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The Accelerating Universe,Inflation, & the Dark Energy

Dark Energy. The Accelerating Universe,Inflation, & the Dark Energy. in the Accelerating Universe. Material based on the book “ Relativity, Gravitation & Cosmology: A basic Introduction ” (Oxford, 2005). Ta-Pei Cheng Univ of Missouri - St. Louis. an expanding universe. We live in.

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The Accelerating Universe,Inflation, & the Dark Energy

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  1. Dark Energy The Accelerating Universe,Inflation, & the Dark Energy in the Accelerating Universe Material based on the book “Relativity, Gravitation & Cosmology: A basic Introduction” (Oxford, 2005) Ta-Pei Cheng Univ of Missouri - St. Louis

  2. an expanding universe We live in Hubble diagram “Standard candle” Luminosity (Distance Dr ) H0Δr=cz H0 = H(t0) H0-1  15 Gyr Hubble time tH Red shift z = Dl/l (recession velocity) red-shift z AccU basics Hubble-1 Exp rate H indept of Δr and z : the same relation for all galaxies “Expansion of the space itself”

  3. an expanding universe We live in Looking further out into space further back into time  COASTING Luminosity (Distance Dr ) ? Decelerating universe (recession velocity) red-shift z AccU basics Hubble-3 decU The universe has matter / energy; their mutual gravitational attraction would cause the expansion to slow down past H larger in the past: for a fixed z=HΔrΔr must be smaller -- the Hubble curve bends downward now

  4. Hubble curve bends upward ! Surprising discovery achievement Remarkable past Accelerating universe Involves catching the light of exploding stars emitted billions of years ago Luminosity (Distance Dr ) … and their intrinsic luminosity understood (recession velocity) red-shift z now past AccU basics Hubble-4 accU To see the bending of the Hubble curve, need to measure objects across enormous distances. Just such ‘standard candles’ have been found: Type-1a Supernovae Monitoring thousands of galaxies  SN/(month) SNe further away. They are dimmer than expected

  5. THE 1998 DISCOVERY by two indept teams: ►Supernova Cosmological Project (LBL: S.Permutter et al.) ►High-z Supernovae Search Team (Australian/American: A. Reiss et al.) Distant SNe ≈25% less luminous than expected 1998 discovery Accelerated expansion = gravitational repulsion? Why accepted so quickly?

  6. Talk’s message GENERAL RELATIVITY is the framework for COSMOLOGY GR key concept: CC This talk's message Acc U leads to a concordant cosmo picture This requires a GR concept: The Cosmological Constant “The Dark Energy”

  7. Field eq eq motion • Field equation: (Electromagnetism: Maxwell’s eqn) GR: Einstein’s eqnGmn = gN Tmnmath property • geometry matter/energy GR field eqn GR = Gravitational field theorysource particle  field  test particle • Einstein:Gravitation field = curved spacetime, Spacetime tells matter how to move Matter tells spacetime how to curve Spacetime described by the metric function gμν (i.e., by distance measurement) ~ relativistic gravitational potential NR weak field limit, it reduces to Newton’s eqn.

  8. Einstein eq in cosmology: Ω = ρ/ρccritical densityρc= 3H2/8πgNwithH=å/a Geometry and mass/energy content determine each other e.g., a flat universe(k = 0) (Ω =1) Cosmology Homogeneous & isotropic universe cosmology • Geometric side has 2 unknowns (k, a): Gmn = gN Tmn • Curvature signaturek= 0, +1, -1(flat, closed, open u) • Scale factora(t)≠ constant → expanding universe • Mass/energy sidehas 2 unknowns (ρ, p) for an ideal fluid.

  9. Introducing the cosmological constant No static U Before Hubble (1929), ‘everyone’ thought we lived in astatic universe … but gravity is an universal attractive force GR does not allow a staticsolution A static universe is an empty universe Einstein modified his GR field equation, by adding a term (~ cosmic repulsion) to counter the usual gravitational attraction, making it possible to have a static universe

  10. Introducing the cosmological constant CC intro 1 Any addition to the Einstein eq Gmn = gNTmn must besymmetric, rank-2, zero-divergenceSimplest possibility:the metric tensorgmnitself Gmn- L gmn = gNTmn not to contradict the Newton’s law: the new term L must be extremely small on normal scales  but, relevant on the cosmic dimension

  11. Move it, from the geometry side, to the energy side Gmn- L gmn = gNTmn Gmn = gN (Tmn + gN-1L gmn )= gN (Tmn + TLmn) “the energy-momentum tensorof the vacuum” InterpretingTLmnin terms of (rΛ , pL): Energy densityuΛ≡ρΛc2 =Λ/gΛ = constant PressurepΛ = -uΛ = negative CC intro 1 For easier physical interpretation of L Cosmo constant = constant energy density and negative pressure

  12. neg pressure What's a negative pressure ? L Negative pressure pulls in the piston Is this physically sensible? Lconstant energy per unit volume, indept of V changeSystem can lower its energy by volume contraction(… pulls inthe piston) DV > 0  DU > 0 … Energy conservation ?1st law:DU= –pDV but we have DU= uDVHence, just the requirednegative pressure of p = -u

  13. repulsive force General (r, p)  2f = gN (r + 3p/c2) not only mass, but also pressure = source of gravity Negative pressure(opposite sign)=repulsion 2fL -L, fL  -L r2,(-fL =)FL=+Lrinstead of the familiar –1/r2forcea repulsive force that increases with distance…can be relevant on the cosmic scale A B Negative pressure = source of gravitational repulsion

  14. Static Solution the geometry of a closed universe The biggest blunder of my life Einstein : biggest blunder (r, p)attraction + (rL, pL)repulsion • But the original proof of stability of the solution is incorrect… then came Hubble’s discovery...

  15. George Gamow(1904-1968) in “My World Line”p.44 … Thus, Einstein’s original gravity equation was correct, and changing it was a mistake. Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder he ever made in his life. But this “blunder”, rejected by Einstein, is still sometimes used by cosmologists even today, and the cosmological constant L rears its ugly head again and again and again. “blunder” - perhaps reflecting more of Gamow’s opinion ... But, no known physics  ( L = 0)

  16. CC-2 a key ingredient of modern cosmology: inflationary epoch&dark energy in the acc U The Cosmological Constant Its discovery should be regarded asone of Einstein’s great achievements

  17. a(t) empty univ accelerating universe k = 0 flat univ decelerating universe k = +1 closed univ NOW t0 0 0 t 0 ⅔tH • Discovery of 2.7o CMB • Light nuclear element abundance (BB nucleosynthesis) tH diff curve diff t=0 origin Time evolution of the universe w/o Λ

  18. Cosmic expansion requires fine-tuned initial conditions • Flatness problem:[W0]obs= O(1) → an extremely flat universe W = 1.000000… • Horizon problem: Far apart regions, outside each other’s horizons,are correlated. How? • Must postulate the existence, at the very beginning, of all energy and particles Requires a theory of the Big Bang itself …. so as to leave behind just the right conditions for subsequent expansion.

  19. Inflationary CosmologyAlan Guth (1980) used particle physics ideas (SSB, “false vac”) to formulate a cosmological theory with a large effective cosmological constant Self-reinforcing nature of L bring about an exponential expansion, reaching superluminary rate Solving the flatness and horizon problems. Furthermore, matter and energy could have been created from energy of the false vacuum. Quantum fluctuations are inflated to cosmic size to be the initial density perturbation, seeding the subsequent cosmic structure: galaxies, clusters… An explosion of the space Leff= 0 after the inflationary epoch?

  20. CMB pic CMB = the “baby picture” of the universe. How does it appear to us is influenced by the geometry of the univ Anisotropy (10-5), a few mK, 1st detected by COBE satellite Finally BOOMERANG and MAXIMA balloon borne detectors had the angular resolution… more recently WMAP confirmed.. A firm prediction of inflationary cosmology:a flat universe 1st evidence came in mid-1990’s fromCMB temperature anisotropy geometry of the universe is flat But a L = 0 flat universe has problems ….

  21. Puzzle #1 ? A missing energy problem puzzle 1 A flat universe must have Ω = 1 (i.e., ρ = ρc) Yetobservation showing Ωlum ≈ 0.005 even with dark matterΩdark +Ωlum ≡ΩMstill … ΩM ≈ 0.3only

  22. Puzzle #2 ? A cosmic age problem puzzle 2 The age of a flat universe t0 = ⅔H0-1< 10Gyr Yetsome stars (e.g., globular clusters, quasars..) are estimated to be as old as 12.5Gyr

  23. L  0 again to the rescue? The vacuum energyrLis themissing energymatter energy + dark energy = total energy W = W M+ WL = 1 ? ► Possibility to solve the missing energy problem An accelerating expansion  the expansion was slower in the pasta longer age for the universe ► Possibility to solve the cosmic age problem then came the 1998 discovery ...

  24. 0.7 +0.3 =1 Distant SNe ≈25% less luminous than expected Omega plot WM+ WL  0.3 + 0.7= 1 ► t0 ≈ 14 Gyr

  25. Mundane explanation SNe less luminous in the past? Gray dust? In all such scenarios, continuing dimming for even higher redshift (earlier epochs) Accelerating universe dark energy could not dominate in the past (a→0): WL~ a0 vs. Wmat~ 1/a3 , Wrad~ 1/a4 Acceleration must be preceded by deceleration Dimming followed by brightening for even higher redshift The “smoking-gun evidence” of an acc univ “Signal dimmer than expected” may be NOT due to “SNe farther sway than expected”? vs.

  26. a(t) k =0 L 0 empty univ (dec) → (acc) transition shows up as accelerating universe k =0, L = 0 A bulge in the Hubble curve decelerating universe NOW k = +1, L = 0 t0 0 ⅔tH tH the cosmic expansion slowed down before it eventually sped up Bulge in Hubble Such a bulge cannot be mimicked by any mundane causes

  27. A.Reiss et al. “The farthest known supernova: support for an acc univ and a glimpse of the epoch of deceleration” Astrophys J 560, 49 (2001) Continuing dimming ↑ z = 1.7 Evidence for deceleration to acceleration transition Also, more recent observations by Hubble ST

  28. Warning! The name “dark energy” is neither descriptive nor accurate ! Dark Energy ≡ negative eqn-of-state energy For example, black holes, neutrinos,… are all “dark”, but they are NOT counted as “dark energy”. Eqn of state: p = wu with w < 0 so as to obtain gravitational repulsion L with w = -1 is thesimplest example of dark energy

  29. Dark matter = ? WM≈ 0.3 (vs. WB≈ 0.04) Bulk of DM is exotic. What is it? neutrino vs.WIMPs. There are natural candidates, but in some yet-to-be-proven particle physics theories: Supersymmetric neutralinos? Axions? etc. There are active programs searching for these cold dark matter particles. Dark energy = ? WL≈ 0.7 What is its physical origin? Quantum field theory provides natural candidate: quantum mechanical vacuum energy But this identification has serious theoretical difficulties. A concordant cosmic picture but understanding?

  30. Quantum vacuum energy has a constant energy density: Field = collection of simple harmonic oscillators Quantized SHO energy spectrum: Zero-point energy: quantum vacuum ≠ nothingness (quantum fluctuation: creation, annihilation of virtual particles) Quantum Mechanical Vacuum Energy as the dark energy ► negative pressure Zero-pt energy crucial in many QM applications, e.g., the Casimir Effect, a macroscopic phenomenon.

  31. But, cannot account for the observed magnitude Tiny but non-zero! quantum gravity = quantized spacetime The size of quantum vac energy density Thus the quantum vac density is more than 120 orders of magnitude too large The cosmological constant problem Namely, need a theory to explain why Yet, 121st ≠ 0

  32. SUMMARY : 1 Summery-1 A key concept in modern cosmology: The Cosmological Constant ~ constant energy density, negative pressure A large L is needed to have the inflation epoch: an explosion of space at the earliest moment of the Big Bang leaving behind just the right conditions for subsequent expansion A small L, the dark energy,fits snugly with the inflation cosmology prediction of a flat universesolving the missing energy and cosmic age problems

  33. SUMMARY : 2 Summery-2 A concordant cosmological picture : A flat universe (withWL+ WM= W = 1) dominated by dark energy (WL= 0.7) > (WM= 0.3) by dark matterWM > (Wlum≈ 0.005) If the dark energy density does not change with time, the expansion will go faster, faster forever Requires new physics to understand its main ingredients: What is the dark matter? What is the dark energy?

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