1 1 The Darkness of the Universe Eric Linder Lawrence Berkeley National Laboratory

2 2 The Night Sky is Dark The dark night sky is a profound cosmological observation! The universe is filled with stars emitting photons. Number of stars at distance r goes as r 2 ; Intensity dies as 1/r 2, so total flux received F tot =  dr F(r) N(r) =  0  dr (L/4  r 2 ) (4  nr 2 ) = Ln  0  dr  Why aren’t we cooked?

3 3 The Night Sky is Dark More rigorously: Energy density of light today E =  ti t0 dt L (1+z) -1 If constant comoving luminosity density L, then finite past gives finite limit E < L t 0.

4 4 The Night Sky is Dark Liouville’s Theorem approach: Photon phase space density N = N/d 3 xd 3 p is conserved, so I = N /(A  t)d d  = N 3 Therefore, I -3 is conserved and the surface brightness I 0 = I e (1+z) -4. Looking far enough, every line of sight should end on a star, and so the sky should be as bright as the surface of a star. The answer again is that we can’t look far enough, due to a finite past. [THA 5.3]

5 5 Expanding Universe? What role does the expanding universe play in Olbers’ Paradox? Almost none! I 0 = I e (1+z) -4 dimming arises from any frequency shift, not just expansion. E =  ti t0 dt L (1+z) -1 has little dependence on redshift. Expansion has factor of ~2 effect. So Newton could not have “discovered” the expanding universe. The solution is not expansion in Big Bang cosmology, but the Big Bang itself!

6 6 Expanding Universe? Caveat 1 (CMB): Photons can be absorbed, and reradiated, e.g. IR degradation. For a diffuse glow like the CMB the sky is dark ( E << M p 4 ) because of the expansion. Caveat 2 (Inflation): In an inflationary epoch, 1+z ~ e H(t0-t), we are saved by the redshift, giving a finite energy density E = L /H even for an infinite past.

7 7 What if Our Eyes Saw Dark (Energy)? The night sky is dark in photons, implying a finite past (Big Bang). The sky is bright in  (dark energy density dominates), implying an infinite future. Will this turn out to be as significant a discovery as the Big Bang?

8 8 Acceleration and Particle Physics Key element is whether (aH) -1 = å -1 is increasing or decreasing. I.e. is there acceleration: >0. Also, å~aH~H/T~T/M p for “classical” radiation, but during inflation this redshifts away and quantum particle creation enters. a.. Comoving scale å -1 Time horizon scale Inflation The conformal horizon scale (aH) -1 tells us when a comoving scale (e.g. perturbation mode) leaves or enters the horizon.

9 9 Today’s Inflation To learn about the physics behind dark energy we need to map the expansion history. subscripts label acceleration: R = (1-q)/2 q = -a /å 2 R=1/4 EdS R=1/2 acc R=1 superacc a..

10 Equations of Motion Expansion rate of the universe a(t) ds 2 =  dt 2 +a 2 (t)[dr 2 /(1-kr 2 )+r 2 d  2 ] Friedmann equations (å/a) 2 = H 2 = (8  /3M p 2 ) [  m +   ] /a = -(4  /3M p 2 ) [  m +   +3p  ] Scalar field theory L = (1/2)(    ) 2 - V(  ) a..  + 3H  = -dV(  )/d  ¨˙ 

11 Scalar field equation of state   = (1/2)  2 + V(  ) p  = (1/2)  2 - V(  ).. Equation of state ratio w = p/  Continuity equation follows KG equation d  /dln a = -3(  +p) = -3  (1+w) 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)]

12 Expansion History Suppose we admit our ignorance: H 2 = (8  /3)  m +  H 2 (a) Effective equation of state: w(a) = -1 + (1/3) dln (  H 2 ) / dln a Modifications of the expansion history are equivalent to time variation w(a). Period. Observations that map out expansion history a(t), or w(a), tell us about the fundamental physics of dark energy. Alterations to Friedmann framework  w(a) gravitational extensions or high energy physics

13 Fundamental Physics Astrophysics  Cosmology  Field Theory a(t)  Equation of state w(z)  V(  ) V (  ( a(t) ) ) SN CMB LSS Map the expansion history of the universe 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

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

15 Matter Dark energy Today Size=2 Size=4 Size=1/2Size=1/4 Cosmic Coincidence Is this mysterious dark energy the original cosmological constant  ? Why is the energy scale so much less than M Pl ? [fine tuning] Why is acceleration occuring just now? [coincidence]

16 Type Ia Supernovae Exploding star, briefly as bright as an entire galaxy Characterized by no Hydrogen, but with Silicon Gains mass from companion until undergoes thermonuclear runaway Standard explosion from nuclear physics Insensitive to initial conditions: “Stellar amnesia” Höflich, Gerardy, Linder, & Marion 2003 SCP

17 Standardized Candle Redshift tells us the expansion factor a Time after explosion Brightness Brightness tells us distance away (lookback time t)

18 Images Spectra Redshift & SN Properties Lightcurve & Peak Brightness dataanalysisphysics  M and   Dark Energy Properties At every moment in the explosion event, each individual supernova is “sending” us a rich stream of information about its internal physical state. What makes SN measurement special? Control of systematic uncertainties

19 Looking Back 10 Billion Years To see the most distant supernovae, we must observe from space. A Hubble Deep Field has scanned 1/25 millionth of the sky. This is like meeting 10 people and trying to understand the complexity of the entire population of the US! STScI

20 Dark Energy – The Next Generation SNAP: Supernova/Acceleration Probe Dedicated dark energy probe

21 Design a Space Mission colorfulcolorful wide GOODS HDF 9000  the Hubble Deep Field plus 1/2 Million  HDF deep Redshifts z=0-1.7 Exploring the last 10 billion years 70% of the age of the universe Both optical and infrared wavelengths to see thru dust.

22 Weighing Dark Energy SN Target

23 Exploring Dark Energy First Principles of Cosmology E.V. Linder (Addison- Wesley 1997)

24 Dark Energy Models Interesting models have dark energy: 1)dynamically important, 2)accelerating, 3)not  ~  [(1+w)  ] ~  (1+w) HM p Damped so H ~ V, and timescale is H -1. Therefore  ~ M p. Unless 1+w << 1, then  << M p and very hard to reconstruct potential. . . ..

25 Dark Energy Models “Normal” potentials don’t work: V(  ) ~  n have minima (n even), and field just oscillates, leading to EOS w = (n-2)/(n+2) n024∞ w-101/31

26 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+c 1  +c 2  2 ] exp(- ) “Tachyon” V(  ) ~ [cosh( )-1] n Stochastic V(  ) ~ [1+sin(  /f)] exp(- )...

27 Scalar Field Dynamics The cosmological constant has w=-1=constant. Essentially no other model does. Dynamics in the form of w/H = w = dw/dln a can be detected by cosmological observations. Dynamics also implies spatial inhomogeneities. Scale is given by effective mass m eff =  V˝ This is of order H ~ eV, so clustering difficult on subhorizon scales. Vaguely detectable through full sky CMB-LSS crosscorrelation..

28 Tying HEP to Cosmology Accurate to 3% in EOS back to z=1.7 (vs. 27% for w 1 ). Accurate to 0.2% in distance back to z lss =1100! Klein-Gordon equation  + 3H  = -dV(  )/d  ¨ ˙ Linder Phys.Rev.Lett following Corasaniti & Copeland 2003 w(a) = w 0 +w a (1-a)

29 Growth History Growth rate of density fluctuations g(a) = (  m /  m )/a Poisson equation  2  (a)=4  Ga 2  m = 4  G  m (0) g(a) In matter dominated universe,  m /  m ~ a so g=const and  =const. Photons don’t interact with structure growth: blueshift falling into well matched by redshift climbing out. Integrated Sachs-Wolfe (ISW) effect = 0.

30 Inflation, Structure, and Dark Energy Matter power spectrum P k =  (  m /  m ) 2  ~ k n Scale free (primordially, but then distorted since comoving wavelengths entering horizon in radiation epoch evolve differently - imprint z eq ). Potential power spectrum  2  L ~ L 4  (  m /  m ) 2  L ~ L 4 k 3 P k ~ L 1-n Scale invariant for n=1 (Harrison-Zel’dovich). CMB power spectrum On large scales (low l), Sachs-Wolfe dominates and power l(l+1)C l is flat.

31 Rise and Fall of Matter Domination CMB power spectrum measures n-1 and inflation. Nonzero ISW measures breakdown of matter domination: at early times (radiation) and late times (dark energy). Large scales (low l) not precisely measurable due to cosmic variance. So look for better way to probe decay of gravitational potentials.

32 Gravitational Lensing Gravity bends light… - we can detect dark matter through its gravity, - objects are magnified and distorted, - we can view “CAT scans” of growth of structure

33 Gravitational Lensing Lensing measures the mass of clusters of galaxies. By looking at lensing of sources at different distances (times), we measure the growth of mass. Clusters grow by swallowing more and more galaxies, more mass. Acceleration - stretching space - shuts off growth, by keeping galaxies apart. So by measuring the growth history, lensing can detect the level of acceleration, the amount of dark energy.

34 Supernovae + Weak Lensing Comprehensive: no external priors required! Independent test of flatness to 1-2% Complementary: w 0 to 5%, w to 0.11 (with systematics) Flexible: if systematics allow, can cover deg 2 √ Bernstein, Huterer, Linder, & Takada

35 The world is w(z) Don’t care if it’s braneworld, cardassian, vacuum metamorphosis, chaplygin, etc. Simple, robust parametrization w(a)=w 0 +w a (1-a) Braneworld [DDG] vs. (w 0,w a )=(-0.78,0.32) Vacuum metamorph vs. (w 0,w a )=(-1,-3) Also agree on m(z) to 0.01 mag out to z=2

36 Revealing Physics Time variation w(z) is a critical clue to fundamental physics. Modifications of the expansion history = w(z). But need an underlying theory -  ? beyond Einstein gravity? Growth history and expansion history work together. w 0 =-0.78 w a =0.32 cf. Lue, Scoccimarro, Starkman Phys. Rev. D69 (2004) for braneworld perturbations Linder Phys.Rev. D70,

37 Testing the Framework Extensions to gravitation E.g. scalar-tensor theories: f/2  -  (  )  ;   ;  -V Take linear coupling to Ricci scalar R: f/  = F R Allow nonminimal coupling F=1/(8  G)+  2 R-boost (note R  0 in radiation dominated epoch) gives large basin of attraction: solves fine tuning yet w ≈ -1. [Matarrese,Baccigalupi,Perrotta 2004] But growth of mass fluctuations altered: S  0 since G  1/F.

38 Dark Energy Surprises You’ll be sort of surprised what there is to be found Once you go beyond  and start poking around. -- à la Dr. Seuss, On Beyond Zebra Dark energy is… Dark Smooth on cluster scales Accelerating Maybe not completely! Clumpy in horizon? Maybe not forever! It’s not quite so simple!

39 Heart of Darkness Is dark energy dark – only interacts gravitationally? Self interaction: pseudoscalar quintessence Coupling to matter: Chaplygin gas Leads to 5 th force: limited by lab tests Unify dark energy with dark matter?  Distorts matter power spectrum: ruled out unless within of  Coupling to gravitation: Scalar-tensor theories = Extended quintessence Can clump on subhorizon scales Can “turn on” from nonlinear structure formation?! Higher dimension gravity: Scalaron quintessence Can be written in terms of scalar-tensor and w eff Sandvik et al The horror!

40 The Next Physics The Standard Model gives us commanding knowledge about physics -- 5% of the universe (or 50% of its age). What is dark energy? Will the universe expansion accelerate forever? Does the vacuum decay? Phase transitions? How many dimensions are there? How are quantum physics and gravity unified? What is the fate of the universe? That 5% contains two fundamental forces and 57 elementary particles. What will we learn from the dark sector?! How can we not seek to find out?