Dark Matter and the Universe Topic 7 Dark Energy and the Fate of the Universe What is dark energy and how does it overcome dark matter to determine our fate? ? Contents of Topic 7 Having covered dark matter, the evidence, candidates and the race to identify what it is, we return now to the wider picture of our Universe. In particular, the astonishing discovery, that the Universe is accelerating. This leads to the concept of Dark Energy. In this short Topic we will cover: ‣ Hubble’s Parameter H & redshift in an accelerating Universe. ‣ How observation of an accelerating Universe and H leads us to the notion of Dark Energy. ‣ The evidence for an accelerating Universe from Type Ia Supernovae and other arguments. ‣ Evolution of the Dark Matter vs. Dark Energy balance. ‣ What could Dark Energy be? - the Cosmological Constant and Quintessence. ‣ The ﬁnal fate of our Universe. What is Dark Energy? ‣ Early on in the course we admitted that although the Observable Universe has large amounts of mysterious Dark Matter in fact the bulk of it is comprised of an even more mysterious contribution we call Dark Energy.

‣ So what do we mean by the term Dark Energy and what is the evidence for Dark Energy? composition of the Universe ‣ The notion arises as a result of the startling discovery, made only in the last decade or so, that the distance between objects (say galaxies) in the Universe is growing at an accelerating amount. What is Dark Energy? ‣ This is surprising because our natural assumption would be that the gravitational pull of the all the matter, including the Dark Matter, would eventually be enough to slow down the expansion, either enough to to halt it, or possibly to reverse it completely. ‣ Complete reversal would of course mean the Universe is “bound” and will eventually end in a so called Big Crunch. The observation of an accelerating Universe implies a slow death, an Unbound Universe, leading to a Big Freeze. What is Dark Energy? ‣ Before examining the evidence for an accelerating Universe (it came ﬁrst from observation of Supernovae) we can start by examining the implications of this discovery in terms of what it implies about the Energy Density in the Universe. ‣ A simple way to do this, without too much complex cosmology theory, is to consider again the Hubble Parameter H. H is what we mean when we say “Expansion Rate” of the Universe. But remember the units of H, [km s-1 Mpc-1]. This is not a speed, it’s a Timescale. ‣ This means if H is constant (meaning a constant expansion rate) then the time for the Universe to expand by a certain amount (say double in size) is constant. For instance, if after 10 billion years we see a galaxy at distance X, then in 20 billion years it will 2X away, in 30 billion, 4x and in 4 billion 8x etc. i.e. it’s accelerating away from us, exponentially. What is Dark Energy? ‣ So a constant Expansion Rate, i.e. constant H, implies accelerated motion away from us for individual galaxies or objects. So if we ﬁnd that indeed there is acceleration, as appears to be the case, and hence that H is constant, what does this tell us about the content of the Universe? We can answer this simply as follows: ‣ In Topic 1 we found a simple relationship between H and the energy density of the Universe, namely ρc = 3Ho2/8πG. ‣ This equation was for a particular time, i.e now (the subscript “o” on the H means the time now) and the density here is the critical density, but this is proportional to the actual density. So in general we can say at any time: 8πG H2 ∝ ρ 3 What is Dark Energy? ‣ Now we just said that H is constant. But what about ρ? if the Universe has a ﬁxed amount of mass-energy (all produced in the Big Bang) surely we expect the density ρ of this (the amount per unit volume of space) will decrease with time as the Universe expands. ‣ So the amazing implication of a constant H, due to an accelerating Universe, is that the density is constant and so extra mass-energy must be being created as the Universe expands! It is this extra stuff being created as the Universe expands that we call Dark Energy! ‣ Of course we know that the Mass-Energy of the Universe also contains matter (both Baryons and Dark Matter). The important aspect here is that the Dark Energy doesn’t dilute away as the Universe expands. You simply get more of it. What is Dark Energy? ‣ In other words the dark energy can’t be a set of particles growing less dense as space expands, but instead appears to be a feature of space itself. The Dark Energy Density is a constant throughout both space and time: about one hundred-millionth of an erg per cubic centimetre. It doesn’t dilute away, even as space expands. ‣ In summary the density of Dark Energy is constant, which means the Hubble Parameter H (the so-called Expansion Rate) is constant, which means the distance between objects is growing exponentially, i.e we have an Accelerating Universe, which is what is observed. ‣ To get a fuller understanding of the arguments we would need to go through cosmology theory that is beyond our scope here. But we can note a few interesting issues as follows: Dark Matter vs. Dark Energy (1) It turns out, from Einstein that this also means the Curvature of Spacetime is constant. (2) At the beginning of the Universe the Mass-Energy Content is of course dominated by matter and radiation created in the Big Bang. Dark Energy only starts to play a role as the Universe expands and more is created from the vacuum of space. At some time we would expect the Dark Energy to take over to supply the dominant contribution. (3) Interestingly, this transition from Dark Matter domination to Dark Energy domination is happening in the present epoch (now). Remember Dark Energy contributes ~70% now and Dark Matter plus Baryons ~30%. This apparent fact that we live in a rather special time of transition in the evolution of the Universe, between dark matter domination and dark energy domination causes a lot of discussion amongst cosmologists. Dark Matter vs. Dark Energy ‣ The plot here shows the evolution of the composition of the Universe on a very contracted time scale. Note how we are witness to the transition between Dark Matter Domination and Dark Energy Domination.

In this plot Wm refers to the matter component, WL refers to the dark energy part.

Wm,0 = 0.3 and WL,0 = 0.7 refers to the respective components at the current time. ‣ So does the fact that the transition is happening in the present epoch tell us something important? Anthropic Principle ‣ Some cosmologists argue that the observations we make will naturally have to be compatible with a Universe tuned to support Intelligent Life. If the Universe were not so tuned, then we would not be around to observe it. In this case it is perhaps not surprising that the Universe we see does have a particular set of observed parameters. For instance the particular fundamental physical constants we see, and possibly that we live in this transition period between Dark Matter and Dark Energy, which is a period best suited for life to exist. ‣ This is a philosophical argument called the Anthropic Principle. A belief that it is unremarkable that the Universe has a certain set of parameters and particular physical parameters as anything else would mean we would not be around to see it. Distances and Redshifts Again ‣ So what is the real evidence for Dark Energy, or rather how can we tell that the Universe is accelerating? ‣ The crux of this comes from the equation we saw early in the course relating the Hubble Parameter now to the Redshift z of an object at distance dL.

where q0 is the so called Deceleration Parameter.

‣ If we could determine q0 from this equation, by seeing how the Redshift of on object depends on its distance dL, then we can see if the Universe is accelerating.

‣ The following plot illustrates how q0 effects the relationship between the distance and redshift. The Distance - Redshift Relationship ‣ Note how a negative Deceleration Parameter gives us an expansion rate increasing with time. The Distance - Redshift Relationship ‣ We can note a few points from this plot: (1) Objects at low z are observed more recently, so their motion relates to Universe expansion at later times. Objects at low z have smaller velocity - the plot is, roughly, a plot of distance of source vs. velocity of source. (2) E.g. if q=-0.2, the rate of increase of recession velocity with distance is greater at later times (small z). So the Universe’s expansion rate is increasing. If the rate of redshift change with distance is smaller at later times than at earlier times, the expansion rate would be decreasing. (3) The force of gravity, plus a non-zero density of matter, dark or baryonic, will cause a decrease in the expansion rate with time if gravity is the dominant force at large distances. Distances and Redshifts Again ‣ We can ﬁnd the distance to objects my measuring the Flux we observe on Earth and assuming that ﬂux falls off as the inverse square of the distance, that is: where is the Intrinsic Luminosity of the object ‣ We can write this as:

‣ Unfortunately, if this equation is to allow us to determine q0 from a measurement of the ﬂux and redshift from a single object, we would need to know the absolute luminosity . ‣ It is hard to know the absolute luminosity of a single object. But suppose we have objects of a type that we know always have the same luminosity, wherever they are in the Universe. Then if we ﬁnd the ﬂux and Redshift for a set of these objects we can plot a graph and extract q0 that way. Evidence for Dark Energy ‣ There is no reason why there should be a class of objects which all have the same luminosity. But remarkably such a class has been discovered - the Type Ia Supernovae. ‣ It is observation of these objects in galaxies at lots of different distances, pioneered by Saul Purlmutter in the last decade, that allowed q0 to be determined for the ﬁrst time and showing that indeed the Universe is accelerating because it turns out q0 = -0.2. Saul Purlmutter

‣ So what are Type Ia Supernovae and why do they all have the same luminosity?.. Type Ia Supernova ‣ A Type 1A SN occurs when a White Dwarf pulls in material from its surroundings, reaches a critical mass and explodes. This mechanism is fairly well understood, and since the critical mass should be similar for all such objects, they should all emit the same amount of light when they explode.

Tycho’s Nova, the remnant of a Type Ia supernova ‣ Distant supernovae like this are bright and observable on Earth. Saul Purlmutter and colleagues, using particle physics analysis techniques, pioneered the observations. Results of Supernovae Survey ‣ The ﬁrst results (from Perlmutter’s Nobel Prize winning Supernova Cosmology Project) are shown here as a plot of source Magnitude (ﬂux) vs. Redshift. We see that the best ﬁt to the data indicates q0 = -0.2, an accelerating Universe.

The lower part of the plot is a blow- up of the full plot shown at top left. Dark Energy & Agreement with CMBR ‣ The Supernovae observations provided ﬁrst clear evidence for an Accelerating Universe and hence the notion that the Universe contains of Dark Energy as well as Dark Matter. The result is shown here (green) as ΩΛ vs. Ωmatter with best ﬁt ΩΛ = 0.7, Ωmatter = 0.3. ‣ But what is striking in this plot is the concordance with latest data from CMBR studies (the blue region marked WMAP) and the results from our Dark Matter Surveys (vertical region) that shows Ωmatter = 0.3. ‣ These three very different measurements intersect and agree that ΩΛ = 0.7, Ωmatter = 0.3, a result known as Lambda-CDM (ΛCDM). ΛCDM and Dark Energy ‣ So these results point clearly to a model of the Universe that has become know as the Lamda-CDM (ΛCDM) Model. But what is this mysterious stuff, the Dark Energy? ‣ It is not a form of matter or energy we’ve seen before. Why? because it counteracts gravity. It seems to be some sort of force ﬁeld, that permeates the vacuum, empty space, and pushes, Anti-gravitates! As space expands there is just more vacuum ﬁlled with it, it’s not diluted by the expansion. ‣ As Dark Energy Anti-gravitates it cannot be any particle, either “normal” Baryonic (p, n, e) or Dark Matter. It is not accounted for by any currently known physics and so is a major challenge to fundamental physics! ‣ In cosmology terms it implies a special Equation of State characterised by a Negative Pressure. What could it possibly be due to? We can consider here two possibilities… Cosmological Constant Λ ‣ A popular solution holds that space has Vacuum Energy, an intrinsic, fundamental energy, called the Cosmological Constant Lambda (Λ), which, because E = mc2, we predict would have a gravitational effect. Particle physics predicts such Vacuum Fluctuations already. ‣ Unfortunately, most such theories predict a value for Λ at >10100 to large. No way has be found in particle physics to get the very small value of Λ required by the observations. ‣ One “Anthropic” solution to this would be to envisage Λ taking hugely different values in different parts of the Universe and that we live, and see, a part with a small Λ simply because that is a requirement for life to exist. Quintessence ‣ A second possibility is called Quintessence. This postulates that the acceleration is due to a Dynamical Field that, unlike the cosmological constant, is designed to take different values in time and space. ‣ Relevant ﬁelds are predicted in the Standard Model of Particle Physics, but they tend to predict that they will produce large gravitational effects. Here is a pictorial depiction of a scalar ﬁeld, such as temperature, where the intensity is shown by different colours. ‣ If Quintessence is correct then we may expect to see a variation in the fundamental constants of nature in different parts of the Universe and at different times. There is no evidence for this so far, but this can’t yet be discounted. Conclusions on the Universe ‣ So ﬁnally, the result of all the astonishing work we have covered comes back to a new picture of our Universe, summarised as: Total Energy Density

Which implies that the Universe’s geometry is Flat, with the overall density broken up in to several pieces:

Matter Density Dark Energy / cosmological constant, 0.29+/-0.07 of which quintessence etc 0.05 : Baryons 0.24 : Dark Matter 0.71+/-0.07 ‣ The multitude of names on the right is a testament to the fact that we don’t really understand what Dark Energy is. As for the left, it is most likely that Dark Matter is WIMPs. The Big Freeze ‣ So what will happen to us as the Dark Energy takes over? ‣ Galaxies will be pulled apart. ‣ Even small mass, long- lived stars will age and die. ‣ Even black holes will evaporate by Hawking Radiation. ‣ Protons, neutrons and electrons will decay. ‣ The result will be an empty Universe ﬁlled with dilute radiation. ‣ The end will be a Big Fizzle with atoms and the very fabric of space being pulled apart Hawking Radiation ‣ Even Black Holes can evaporate. This comes from the famous Hawking Radiation. Particle pairs are produced by quantum effects in the vacuum near the Event Horizon. One part of the virtual pair can disappear into the Black Hole but the other escape, allowing a route by which energy can be released from the Black Hole so that it eventually, after a huge time, will evaporate. On that Happy Note

The End Summary of Topic 7 A guide for the exam ‣ We now know that the Universe is expanding at an accelerating rate, this leads to the idea that there is Dark Energy as well as Dark Matter - understand the concept of dark energy and how this ﬁts into our understanding of the composition of the Universe. ‣ Understand the basic arguments from consideration of the Hubble parameter and mass-energy density that leads us to dark energy and how the dark energy/dark matter balance evolves with time. ‣ Know about the evidence for an accelerating Universe form Type Ia Supernovae and other observations. ‣ Know in broad terms about the possibility of a cosmological constant and Quintessence in relation to dark energy. ‣ Know about the term Lambda-CDM. ‣ Understand arguments about the the eventual fate of the Universe including the so-called Big Freeze or Big Crunch. Terms to know from Topic 7 A guide for the exam ‣Observable Universe, Unbound Universe, Big Freeze, Big Crunch ‣Supernovae, Type Ia Supernovae, Hubble Parameter, Intrinsic Luminosity ‣Mass-Energy of the Universe, Dark Energy Density, Accelerating Universe ‣Curvature of Spacetime, Dark Matter Domination, Dark Energy Domination ‣Intelligent Life, Anthropic Principle, Deceleration Parameter, Redshift ‣White Dwarf, Magnitude vs. Redshift, CMBR, Lambda-CDM, ΛCDM ‣Quintessence, Hawking Radiation, Event Horizon, Big Fizzle Questions on Topic 7 to help with exam revision ‣ Brieﬂy explain how it is that a constant value for the Hubble parameter implies the existence of dark energy. ‣ What are the implications of an accelerating Universe for the fate of the Universe? ‣ Measurement of the acceleration of the Universe has come from observations of Type Ia supernovae. State a key assumption made about such events that is required for the results to be reliable. ‣ What is the deceleration parameter in cosmology? ‣ What is meant by the term vacuum energy and how is it relevant to dark energy? ‣ State an essential difference between the idea of Quintessence and that of a cosmological constant as explanations for the dark energy. ‣ What is the Lamda-CDM model of the Universe? ‣ Why is Hawking radiation important when it comes to the ﬁnal fate of the Universe? Equations from Topic 7 Equation reminders for the exam

8πG H2 ∝ ρ 3