! 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 #c = 3Ho2/8$G. " 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 #? if the Universe has a fixed amount of mass-energy (all produced in the Big Bang) surely we expect the density # 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 .