PHY326/426:Lecture 19 Dark Energy Finish WIMP signals Evidence for Dark Energy Type Ia Supernovae What is Dark Energy The fate of the Universe The Distance-Redshift relation Recall from lecture 2: The flux and luminosity of an object are related to its luminosity distance by Here is the flux (energy per square metre of detector per second detected on Earth), is the luminosity of the source, and is the luminosity distance, distance measured by assuming that flux falls off as the inverse square of the distance. With this definition of d L, redshift is related to d L by a form of Hubbleʼs law remember this equation (neglecting terms higher order than z 2 ) So how do we know there is Dark Energy It comes from observation that the distance between objects in the Universe is increasing at an accelerating rate This can be measured by observation of Type I supernovae d L vs. z for 0 < z < 5 and different q 0 distance (MPc) expansion rate constant expansion rate da/dt INCREASING with time q0 =-0.2 q0 =0 q0 =0.5 q0 =1 q0 =1.3 redshift z expansion rate decreasing with time
Slope of d L vs z and Connection to Expansion Rate vs Time Objects at smaller z are observed more recently, so their dynamics relates to the expansion of the universe at later times. Objects at smaller z have smaller recession velocity, so the plot is, roughly, a plot of distance of source vs. velocity of source. E.g. if q=-0.2, the rate of increase of recession velocity with distance is greater at later times (smaller redshifts) than earlier times (larger redshifts). Therefore the Universeʼs expansion rate is increasing. If the rate of redshift change with distance is smaller at later times (smaller redshifts) than at earlier times (larger redshifts), the expansion rate is decreasing. 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 distance scales. Type 1A Supernovae Type 1A SN occur when white dwarfs pulling in material from their neighbourhood reach a critical mass and explode. This mechanism is fairly well understood, and since the critical mass should be similar for all of these objects, they should all emit the same amount of light when they explode. Distant supernovae are observable on earth as they are very bright. Therefore, survey the sky for very distant supernovae, measure the energy flux from them. Supernova Cosmology Project, Perlmutter et al. Determining Distances and Redshifts Simultaneously Suppose we donʼt know the absolute luminosity of sources, but we do know that all the sources of a certain type have similar luminosities. Results of Supernova Surveys Since the luminosity is fixed, the distance is proportional to The unknowns q 0 and can be determined by a fit of data from multiple sources having the same luminosity.
Results of Supernova Surveys Dark Mater vs. Dark Energy All Data Agree (ΩM,ΩΛ) = (0.25, 0.75) (0.25, 0.0) (1.0, 0.0). SN CMB CMB+HST ALL Graphs for Type Ia supernovae magnitude residuals relative as a function of redshift relative to various dark matter and dark energy scenarios The best fit is for (ΩM,ΩΛ) = (0.25, 0.75) Lewis & Bridle 2002 Results on Expansion So the supernovae appear a bit too dim at given expansion velocity (red shift) Further away than expected for a normal gravitating Universe How do you get further away in a given time? Universe has been accelerating!! Other arguments, especially careful study of the small irregularities of the temperature in the Cosmic Microwave Background Radiation left over from the Big Bang, confirm the evidence from supernovae Accelerating Universe - confirmed by all tests applied so far. Universe is filled with an even more mysterious Dark Energy, What is Dark Energy? What is this mysterious stuff? It is NOT a form of matter or energy that we have encountered before. Why? because it counteracts the effect of gravity on large scales. The dark energy seems to be some sort of force field (like a magnetic field, only different), that permeates the vacuum, empty space, and that pushes, anti-gravitates! As space expands there is just more vacuum filled with this force field, so the effect is not diluted by the expansion. As Dark Energy Anti-gravitates it cannot be any particle, either normal baryonic (p, n, e) or Dark Matter, that gravitates. Dark Energy force field is not accounted for by any currently known physics. A major challenge to fundamental physics! This means it has a very special equation of state.
Energy and Pressure In the Universe Consider energy density and pressure for conventional gases: An equation of state relates pressure P exerted by a substance on its container to the energy density ε of the substance. What is Needed for a Deccelerating Expansion Rate? This effect is larger at earlier times, when the energy density, and therefore the pressure, is higher. Here w is a number depending on what is in the container. For a non-relativistic ideal gas PV = nkt. kt is the average kinetic energy of the gas particles which is kt = 1 3 mv 2 The expansion rate is increased by the pressure more at earlier times than it is at later times. Therefore the rate of change of the expansion rate with increasing time, and decreasing energy density, is reduced by the presence of a gas of particles with a positive w. This results in an expansion rate that decreases with time, d 2 a(t)/dt 2 <0. What is Needed for a Deccelerating Expansion Rate? A rough explanation: Consider a volume of the universe bounded by some artificial walls that let particles in or out. The volume is comoving with the expansion, so in the absence of a gas exerting pressure, the flux of particles through the walls is zero. Now turn on the equation of state. For relativistic PARTICLES, there is a positive pressure on the walls. This is due to random motions of the particles beyond their motion due to the expansion. The expansion rate will slow as the volume of a fixed particle population increases and the pressure on the walls goes down. What is Needed for an Accelerating Expansion Rate? Now consider a gas which has a negative pressure for positive energy density. P = -!" This results in a net flux of particles IN to the volume. Therefore as the volume increases in size, the number of ʻparticlesʼ in the volume actually goes up. This increase in energy density could be balanced by the size of the volume increasing more rapidly, Put another way, if there is a negative pressure, and we define comoving expansion as expansion keeping pace with the movement of mass and energy, the expansion has to go quicker as time goes on when the dominant component of the Universeʼs
Ideas for Dark Energy and Quintessence So for the expansion rate to increase, the universe must contain something with an equation of state with w < 0. Such material, unknown in nature, is called quintessence, or ʻdark energyʼ. This is one of the great puzzles of modern cosmology. There are many ideas, and nobody knows which is right. The simplest solution is a purely mathematical one, the so-called cosmological constant due to Einstein. The mass energy content of the Universe is described by an energy-momentum tensor - basically a 4x4 matrix of numbers. The energy and pressure go on the diagonal thus: Conclusions on the Universe The overall density can be broken up in to several pieces: Matter density Dark energy / 0.29+/-0.07 of which 0.05 : baryons 0.24 : dark matter Total energy density This implies that the Universeʼs geometry is very flat. quintessence / cosmological constant 0.71+/-0.07 The multitude of names for the right hand component are a testament to the fact that we donʼt really understand what it is. Cosmological Constant Λ? The cosmological constant is added into cosmology in equations of general relativity like this, for a small portion of a large, low density universe: cosmological constant The right hand matrix (-1,1,1,1) is the metric in the absence of curvature, which is OK since we know that the Universe is flat from cosmic background radiation measurements. (ALL BLANK ELEMENTS ZERO) NOTICE that where the components of the pressure appear in the left hand matrix, representing an ordinary gas, the right hand matrix will have negative numbers, which means the cosmological constant term implies negative pressure. Conclusions OF the Universe Why Dark Energy wins at late times If you think of dark energy as a source of energy out of the vacuum, the bigger the volume of spacetime, the more dark energy there is. But if spacetime is full of matter, and then expands, this does not increase the amount of matter, so that as time increases, the dark energy content of the Universe increases, but the matter content stays constant. In terms of densitites, the matter density of the Universe drops as it expands, but the vacuum energy content of the Universe maintains a constant energy density, or at least drops less rapidly than the mass energy density.
Conclusions of the Universe If the acceleration stays constant, the fate is dismal: galaxies will be pulled infinitely far apart, then even small mass, long-lived stars age and die, protons, neutrons and electrons will decay to photons, black holes will evaporate by Hawking Radiation. The result would be an empty Universe filled with dilute radiation. We know so little about the Dark Energy, that it could do other things. It could get stronger, leading to a Big Rip with atoms and the very fabric of space being pulled apart (most physicists think this unlikely) END It could reverse sign and gravitate, leading to the recollapse of the Universe in a Big Crunch. Questions What is q 0 and what values gives us an expansion rate increasing with time?: What assumptions are made in the observations of type Ia SNs that lead to the conclusion that dark energy exists? Use the ideal gas law by volume to show that for relativistic particles Hint: divide the ideal gas law by volume to get