Dark Energya cosmic mystery Dunkle Energie Ein kosmisches
- Slides: 83
Dark Energya cosmic mystery Dunkle Energie – Ein kosmisches Raetsel
Quintessence C. Wetterich A. Hebecker, M. Doran, M. Lilley, J. Schwindt, C. Müller, G. Schäfer, E. Thommes, R. Caldwell
What is our universe made of ? quintessence ! fire , air, water, soil !
Dark Energy dominates the Universe Energy - density in the Universe = Matter + Dark Energy 30 % + 70 %
What is Dark Energy ?
Matter : Everything that clumps Abell 2255 Cluster ~300 Mpc
critical density n ρc =3 H² M² critical energy density of the universe ( M : reduced Planck-mass , H : Hubble parameter ) n Ωb=ρb/ρc fraction in baryons energy density in baryons over critical energy density
Dark Matter Most matter is dark ! So far tested only through gravity n Every local mass concentration gravitational potential n Orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution n
Ωm= 0. 3 gravitational lens , HST
spatially flat universe Ωtot = 1 n theory (inflationary universe ) Ωtot =1. 0000………. x n observation ( WMAP ) Ωtot =1. 02 (0. 02)
picture of the big bang
Ωtot=1
Dark Energy Ωm + X = 1 Ωm : 30% Ωh : 70% Dark Energy h : homogenous , often ΩΛ instead of Ωh
Space between clumps is not empty : Dark Energy !
Dark Energy density is the same at every point of space “ homogeneous “ No force – “ In what direction should it draw ? “
Two important predictions The expansion of the Universe accelerates today ! Structure formation : One primordial fluctuation- spectrum
consistent cosmological model !
Composition of the Universe Ωb = 0. 045 visible clumping Ωdm= 0. 22 invisible clumping Ωh = 0. 73 invisible homogeneous
Dark Energya cosmic mystery Dunkle Energie – Ein kosmisches Raetsel
What is Dark Energy ? Cosmological Constant or Quintessence ?
Cosmological Constant - Einstein n Constant λ compatible with all symmetries n No time variation in contribution to energy density n Why so small ? λ/M 4 = 10 -120 n Why important just today ?
Cosm. Const. | Quintessence static | dynamical
Cosmological mass scales n Energy density ρ ~ ( 2. 4× 10 -3 e. V )- 4 Reduced Planck mass M=2. 44× 1018 Ge. V n Newton’s constant GN=(8πM²) n Only ratios of mass scales are observable ! homogeneous dark energy: ρh/M 4 = 6. 5 10ˉ¹²¹ matter: ρm/M 4= 3. 5 10ˉ¹²¹
Time evolution tˉ² matter dominated universe n ρm/M 4 ~ aˉ³ ~ n ρr/M 4 ~ aˉ4 ~ t -2 radiation dominated universe Huge age tˉ3/2 radiation dominated universe small ratio Same explanation for small dark energy?
Quintessence Dynamical dark energy , generated by scalar field (cosmon) C. Wetterich, Nucl. Phys. B 302(1988)668, 24. 9. 87 P. J. E. Peebles, B. Ratra, Ap. J. Lett. 325(1988)L 17,
Prediction : homogeneous dark energy influences recent cosmology - of same order as dark matter Original models do not fit the present observations …. modifications
Quintessence Cosmon – Field φ(x, y, z, t) similar to electric field , but no direction ( scalar field ) Homogeneous und isotropic Universe : φ(x, y, z, t)=φ(t) Potential und kinetic energy of the cosmon -field contribute to a dynamical energy density of the
Evolution of cosmon field Field equations Potential V(φ) determines details of the model e. g. V(φ) =M 4 exp( - φ/M ) for increasing φ the potential decreases towards zero !
Cosmon n Scalar field changes its value even in the present cosmological epoch n Potential und kinetic energy of cosmon contribute to the energy density of the Universe n Time - variable dark energy : ρh(t) decreases with time !
Cosmon n Tiny mass n mc ~H n New long - range interaction
Dynamics of quintessence n Cosmon j : scalar singlet field n Lagrange density L = V + ½ k(φ) ¶j ¶j (units: reduced Planck mass M=1) V=exp[-j] n Potential : n “Natural initial value” in Planck era j=0 n today: j=276
cosmon mass changes with time ! for standard kinetic term n mc 2 = V” for standard exponential potential , k = const. n mc 2 = V”/ k 2 = V/( k 2 M 2 ) = 3 Ωh (1 - wh ) H 2 /( 2 k 2 )
“Fundamental” Interactions Strong, electromagnetic, weak interactions On astronomical length scales: graviton + cosmon gravitation cosmodynamics
Cosmological equations example: ^ cosmon +matter
Cosmological equations
Cosmic Attractors Solutions independent of initial conditions typically V~t -2 φ ~ ln ( t ) Ωh ~ const. details depend on V(φ) or kinetic term early cosmology
Quintessence becomes important “today”
Equation of state p=T-V ρ=T+V pressure energy density kinetic energy Equation of state Depends on specific evolution of the scalar field
Negative pressure n w<0 Ωh increases (with decreasing z ) late universe with small radiation component : n w < -1/3 expansion of the Universe is accelerating n w = -1 cosmological constant
small early and large present dark energy fraction in dark energy has substantially increased since end of structure formation expansion of universe accelerates in present epoch
Quintessence becomes important “today”
SN and equation of state Riess et al. 2004
How can quintessence be distinguished from a cosmological constant ?
Time dependence of dark energy cosmological constant : Ωh ~ t² ~ (1+z)-3 M. Doran, …
Measure Ωh(z) !
Early dark energy A few percent in the early Universe Not possible for a cosmological constant
Early quintessence slows down the growth of structure
A few percent Early Dark Energy If linear power spectrum fixed today ( σ8 ) : More Structure at high z ! Bartelmann, Doran, …
Anisotropy of cosmic background radiation with a few percent Early Dark Energy Caldwell, Doran, Müller, Schäfer, …
How to distinguish Q from Λ ? A) Measurement Ωh(z) H(z) i) Ωh(z) at the time of structure formation , CMB - emission or nucleosynthesis ii) equation of state wh(today) > -1 B) Time variation of fundamental “constants”
Quintessence and time variation of fundamental constants Generic prediction Strong, electromagnetic, weak interactions Strength unknown C. Wetterich , Nucl. Phys. B 302, 645(1988 ) gravitation cosmodynamics
Time varying constants It is not difficult to obtain quintessence potentials from higher dimensional or string theories n Exponential form rather generic ( after Weyl scaling) n But most models show too strong time dependence of constants ! n
Are fundamental “constants” time dependent ? Fine structure constant α (electric charge) Ratio nucleon mass to Planck mass
“Fifth Force” n Mediated by scalar field R. Peccei, J. Sola, C. Wetterich, Phys. Lett. B 195, 183(198 7) Coupling strength: weaker than gravity ( nonrenormalizable interactions ~ M-2 ) n Composition dependence violation of equivalence principle n Quintessence: connected to time variation of fundamental couplings n C. Wetterich , Nucl. Phys. B 302, 645(1988)
Quintessence and Time dependence of “fundamental constants” n Fine structure constant depends on value of cosmon field : α(φ) (similar in standard model: couplings depend on value of Higgs scalar field) n Time evolution of φ Time evolution of α Jordan, …
Standard – Model of electroweak interactions : Higgs - mechanism n n The masses of all fermions and gauge bosons are proportional to the ( vacuum expectation ) value of a scalar field φH ( Higgs scalar ) For electron, quarks , W- and Z- bosons : melectron = helectron * φH etc.
Restoration of symmetry at high temperature in the early Universe Low T SSB <φH>=φ0 ≠ 0 High T SYM <φH>=0 high T : less order more symmetry example: magnets
In the hot plasma of the early Universe : No difference in mass for electron and myon !
Strong bounds on the variation of couplings interesting perspectives for observation !
Abundancies of primordial light elements from nucleosynthesis A. Coc
if present 2 -sigma deviation of He –abundance from CMB/nucleosynthesis prediction would be confirmed : Δα/α ( z=1010 ) = -1. 0 10 -3 GUT 1 Δα/α ( z=1010 ) = -2. 7 10 -4 GUT 2 C. Mueller, G. Schaefer, …
Variation of fine structure constant as function of redshift Three independent data sets from Keck/HIRES Δα/α = - 0. 54 (12) 10 -5 Murphy, Webb, Flamm baum, june 2003 VLT Δα/α = - 0. 06 (6) 10 -5 Srianand, Chand, Petitje an, Aracil, feb. 2004 z≈2
Time variation of coupling constants must be tiny – would be of very high significance ! Possible signal for Quintessence
Cosmodynamics Cosmon mediates new long-range interaction Range : size of the Universe – horizon Strength : weaker than gravity photon electrodynamics graviton gravity cosmon cosmodynamics Small correction to Newton’s law
Violation of equivalence principle Different couplings of cosmon to proton and neutron Differential acceleration p, n earth “Violation of equivalence principle” only apparent : new “fifth force” ! cosmon p, n
Differential acceleration η For unified theories ( GUT ) : η=Δa/2 a Q : time dependence of other parameters
Link between time variation of α and violation of equivalence principle typically : η = 10 -14 if time variation of α near Oklo upper bound to be tested by MICROSCOPE
Summary o Ωh = 0. 7 o Q/Λ : dynamical und static dark energy will be distinguishable o Q : time varying fundamental coupling “constants” violation of equivalence principle
? ? ? ? ? ? Why becomes Quintessence dominant in the present cosmological epoch ? Are dark energy and dark matter related ? Can Quintessence be explained in a fundamental unified theory ?
Quintessence and solution of cosmological constant problem should be related ! “fate of dilatation symmetry”
End
A few references C. Wetterich , Nucl. Phys. B 302, 668(1988) , received 24. 9. 1987 P. J. E. Peebles, B. Ratra , Astrophys. J. Lett. 325, L 17(1988) , received 20. 1987 B. Ratra, P. J. E. Peebles , Phys. Rev. D 37, 3406(1988) , received 16. 2. 1988 J. Frieman, C. T. Hill, A. Stebbins, I. Waga , Phys. Rev. Lett. 75, 2077(1995) P. Ferreira, M. Joyce , Phys. Rev. Lett. 79, 4740(1997) C. Wetterich , Astron. Astrophys. 301, 321(1995) P. Viana, A. Liddle , Phys. Rev. D 57, 674(1998) E. Copeland, A. Liddle, D. Wands , Phys. Rev. D 57, 4686(1998) R. Caldwell, R. Dave, P. Steinhardt , Phys. Rev. Lett. 80, 1582(1998) P. Steinhardt, L. Wang, I. Zlatev , Phys. Rev. Lett. 82, 896(1999)
Growth of density fluctuations n Matter dominated universe with constant Ωh : P. Ferreira, M. Joyce n n n Dark energy slows down structure formation Ωh < 10% during structure formation Substantial increase of Ωh(t) since structure has formed! negative wh Question “why now” is back ( in mild form )
Cosmon and fundamental mass scales Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings, …) n Mp~ χ , mproton~ χ , ΛQCD~ χ , MW~ χ , … n χ may evolve with time n mn/M : ( almost ) constant - observation ! n Only ratios of mass scales are observable
Dilatation symmetry n Lagrange density: n Dilatation symmetry for n Conformal symmetry for δ=0
Dilatation anomaly Quantum fluctuations responsible for dilatation anomaly n Running couplings: n V~χ4 -A , Mp(χ )~ χ n V/Mp 4 ~ χ-A : decreases for increasing χ n E>0 : crossover quintessence n
Cosmology : χ increases with time ! ( due to coupling of χ to curvature scalar ) “ late time cosmology explores the ultraviolet” for large χ the ratio V/M 4 decreases to zero Effective cosmological constant vanishes asymptotically for large t !
Weyl scaling Cosmology : χ increases with time ! (“ late time cosmology explores the ultraviolet”) Weyl scaling : gμν→ (M/χ)2 gμν , φ/M = ln (χ 4/V(χ)) Exponential potential : V = M 4 exp(-φ/M)
Crossover Quintessence ( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k²(φ )= “ 1/(2 E(φc – φ)/M)” if j c ≈ 276/M ( tuning ! ) Relative increase of dark energy in present cosmological epoch
Quintessence models n Kinetic function k(φ) : parameterizes the details of the model - “kinetial” n n k(φ) = k=const. k(φ ) = exp ((φ – φ1)/α) k²(φ )= “ 1/(2 E(φc – φ))” Exponential Q. Inverse power law Q. Crossover Q. Naturalness criterion: k(φ=0) not tiny or huge ! – no very small parameter at Planck scale - else: explanation needed -
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