quantum universe? It seems to me that there is still plenty of room to play with the nature of dark energy itself before we must start rewriting physics. Dark matter, on the other hand (tackled in the previous article) seems far more likely to eventually force a rewrite of gravity, depending on what we see in upcoming collider experiments.

Perhaps all this wrangling isn't necessary. The cosmological constant is not the only contender for dark energy, as we'll see next in Dark Energy Part 12.

Wednesday, December 4, 2013

Dark Energy Part 10

Third Line of Evidence For Dark Energy Comes From An Extensive Galaxy Survey

A third line of evidence comes from the 2011 WiggleZ galaxy survey. The redshifts of over 200,000 galaxies were measured at distances up to 8 billion light years away, going more than halfway back to the Big Bang. This method introduces a new method to measure large distances in space. We already explored the use of Type 1a supernovae as standard candles. You can't use galaxies as standard candles because galaxies evolve. Even spiral galaxies, which might seem similar to one another, vary widely in mass, brightness and overall size, as well as in the size of their halos and central bulges. The light they emit is not consistent. Researchers instead capitalized on the fact that galaxies have a tendency to be spaced about the same distance apart from each other (a little known fact that hints once again at the cosmic microwave background (CMB)). They used regular voids (large areas containing no stars) that are approximately 500 million light years across. The NASA image below compares the use of Type 1a supernovae as standard candles (left) with the use of intergalactic voids as standard rulers (right). Both achieve the same goal - measuring distances in expanding space.

These voids were left behind from baryon acoustic oscillations in the CMB and they can be used as standard rulers to measure distances between the galaxies. These oscillations are described in detail in the Dark Matter article, but let's review them here.

Galaxies tend to form in pairs or clusters separated from each other by approximately 500 million light years (150 megaparsecs). They formed within regularly spaced slightly denser pockets of space left behind by microscopic (quantum-sized) oscillations that occurred when the universe was a mere 380,000 years old. The universe at that time was an extremely dense hot plasma that acted like a fluid. Acoustic oscillations arose from the competition between particles of matter and photons within the fluid plasma. Photons exerted an outward pressure that tended to erase denser pockets, while matter particles are gravitationally attracted to each other so they tended to collapse into denser patches, increasing their density. These two counteracting forces created a spherical oscillation in the plasma, working exactly the same way as sound waves moving through air do, except that this "sound" wave was made of photons and matter particles, whereas a sound wave in air is made of air molecules.

Gravity pulled matter into the denser center of each oscillation. This oscillation is quantum-originated, so it was once quantum-sized, but it grew thanks to the rapid expansion of the universe. As it expanded, matter increasingly collapsed into it. The current pattern of galaxy clusters in the universe is thought to be the leftover frozen signature of not just one oscillation or ripple, but many overlapping ripples, like waves emanating from an object dropped in a pond, except in three dimensions rather than two.

The regular intergalactic distance gives researchers a standard ruler. In the night sky it is measured by something called a preferred angular separation. Taking these angular measurements along with different redshifts of galaxy pairs allows physicists to figure out redshift as a function of cosmic distance.

They were able to show, using a method independent of the Type 1a supernova data, not only that the universe's expansion is accelerating but also when that acceleration began.

A Fourth Line Of Evidence From the Late-time Integrated Sachs-Wolfe Effect

There is also direct evidence for dark energy in the flattening of gravitational wells and hills observed in the CMB. These are the pockets of greater and lesser density I mentioned earlier - the ones formed by the competition between photons and matter particles when the universe was very young. These density wells and hills produced lightly warmer and cooler spots in the CMB (these temperatures are what the WMAP mapped). The reason for these tiny temperature variations is that each photon gains a little energy going into a well (a sort of a gravity assist except that for complex reasons it keeps some of its extra energy) and it loses a little energy passing through a hill. Flattening is caused by the accelerating expansion of space. The wells and hills flattened in the time it took photons to pass through them. Those once-tiny gravitational wells tend to correspond to the large structures we see today, such as galaxies and superclusters. This flattening phenomenon is called the late-time integrated Sachs-Wolfe effect. These kinds of measurements offer a picture of what kind of gravitational environments the photons experienced on their long journey from the point of last scattering to Earth, but they focus especially on the end of the matter-dominated era (when the effect of dark energy begins to take over), hence the use of "late-time" in the name. This effect offers proof for dark energy because accelerating expansion is required to explain the extent of the flattening that occurred. If the universe wasn't expanding at an accelerating rate, the temperature variations in the CMB would be far greater than those observed.

The evidence for dark energy is very good. But none of these observations tell us what dark energy is. We'll explore that next in Dark Energy Part 11.

Tuesday, December 3, 2013

Dark Energy Part 9

Second Line Of Evidence From WMAP Data

WMAP (Wilkinson Microwave Anisotropy Probe) data of the cosmic microwave background (CMB) also lends convincing evidence for dark energy. Anisotropies in the CMB tell us that the universe is flat, like the bottom image in the diagram below. An anisotropy is any directionally dependent property. Two simple examples of this are sunlight going through polarized sunglasses and wood - it's easiest to split along its grain). There are three possible shapes of the universe depending on the ratio between the universe's actual mass/energy density and its critical density. This ratio is called relative density, Ω0. Critical density is the tipping-point density where the universe neither expands nor contracts.

If the relative density Ω0 is greater than 1, the universe would be spherical (top image above). This universe would have greater density than critical density. If Ω is less than 1, the universe would be saddle-shaped (middle image above; it would have less density than critical density). The CMB tells us that the universe's density equals or is very close to the critical density. It is flat.

How does the CMB tell us that the universe is flat? CMB fills the universe. It was very accurately mapped by WMAP, and it shows that there is only a very slight variation in temperature across the sky. The angular scale of these fluctuations depends on the curvature of the universe. The very tiny almost non-existent angular scale of the WMAP data tells us that there is no curvature in the universe and the density of the universe must be very close to its critical density. Ω0 is zero.

The Universe Is Flat . . . Wait A Minute!

How can the universe be flat when we are taught that it is an expanding (three-dimensional) volume of space? And besides that, Einstein's theory of general relativity says that energy/mass curves spacetime. Spacetime does indeed curve, but that doesn't disprove that the large-scale space of the universe is flat.

In general relativity, the geometric curvature is represented by a special tensor called the Riemann tensor. In special relativity, the Riemann tensor is zero and physicists therefore sometimes call Minkowski spacetime, the geometry of spacetime in special relativity, flat. Minkowski spacetime does not allow for the curvature that is required by the metric expansion of space. If one were to calculate the diameter of the universe using Minkowski spacetime, the universe would simply be 13.8 billion light years across, but it is actually much larger than this because space has expanded. The Riemann tensor allows for spacetime expansion curvature.

To understand the curvature of spacetime, imagine that you fly three ships equipped with lasers into outer space and have them arrange themselves an equal distance (ignore the trickiness of distance in an expanding universe) from each other, forming an equilateral triangle by lining up their lasers on each other. An equilateral triangle should always consist of three 60-degree angles adding up to 180 degrees, but in spacetime they might not add up to 180 degrees. Why? Because spacetime can be curved. You can visualize this by imagining an equilateral triangle drawn on a globe. Those angles won't add up to 180 degrees either (the number will be larger), because the triangle you form is curved just like the one in spacetime might be, especially near any significant mass. This curviness is the nature of non-Euclidean (curved) spacetime. Physicists refer to this as the local geometry of the universe. Another term, global geometry, covers the geometry of the entire universe including what extends beyond what we can observe, and in particular, it describes the topology of the universe as a whole. Topology, a purely mathematical description of a shape or space, should not be confused with topography. Topology as a field of study first struck me as something that would be really fun. You get to play around with things like Mobius strips, shown below.

David Benbennick;Wikipedia

This was until I tried to figure out topological space, which is what you need to describe the flatness of the universe. Perhaps you can make head or tails of it. I could not and, as a result, I found the video below called "Hitler Learns Topology" hilarious. Warning: there is a lot of swearing in it.

Topology and local geometry can be different from each other. Our universe has a flat topology but it has curved spacetime. Here, a distinction is made between the observable curved spacetime of the universe and the universe as a whole (not easy to grasp for sure!).

Here is my effort to describe the universe as flat: the topology of the universe is Euclidean, which means that two parallel lines will never meet up. The universe is flat, but not in the sense that a piece of paper is flat. It means instead only that the global geometry of the universe is such that the angles in a triangle will always add up to 180 degrees, and the corners of cubes will always make right angles. You can think of this flatness in the same way that you could curve a flat sheet of paper around a ball. On the paper, you can draw an equilateral triangle with angles that add up to 180 degrees. The universe is four-dimensional so instead of curving a 2-D sheet of paper around a 3-D ball, 3-D space is curved around a 4-D surface of spacetime.

This flatness (the actual shape of the universe) should not be confused with the observable universe, which is a spherical volume of space centered on the observer (Earth) where electromagnetic radiation dating back to photon decoupling (the CMB) can be detected.

The proper distance from the origin of the CMB to Earth is almost 46 billion light years, making the diameter of the observable universe about 93 billion light years across. As mentioned before, it is easy to assume that the CMB should be just 13.8 billion light years away, since that's how long light has been traveling (at light speed). The much greater distance takes into account the metric expansion of space that occurred while the photons traveled through it to get here. Yes, it might seem that light traveled faster than light speed but it did not because space itself expanded - because space itself expanded, Einstein's special relativity remains intact. An "Aside" follows this series of articles in which I tackle how difficult it is for me (and I suspect a lot of us) to visualize the universe and our place in it.

If the universe is flat, then it's total mass/energy density must equal its critical density. The densities of atomic matter and dark matter account for only a third of the critical density. The rest must be made up of another form of energy (dark energy) in order to maintain a flat universe that is in keeping with the WMAP observations. Sure, this stuff is tough slogging at times, but the experience of pure amazement makes it worth the effort. I find it absolutely amazing that the CMB reveals so much information about the evolution and nature of the universe! Next, I will describe two more lines of evidence for dark energy. Altogether, these provide almost rock-solid proof that it exists, in Dark Energy Part 10.