Course on Dark Energy Cosmology at the Beach

Course on Dark Energy Cosmology at the Beach 2009 Eric Linder University of California, Berkeley Lawrence Berkeley National Lab JDEM constraints 11

Outline Lecture 1: Dark Energy in Space The panoply of observations Lecture 2: Dark Energy in Theory The garden of models Lecture 3: Dark Energy in your Computer The array of tools – Don’t try this at home! 22

Nature of Acceleration Is dark energy static? Einstein’s cosmological constant . How do we learn what it is, not just that it is? Is dark energy dynamic? A new, time- and spacevarying field. How much dark energy is there? energy density How springy/stretchy is it? equation of state w, w 33

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. This is modestly called the fine tuning problem. 44

Cosmic Coincidence Why not just settle for a cosmological constant ? We cannot calculate the vacuum energy to within 10120. 90 Butyears it gets Thinktoofunderstand the energywhy in For weworse: have tried 120 the asatthe level quantum At would most times is least 10 of times smaller“sea”. than we expect history, matter is either drowned or dry. –inand failed. We know there was an epoch of time varying vacuum once – inflation. Dark energy Matter Size=1/4 Size=1/2 Today Size=2 Size=4 55

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, String theory New gravitational physics? Is nowhere somewhere? Quantum gravity, supergravity, extra dimensions? We need new, highly precise data 66

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 77

Scalar Field Equation of State Equation of state ratio w = p/ Klein-Gordon equation (Lagrange equation of motion) ¨ + 3 H ˙ = -d. V( )/d Continuity equation follows KG equation. . [(1/2) 2] + 6 H [(1/2) 2 ] = -V. . . - V + 3 H ( +p) = -V d /dln a = -3( +p) = -3 (1+w) 88

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 99

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)] . 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! 10 10

Dynamics of Quintessence Equation of motion of scalar field ¨ + 3 H ˙ = -d. V( )/d • 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 11 11

Limits of Quintessence. 2 /2 - V( ) w =. 2 /2 + V( ) Distinct, narrow regions of w-w Caldwell & Linder 2005 PRL 95, 141301 Entire “thawing” region looks like <w> = -1 ± 0. 05. Need w experiments with (w ) ≈ 2(1+w). 12 12

Calibrating Dark Energy Models have a diversity of behavior, within thawing and freezing. But we can calibrate w by “stretching” it: w w (a )/ a. Calibrated parameters w 0, wa. de Putter & Linder JCAP 0808. 0189 The two parameters w 0, wa achieve 10 -3 level accuracy on observables d(z), H(z). This is from physics (Linder 2003). has nothing to do with a Taylor 13 w(a)=w 0+wa(1 -a) Itexpansion. 13

Latest Results for w Systematics already dominate error budget We do not know w(z) = -1 or what dark energy was doing at z>1. Kowalski et al. 2008, Ap. J [ar. Xiv: 0804. 4142] 14 14

Beyond Lambda Compare current data (SN+CMB+BAO) vs. 10 dark energy models. Choose “motivated” models widely covering Beyond physics. Includes thawing, freezing, phase transition, mod. GR, geometric. Most models have limit approaching but two don’t. Rubin et al. 2008, Ap. J [ar. Xiv: 0807. 1108] 15 15

Doomsday Model First dark energy model - Linde 1986 V( ) = V 0 + V 0 ( - 0) Linear potential (also see Weinber g 2008) 2 parameters - m and w 0 or tdoom or V 0 Rolls down potential to negative density and universe collapses in finite time. 16 16

DGP Braneworld 2 parameters - m and k or bw or rc H 2=(8 G/3) m+H/rc 17 17

Beyond Lambda While is consistent with data, many varieties of physics are also. (2 models do better than . ) Improvements in systematics will have large impact - e. g. Braneworld disfavored at 2=+15 if statistical errors only. Uniform data set / analysis key, as is next generation ability to see w. Apart from testing “exotic cosmologies”, such comparisons are useful because model variety includes sensitivity to systematics that don’t “look like” . No indication of any such systematics. Diversity highlights need for physical priors before model selection useful. 18 18

Beyond Scalar Fields 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) Suppose we admit our ignorance: H 2 = (8 /3) m + H 2(a) gravitational extensions or high energy physics 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. 19 19

Gravity Beyond 4 D z=3 z=2 =1/2 =1 (BW) z=1 DGP Braneworld, and H mods, obey freezer dynamics in w-w Can reproduce expansion or growth with quintessence, but not both. 20 20

Physics of Growth Perturb the acceleration equation by which conserves mass This determines growth of density inhomogeneities = / Fitting function Peebles 1980 (pre-DM!) Generalization Growth index = 0. 55+0. 05[1+w(z=1)] [Linder 2005, Linder & Cahn 2007] Accurate to 10 -3 level for dark energy and can describe deviations from Einstein gravity growth (as long as usual matter domination at high z). 21 21

Physics of Growth g(a)=( / )/a depends purely on the expansion history H(z) -- and gravity theory. 0 Expansion effects via w(z), but separate effects of gravity on growth. g(a) = exp { 0 ad ln a [ m(a) -1] } Linder 2005 Growth index is valid parameter to describe modified gravity. Accurate to 0. 1% in numerics. Similar to Peebles 1980 ( =0. 6) and Wang & Steinhardt 1998 (constant w). 22 22

Growth Beyond Gravitational growth index is nearly constant, i. e. single parameter (not function) to describe growth separately from expansion effects. Derivable from 1 st principles, even for modified gravity, accurate to 0. 1% in growth. Minimal Modified Gravity (aka Beyond the Standard Model 2) uses simultaneous fit to expansion and growth { m, w 0, wa, }, as a benchmark model to explore the accelerating universe (cf. m. SUGRA for dark matter). 23 23

The Nature of Gravity To test Einstein gravity, we need growth and expansion. Tension between distance and LSS mass growth reveals deviations from GR. Keep expansion history as w(z), growth deviation from expansion (mod. GR) by . Fit both simultaneously. Bias: gives deviations in growth from GR Huterer & Linder 2006 24 24

Violating Matter Domination Gravitational growth index depended on early matter domination. Need calibration parameter for growth, just like for SN (low z) and BAO (high z) distances. g(a) = g* exp { 0 ad ln a [ m(a) -1] } Linder 2009 0901. 0918 g* is nearly constant, single parameter, handles early time deviations: mod. GR, early DE, early acceleration. Separate from , w; accurate to 0. 1%. Beyond the Standard Model 3 simultaneous fit to { m, w 0, wa, , g*}. Next generation data can test ( e)=0. 005, Gearly/G=1. 4%, ln a=1. 7%. 25 25

Paths to Testing Gravity Alternate approaches: Solve for metric potentials , [e. g. Hu & Sawicki 2007] or parametrize / -1 (PPN) [e. g. Caldwell, Cooray, Melchiorri 2007; Jain & Zhang 2007; Zhang, Bean, Liguori, Dodelson 2007; Amendola, Kunz, Sapone 2007] . Test by spectroscopic vs. imaging surveys. Blue (dynamics) Red (lensing/ISW) - Galaxies Galaxy Clusters Linear regime LSS Jain & Zhang 2007 26 26

Dark Energy Surprises Dark energy is… • Dark Maybe not completely! • Smooth on cluster scales Clumpy in horizon? • Accelerating Maybe not forever! It’s not quite so simple! There is still much theoretical research needed! Research is what I'm doing when I don't know what I'm doing. - Wernher von Braun 27 27

Finding Our Way in the Dark energy is a completely unknown animal. Not completely dark? [coupling to (dark) matter, to itself] Not energy? [modified gravity -- physics, not physical] Track record: Inner solar system motions General Relativity Outer solar system motions Neptune Galaxy rotation curves Dark Matter Moral: Given the vast uncertainties, go for the most unambiguous insight. 28 28

Clean Physics What could go wrong? Potentials , ; anisotropic stress s ; gravitational strength G(k, t) ; sound speed cs ; coupling . SN distances come from the FRW metric. Period. Lensing distances depend on deflection law (gravity) even if separate mass (gravity) -- ( - ), cs, s, G(k, t) BAO depends on standard CDM (matter perturbations being blind to DE). -- ( + ), cs, , s, G(k, t) What could go right? Ditto. “Yesterday’s sensation is Today’s calibration and Tomorrow’s background. ” --Feynman 29 29

END Lecture 2 Lecture 1: Dark Energy in Space The panoply of observations Lecture 2: Dark Energy in Theory The garden of models Lecture 3: Dark Energy in your Computer The array of tools – Don’t try this at home! For more dark energy theory resources, see Dynamics of Dark Energy http: //arxiv. org/abs/astro-ph/06043057 (Copeland, Sami, Tsujikawa 2006) Dynamics of Quintessence, Quintessence of Dynamics http: //arxiv. org/abs/0704. 2064 (Linder 2007) and the references cited therein. 30 30