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Dark Energy: Accelerating the Universe

Dark Energy: Accelerating the Universe. Eric Linder University of California, Berkeley Lawrence Berkeley National Lab. Our Expanding Universe. Simulation courtesy of Bertschinger & Ma. Discovery! Acceleration. New Frontiers.

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Dark Energy: Accelerating the Universe

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  1. Dark Energy: Accelerating the Universe Eric Linder University of California, Berkeley Lawrence Berkeley National Lab

  2. Our Expanding Universe Simulation courtesy of Bertschinger & Ma

  3. Discovery! Acceleration

  4. New Frontiers Beyond Einstein: What happens when gravity is no longer an attractive force? Scientific American Discovery(SCP,HiZ 1998):70% of the universe acts this way! Fundamentally new physics. Cosmology is the key.

  5. Knop et al. (2003) cf. Tonry et al. (2003) SNLS (Astier et al. 2005) accelerating accelerating decelerating decelerating Cosmic Concordance • Supernovae aloneAccelerating expansion •  > 0 • CMB (plus LSS) •  Flat universe •   > 0 • Any two of SN, CMB, LSS •  Dark energy ~75%

  6. Frontiers of Cosmology Us STScI 95% of the universe is unknown!

  7. Dark Energy Is... Dark Energy Is!!! • 70-75% of the energy density of the universe • Accelerating the expansion, like inflation at 10-35s • Determining the fate of the universe ! 70-75% of the energy density of the universe 95% of the universe unknown! ! Accelerating the expansion, like inflation at 10-35s Repulsive gravity! ! Determining the fate of the universe Fate of the universe! Is this mysterious dark energy the original cosmological constant , a quantum zeropoint sea?

  8. What’s the Matter with Energy? Why not just bring back the cosmological constant ()? When physicists calculate how big  should be, they don’t quite get it right. They are off by a factor of 1,000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000, 000,000,000,000. This is modestly called thefine tuningproblem.

  9. : Ugly Duckling Field Theorist: Vacuum – Lorentz invariant Tab ~ab = diag { -1, 1, 1, 1} p = - Naturally, Evac ~ 1019 GeV E ~ (meV)4 =0? Astrophysicist: Einstein equations – gab  p = - Naturally,  =const= PL = 10120 Today M • Fine Tuning Puzzle – why so small? • Coincidence Puzzle – why now?

  10. Cosmic Coincidence Size=2 Size=1/4 Size=1/2 Size=4 Is this mysterious dark energy the original cosmological constant , a quantum zeropoint sea? Think of the energy in  as the level of the quantum “sea”. At most times in history, matter is either drowned or dry. Dark energy Matter Today

  11. On Beyond ! We need to explore further frontiers in high energy physics, gravitation, and cosmology. New quantum physics?Does nothing weigh something?Einstein’s cosmological constant, Quintessence, M/String theory New gravitational physics? Is nowhere somewhere?Quantum gravity, supergravity, extra dimensions? We need new, highly precise data [Lecture 1] [Lecture 3] [Lecture 2]

  12. Redshifts are changes in scale/position (“velocities”): z=[a(t0)-a(te)]/a(te)  H0t Redshift shifts are changes in changes (“acceleration”): dz/dt0 = [a0-ae]/ae = H0(1+z)-H(z)  -zq0H0 t . . Dark Energy – the Easy Way? Direct detection? (Dark energy in solar system = 3 hours of sunlight). Variations of fundamental constants: lab and accelerator and universe. Direct acceleration? Redshift drift(Sandage 1959; Linder 1991,1997) dz=10-8 over 100 years

  13. What Dark Energy Isn’t Is dark energy related to dark matter? Probably not. DM: clumps around galaxies and clusters DE: smoothly distributed DM: pressureless, dominated by rest mass DE: strongly negative pressure, of order energy density DM: important to evolution of universe since zeq: t=100,000 y DE: important to evolution of universe since t≈7 billion y DM: interacts through gravity and (presumably) weak force DE: interacts only through gravity DM: makes up 20% of total energy density today, 70% at zdec DE: makes up 75% now, negligible amount at zdec

  14. What Dark Energy Isn’t Is dark energy related to inflation? Probably not. Inflation: at energy scale around 1024 eV DE: at energy scale around 10-3 eV [Energy density goes as (scale)4, making the ratio 10108.] Inflation: began at perhaps t≈10-35 s DE: acceleration began at t≈7 billion y Is dark energy related to Casimir energy? Probably not. Casimir: depends on physical boundaries DE: universe has no physical boundaries Casimir: can have positive pressure, depending on boundary geometry DE: negative pressure, universe has no physical boundaries Casimir: detected effect arises from vector field (EM) DE: not a vector field (no charge), maybe scalar field Casimir: dies off rapidly with distance (~d-4) DE: repulsion (tension) increases with distance

  15. Dark Energy Dark energy is likely to be a fundamentally new physical phenomenon.

  16. Acceleration and Dark Energy Einstein says gravitating mass depends on energy-momentum tensor: both energy density and pressurep,as +3p Negative pressure can give negative “mass” Newton’s 2nd law: Acceleration = Force / mass R = -GM/R2 = - (4/3)G  R Einstein/Friedmann equation: a = - (4/3)G (+3p) a Negative pressure can accelerate the expansion .. ..

  17. Negative pressure Relation between and p (equation of state) is crucial: w = p /  Acceleration possible for p < -(1/3) or w < -1/3 What does negative pressure mean? Consider 1st law of thermodynamics: dU = -p dV But for a spring dU = +k xdx or a rubber band dU = +T dl

  18. Vacuum Energy Quantum physics predicts that the very structure of the vacuum should act like springs. Space has a “springiness”, or tension, or vacuum energy with negative pressure. Review -- Einstein: expansion acceleration depends on +3p Thermodynamics: pressure p can be negative Quantum Physics: vacuum energy has negative p Supernova markers can map the expansion history, measure acceleration, detect vacuum energy.

  19. At every point in a trampled field of grass, you can measure the length of the grass and the direction it is lying: a vector g(x).  Theory of Fields Vector fields: Scalar field: At every point in a field of grass, you can measure the height of the grass: a single number or scalar h(x).

  20. Nature of Acceleration • How do we learnwhatit is, not justthatit is? • Longer “lever arm” (higher redshift, more history) • Many more supernovae, more precisely • High accuracy How much dark energy is there? energy density How springy is it? equation of statew How does it vary with time (how stretchy)?w

  21. Scalar Field Theory Scalar field Lagrangian - canonical, minimally coupled L = (1/2)()2 - V() Noether prescription  Energy-momentum tensor T=(2/-g) [ (-g L )/g ] Perfect fluid form (from RW metric) . Energy density  = (1/2)  2 + V() + (1/2)()2 Pressure p = (1/2)  2 - V() - (1/6)()2 .

  22. Scalar Field Equation of State ¨ ˙  + 3H = -dV()/d Equation of state ratio w = p/ Klein-Gordon equation (Lagrange equation of motion) Continuity equation follows KG equation [(1/2) 2] + 6H [(1/2) 2 ] = -V  - V + 3H (+p) = -V d/dln a = -3(+p) = -3 (1+w) . . . . . . .

  23. Equation of State Reconstruction from EOS: (a) =  c exp{ 3 dln a [1+w(z)] } (a) = dln a H-1 sqrt{ (a) [1+w(z)] } V(a) = (1/2) (a) [1-w(z)] K(a) = (1/2) 2 = (1/2) (a) [1+w(z)] .

  24. Equation of State Limits of (canonical) Equations of State: w = (K-V) / (K+V) Potential energy dominates (slow roll) V >> K  w = -1 Kinetic energy dominates (fast roll) K >> V  w = +1 Oscillation about potential minimum (or coherent field, e.g. axion) V = K w = 0

  25. Equation of State Examples of (canonical) Equations of State: d/dln a = -3(+p) = -3 (1+w) = (Energy per particle)(Number of particles) / Volume = E N a-3 Constant w implies ~ a-3(1+w) Matter: E~m~a0, N~a0 w=0 Radiation: E~1/~a-1, N~a0 w=1/3 Curvature energy: E~1/R2~a-2, N~a0 w=-1/3 Cosmological constant: E~V, N ~a0 w=-1 Anisotropic shear: w=+1 Cosmic String network: w=-1/3 ; Domain walls: w=-2/3

  26. Dark Energy Models Scalar fields can roll: fast -- “kination” [Tracking models] slow -- acceleration [Quintessence] steadily -- acceleration deceleration [Linear potential] oscillate -- potential minimum, pseudoscalar, PNGB [V~ n]

  27. Power law potential “Normal” potentials don’t work: V() ~ n have minima (n even), and field just oscillates, leading to EOS w = (n-2)/(n+2) n 0 2 4 ∞ w -1 0 1/3 1

  28. Oscillations K=0 Vmax=  Oscillating field w = (n-2)/(n+2) Take osc. time << H-1 and  constant over osc. 2 = dt 2 / dt = d  / d / = 2 d [1-V/Vmax]1/2 / [1-V/Vmax]-1/2 If V = Vmax( /max)n then w = -1 + 201dx (1-xn)1/2 / 01dx (1-xn)-1/2 = -1 +2n/(n+2) Turner 1983 . . . .

  29. Linear Potential a t Linear potential [Linde 1986] V()=V0+ leads to collapsing universe, can constrain tc curves of 

  30. Tracking fields Can start from wide variety of initial conditions, then join attractor trajectory of tracking behavior. Criterion  = VV/(V)2 > 1, d ln (-1)/dt <<H. However, generally only achieves w0 > -0.7. Successful model requires fast-slow roll.

  31. Dark Energy Models Inverse power law V() ~ -n “SUGRA” V() ~ -n exp(2) Running exponential V() ~ exp[- ()] PNGB or “axion” V() ~ 1+cos(/f) Albrecht-Skordis V() ~ [1+c1 +c22] exp(-) “Tachyon” V() ~ [cosh()-1]n Stochastic V() ~ [1+sin(/f)] exp(-) ...

  32. Equation of State . .   . But, ~ [(1+w)] ~ (1+w) HMp So if 1+w << 1,then  ~ /H << Mp. It is very hard to directly reconstruct the potential. Goldilocks problem:Dark energy is unlike Inflation!  Reconstruction from EOS: (a) =  c exp{ 3 dln a [1+w(z)] } (a) = dln a H-1 sqrt{ (a) [1+w(z)] } V(a) = (1/2) (a) [1-w(z)] K(a) = (1/2)2 = (1/2) (a) [1+w(z)]

  33. Tying HEP to Cosmology ˙ ¨ Klein-Gordon equation  + 3H = -dV()/d w(a) = w0+wa(1-a) Accurate to 3% in EOS back to z=1.7 (vs. 27% for w1). Accurate to 0.2% in distance back to zlss=1100!

  34. Dynamics of Quintessence   ¨ ˙  + 3H = -dV()/d • Equation of motion of scalar field • driven by steepness of potential • slowed by Hubble friction • Broad categorization -- which term dominates: • field rolls but decelerates as dominates energy • field starts frozen by Hubble drag and then rolls • Freezers vs. Thawers

  35. Limits of Quintessence Driven by steepness of scalar potential, Dragged by Hubble expansion. Analysis shows distinct, narrow regions of w-w Caldwell & Linder 2005 Phys.Rev.Letters 95, 141301 Entire “thawing” region looks like <w> = -1±0.05. Need w experiments with  (w) ≈2(1+w).

  36. Fundamental Physics Astrophysics  Cosmology  Field Theory a(t)  Equation of state w(z)  V() V ( ( a(t) ) ) SN CMB LSS The subtle slowing and growth of scales with time – a(t) – map out the cosmic history like tree rings map out the Earth’s climate history. STScI Map the expansion history of the universe

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