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Could Dark Energy be novel matter or modified gravity?

Could Dark Energy be novel matter or modified gravity?. Rachel Bean Cornell University. Modern (20th century) Cosmology. Observations. Theory. Einstein. Hubble. Modern (20th century) Cosmology. Philosophy. As we know, There are known knowns . There are things we know we know.

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Could Dark Energy be novel matter or modified gravity?

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  1. Could Dark Energy be novel matter or modified gravity? Rachel Bean Cornell University 1/46

  2. Modern (20th century) Cosmology Observations Theory Einstein Hubble 2/46

  3. Modern (20th century) Cosmology Philosophy As we know, There are known knowns. There are things we know we know. We also know There are known unknowns. That is to say We know there are some things We do not know. But there are also unknown unknowns, The ones we don't know We don't know. —Feb. 12, 2002, Department of Defense news briefing 3/46

  4. Overview The `known knowns’ • kinematical acceleration The ‘known unknowns’ • theoretical approaches to dark energy Can we know the known unknowns? • Observational tests for dark energy 4/46

  5. Expansion today • Observe a cosmological redshift <-> expansion rate and acceleration • Luminosity distance F = L/4dL2 a(t) today t Hubble factor Deceleration parameter dL 5/46

  6. Hubble’s law: true to even larger distances Observations of distant Supernovae 1000 Velocity (km/sec) 500 Hubble 1929 0 0 6 million 3 million 0 Distance (lightyears) Velocity (km/sec) Riess 1996 0 0 300 1200 1500 900 600 Distance (millions of lightyears) 6/46

  7. In this model, the universe will always look the same, and had no beginning The universe is expanding but new matter is being created all the time (from nothing!). Universe is expanding and is always changing, matter becomes less dense & cooler Universe had a hot and incredibly small beginning: “The Hot Big Bang” Two alternative explanations for the expanding universe vs. Big-Bang Model Steady State Model 7/46

  8. Which theory was correct? Penzias & Wilson in NJ in 1964 observed electromagnetic radiation from all directions in the sky, all at the same temperature, 2.7 Kelvin. What was causing it? Pigeons? Primordial radiation? 8/46

  9. z evolution of luminosity distance of Supernovae in HST/Goods survey z Evidence of deceleration followed by recent acceleration Riess et al 2004 9/46

  10. Overview The `known knowns’ • kinematical acceleration The ‘known unknowns’ • theoretical approaches to dark energy Can we know the known unknowns? • Observational tests for dark energy 10/46

  11. Observations have driven key theoretical developments 1000 Velocity (km/sec) 500 0 0 Hubble 1929 2 0 1 Distance (Mpc) Cosmic microwave background Galaxy outer rotation velocities An accelerating universe An expanding universe Hot Big Bang Dark matter General relativity Applied to the cosmos Dark energy But also create many unanswered questions in themselves! What happened right at the beginning? What is dark matter? Can we detect the dark matter in ground based experiments? What is dark energy? 11/46

  12. Gmn = 8p G Tmn c4 Einstein’s description of the cosmos • On the largest scales the universe is controlled by gravity. • Our best description of gravity is GR, as formulated by Einstein: Stress-Energy Tensor: Evolution of matter density and pressure Einstein’s Tensor: Evolution of space and time Matter tells space how to bend/expand Space tells matter how to move Matter makes the universe expand 12/46

  13. Friedmann-Lemaitre-Robertson-Walker Universe • The CMB shows that the universe is homogeneous and isotropic • FLRW applies Einstein’s equations to this simplified case • Described by single number, the size of the universe, a(t) • Acceleration possible only if dominant matter has negative pressure, w<-1/3 Friedmann 13/46

  14. z evolution of luminosity distance of Supernovae in HST/Goods survey z Riess et al 2004 Evidence of deceleration followed by recent acceleration 14/46

  15. Einstein’s `Biggest Blunder’? • Prior to Hubble’s observations, scientists believed the universe was static • Einstein added in a fudge factor to his equations, called the “cosmological constant” to enable a static universe. • Later when Hubble’s discovery of expansion was made, Einstein is said to have called the cosmological constant “my biggest blunder”. 15/46

  16. Current conclusions • Observations from supernovae, cosmic microwave background and large scale structure all give a remarkably consistent picture • However, this picture is dumbfounding since we do not understand 96% of it! w=-1 w~0 16/46

  17. The key dark energy questions • How do we modify Einstein’s Field Equations to explain acceleration? Adjustment to gravity? Adjustment to matter? Cosmological constant “”? • - Non-minimal couplings to gravity? • Higher dimensional gravity? • Effects of anisotropy and inhomogeneity • “Vacuum energy” left over from early phase transitions? • Holographic? • Anthropic? • -An ‘exotic’, dynamical matter component “Quintessence”? • ‘Unified Dark Matter’? 17/46

  18. Why so small? UV divergences are the source of a dark energyfine-tuningproblem The cut off scale would have to be way below the scales currently in agreement with QFT (Casimir effect, Lamb shift) Why now? Coincidence problem Any later  still negligible, we would infer a pure matter universe Any earlier  chronically affects structure formation; we wouldn’t be here Inevitably led to anthropic arguments At most basic predict /m<125 e+ e-  - The problems with it = ? a) QFT = ∞? b) regularized at the Planck scale = 1076 GeV4? c) regularized at the QCD scale = 10-3 GeV4? d) 0 until SUSY breaking then = 1 GeV4? e) all of the above = 10 -47 GeV4? f) none of the above = 10 -47 GeV4? g) none of the above = 0 ? Transition to dark energy domination 18/46

  19. Scalar fx,t - spin 0 particle (e.g Higgs) Accelerative expansion when potentialdominates Scalingpotentials Evolve as dominant background matter Need corrections to create eternal or transient acceleration Tracker potentials Insensitive to initial conditions Tackling the fine-tuning problem . Scaling potentials Wetterich 1988, Ferreira & Joyce 1998 Tracker potentials Ratra & Peebles 1988 Potential V(f) Wang, Steinhardt, Zlatev 1999 . Kinetic f2/2 19/46

  20. We’re not special: universe sees periodic epochs of acceleration We are special: the key is our proximity to the matter/ radiation equality Non-minimal coupling to matter (Amendola 2000, Bean & Magueijo 2001) k-essence : A dynamical push after zeq with non-trivial kinetic Lagrangian term (Armendariz-Picon, et al 2000) the coincidence is a result of a coupling to the neutrino (Fardon et al 2003), ghostlike behavior (de la Macorra et al 2006) Tackling the coincidence problem: are we special? w(z) evolution with an oscillatory potential Dodelson , Kaplinghat, Stewart 2000 V~M4e-(1+Asin ) Wtot log(a) Dodelson , Kaplinghat, Stewart 2000 w(z) evolution with a non-minimal coupling to dark matter wtot log(a) Bean & Magueijo 2001 20/46

  21. Tackling the L problems: implications for BBN Dark energy vs baryon density BBN constraints • Scaling potentials can predict significant dark energy at earlier times • treating Q as NrelFerreira & Joyce 1998,Bean, Hansen, Melchiorri 2001 • Bounds on Helium mass fraction, YHe • YHe=0.24815 ± 0.00033 ±0.0006 (sys) Stegiman 2005 • Relative Deuterium abundance D/H • D/H=(2/58+0.14-0.13).10-5Steigman(2005) • But collated more recent value D/H = 2.6±0.4).10-5Kirkman et al (2003) • Abundance limits conservatively correspond to Nrel<0.2 • This translates into Q (MeV)<0.05 (2s) Early constraints on dark energy density Bean, Hansen, Melchiorri 2001 21/46

  22. Tackling the dark matter and dark energy problems as one • ‘Unified’ dark matter/ dark energy • Clustering at early times like CDM, w~0, cs2~0 • Accelerating expansion at late times like L, w <0 • Phenomenology: Chaplygin gases • an adiabatic fluid, parameters w0, a • Strings interpretation? Born-Infeld action is of this form with a =1(e.g. Gibbons astro-ph/0204008 ) Evolution of equation of state for Chaplygin Gas w lg(a) Bean and Dore PRD 68 2003 22/46

  23. Quintessential inflation (e.g. Copeland et al 2000, Binetruy, Deffayet,Langlois 2001) Brane world scenario r2 term increases the damping of  as rolls down potential at early (inflationary) times inflation possible with V () usually too steep to produce slow-roll Curvature on the brane (Dvali ,Gabadadze Porrati 2001) Gravity 5D (Minkowski) on large scales l>lc~H0-1 i.e. only visible at late times Although 4D on small scales not Einstein gravity Potential implications for solar system tests as well as horizon scales Large scale modifications to GR Modify action so triggered at large scales R~H02 Potential implications for solar system tests as well as horizon scales Modifications to gravity rather than matter 23/46

  24. Overview The `known knowns’ • kinematical acceleration The ‘known unknowns’ • theoretical approaches to dark energy Can we know the known unknowns? • Observational tests for dark energy 24/46

  25. Dark energy perturbations: an important discriminator? • Natural extension to looking for w≠-1 ,dw/dz≠0 from (a) • Include constraints on (a) sensitive to cs2 = dP/d • To distinguish between theories … • only effecting the background (L, alterations to FRW cosmology) • with negligible clustering cs2 = 1 (minimally coupled quintessence) • that could contribute to structure formation (non-minimally coupled DE, k-essence) • To test if dark matter and dark energy are intertwined? • unified dark matter? • From a theorist’s perspective, to decipher the dark energy action • probing the dark energy external and self-interactions (or lack of) bound up in an effective potential • From an observational perspective, to check that a prior assuming no perturbations is fair • Does it effect the combination of perturbation independent (SN) and potentially dependent (CMB/LSS/WL) observations? 25/46

  26. Late time probes of w(z) Luminosity distance vs. z Angular diameter distance vs. z Probes of weff Angular diameter distance to last scattering Age of the universe Linking theory and observations SN 1a HST Legacy, Essence, DES, SNAP Baryon Oscillations SDSS Alcock-Paczynski test CMB WMAP CMB/ Globular cluster Tests probing background evolution only 26/46

  27. Late time probes of w(z) Luminosity distance vs. z Angular diameter distance vs. z Probes of weff Angular diameter distance to last scattering Age of the universe Late time probes of w(z) and cs2(z) Comoving volume * no. density vs. z Shear convergence Late time ISW Linking theory and observations Tests probing perturbations and background Galaxy /cluster surveys, SZ and X-rays from ICM SDSS, ACT, APEX, DES, SPT Weak lensing CFHTLS, SNAP, DES, LSST CMB and cross correlation WMAP, PLANCK, with SNAP, LSST, SDSS 27/46

  28. Early time probes of Q(z) Early expansion history sensitivity to relativistic species Late time probes of w(z) Luminosity distance vs. z Angular diameter distance vs. z Probes of weff Angular diameter distance to last scattering Age of the universe Late time probes of w(z) and cs2(z) Comoving volume * no. density vs. z Shear convergence Late time ISW Linking theory and observations BBN/ CMB WMAP Tests probing early behavior of dark energy 28/46

  29. Late time probes of w(z) Luminosity distance vs. z Angular diameter distance vs. z Probes of weff Angular diameter distance to last scattering Age of the universe Late time probes of w(z) and cs2(z) Comoving volume * no. density vs. z Shear convergence Late time ISW Early time probes of Q(z) Early expansion history sensitivity to relativistic species Alternate probes of non-minimal couplings between dark energy and R/ matter or deviations from Einstein gravity Equivalence principle tests Deviation of solar system orbits Varying alpha tests Linking theory and observations Tests probing general deviations in GR or 4D existence 29/46

  30. In a flat universe, many measures based on the comoving distance Luminosity distance Angular diameter distance Comoving volume element Age of universe Evolution of H(z) is the primary observable r(z) = ∫0z dz’ / H(z’) dL(z) = r(z) (1+z) dA(z) = r(z) / (1+z) dV/dzdΩ(z) = r2(z) / H(z) t(z) = ∫ z∞ dz/[(1+z)H(z)] 30/46

  31. Acoustic baryon oscillations • Compares tranverse + radial scale • Observe the ‘sound wave’ generated at last scattering surface • 500 million light years across • Expect correlations in the large scale structure on this scale • Systematics do not mimic features in correlation (Seo and Eisenstein 2003) • Dust extinction, • galaxy bias, • redshift distortion • non-linear corrections SDSS ~48000 galaxies with z~0.35 w Distance to z=0.35 (Mpc) Wmh2 Wmh2 Eisenstein et al 2004 31/46

  32. Kinematical constraints on constant w and w(a) wa w0 w0 Davis et al 2007 32/46

  33. Kinematical constraints on DGP background Davis et al 2007 33/46

  34. Kinematical constraints on Chaplygin gas as dark energy w0 w0 Davis et al 2007 34/46

  35. f(R) gravity has difficulties fitting observations Bean et al 2006 35/46

  36. Reconstructing dynamic evolution w=-0.7+0.8z with constant w w>-1 fit Constant w fit Reconstructing dark energy : a cautionary note • Ansatz for H(z), dl(z) or w(z) • w(z) applies well to scalar fields as well as many extensions to gravity Linder 2003 • Taylor expansions robust for low-z • Do parameterizations relate to microphysical properties (w=p/r, andcs2 =dp/dr) or just an effective description? • Need to have multi pronged observational approach • But, parameterizations can mislead • Need to consider additional parameter dependencies (Curvature, neutrino mass) Maor et al 2002 36/46

  37. Beyond CDM: Dark Energy Robust w + curvature CMB + SN + LSS w + massive neutrinos w CMB + SN + LSS w k mv (eV) Spergel et al 2006 37/46

  38. Should also leverage evolution on different spatial scales From Max Tegmark for SDSS 38/46

  39. Dark energy domination suppresses growth in gravitational potential wells , Y 2F = 4p Ga2 rd Late time Integrated Sach’s Wolfe effect (ISW) in CMB photons results - Net blue shifting of photons as they traverse gravitational potential well of baryonic and dark matter on way. ISW important at large scales Dark energy clustering counters suppression due to accelerative expansion Decreases ISW signature CDM dominated or clustering DE Y(x) dominated or Non clustering DE x(t) ISW: Dark energy signature in CMB photons CMB spectra for DE models incl/excl perturbations w>-1 w<-1 without without with with Hu 1998, Bean & Dore PRD 69 2003 Lewis & Weller 2003 39/46

  40. Beyond CDM: Dark Energy Clustering dark energy cs2=1 w≠-1 If fluctuations in DE negligible w w w w WMAP WMAP+SDSS WMAP WMAP+2dF WMAP WMAP+SDSS WMAP WMAP+2dF m m m m w w w w WMAP WMAP+SN (HST/GOODS) WMAP WMAP+SN (HST/GOODS) WMAP WMAP+SN (SNLS) WMAP WMAP+SN (SNLS) m m m m Spergel et al 2006 Sensitive to assumptions about clustering properties of Dark Energy 40/46

  41. Degeneracies & cosmic variance prevent constraints on clustering itself Large scale anisotropies also altered by spectral tilt, running in the tilt and tensor modes Dark energy clustering will be factor in combining future high precision CMB with supernova data. Avoid degeneracies by cross correlating ISW with other observables …. galaxy number counts Radio source counts Weak lensing of galaxies or CMB …. ‘Constraints’ on w and cs2 from WMAP ISW: Perturbations and CMB & LSS inferences Bean & Dore 2003, Lewis & Weller 2003 41/46

  42. ISW: CMB cross correlation with LSS Cross correlation of radio source number counts and WMAP ISW • ISW intimately related to matter distribution • Cross-correlation of CMB ISW with LSS. e.g. NVSS radio source survey (Boughn & Crittenden 2003 Nolta et al 2003, Scranton et al 2003) • WMAP+SDSS LRG +SDSS QSO +NVSS 6 sigma detection (Scranton et al in progress) • Current observations cannot distinguish dark energy features (Bean and Dore PRD 69 2003) • Future large scale surveys which are deep, ~z=2, such as LSST might well be able to (if w≠ -1) (Hu and Scranton 2004) 50 WLcontours 40 30 CNT (cntsmk) 20 10 0 0 20 10 5 15 q(deg) Nolta et al. 2003 18 1 Likelihood c2 0 12 0 1 Nolta et al 2003 WL 42/46

  43. Weak lensing: recent constraints from CFHT Constraints on CDM density and dark energy equation of state from Weak lensing 0. 0. -0.5 -0.5 8 w w -1.0 -1.0 -1.5 -1.5 -2.0 -2.0 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 m m CFHT Legacy Survey Wide Field +Deep Surveys (2x 1 deg) CFHT Legacy Survey Wide Field Survey (22sq deg) m Spergel et al 2006 Hoekstra et al 2005, Semboloni et al 2005 43/46

  44. Weak lensing tomography :prospects • SNAP and LSST offer exciting prospects for WL • e.g. SNAP measuring 100 million galaxies over 300 sqdeg • Tomography => bias independent z evolution of DE • Ratios of growth factor (perturbation) dependent observables at different z give growth factor (perturbation) independent measurement of w, w’ • Possibly apply technique to probe dark energy clustering ? • Understanding theoretical and observational systematics key • effect of non-linearities in power spectrum • Accurately reconstructing anisotropic point spread function • z-distribution of background sources and foreground halo • inherent ellipticities … • Use of higher order moments to reduce these … Prospective constraints on w from the SNAP SN1a + WL measurements 0.0 SNAP SN1a Deep survey -0.5 w Wide survey -1.0 -1.5 Wide survey+ non-Gaussian info -2.0 0.0 0.2 0.4 0.6 0.8 WM SNAP collaboration Aldering et al 2004 44/46

  45. Acoustic baryon oscillations: prospects • 30,000 sq degree survey with ~54 galaxies per arcminute2 • Redshift slices between z=0.2 and 3 • Competitive predictions with WL tomography and future large supernovae surveys • Cross correlation of weak lensing and BAO ? 2000 SN1a 45/46

  46. Linking Dark Energy Observations and Theory Einstein on Observation: "Joy in looking and comprehending is nature's most beautiful gift.” Einstein on Theory: “If an idea does not appear absurd at first then there is no hope for it” 46/46

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