The Accelerating Universe,Inflation, & the Dark Energy
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The Accelerating Universe,Inflation, & the Dark EnergyTa-Pei ChengUniv of Missouri - St. Louis
Material based on the bookRelativity, Gravitation & Cosmology: A basic Introduction (Oxford, 2005)
Hubble-1AccU basics Expansion of the space itselfExp rate H indept of r and z : the same relation for all galaxies
Hubble-3 decUpastnowThe universe has matter / energy; their mutual gravitational attraction would cause the expansion to slow downAccU basics H larger in the past: for a fixed z=Hr r must be smaller -- the Hubble curve bends downward
Hubble-4 accUAccU basics SNe further away. They are dimmer than expectedTo 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)
1998 discoveryTHE 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.)
Accelerated expansion = gravitational repulsion?Why accepted so quickly?
GR key concept: CCThis requires a GR concept:The Dark EnergyGENERAL RELATIVITY is the framework for COSMOLOGYTalks message
GR = Gravitational field theory source particle field test particle
Einstein: Gravitation field = curved spacetime, Spacetime tells matter how to move Matter tells spacetime how to curve GR field eqnSpacetime described by the metric function g (i.e., by distance measurement) ~ relativistic gravitational potentialNR weak field limit, it reduces to Newtons eqn.
cosmologyHomogeneous & isotropic universeGeometric side has 2 unknowns (k, a): Gmn = gN Tmn Curvature signature k = 0, +1, -1 (flat, closed, open u)Scale factor a(t) constant expanding universeMass/energy side has 2 unknowns (, p) for an ideal fluid.
No static UGR does not allow a static solution
A static universe is an empty universe Before Hubble (1929), everyone thought we lived in a static universe but gravity is an universal attractive force 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
CC intro 1Any addition to the Einstein eq Gmn = gN Tmn must be symmetric, rank-2, zero-divergence Simplest possibility: the metric tensor gmn itself Gmn - L gmn = gN Tmn
not to contradict the Newtons law: the new term L must be extremely small on normal scales but, relevant on the cosmic dimension
For easier physical interpretation of LCC intro 1Cosmo constant = constant energy density and negative pressure
neg pressure DV > 0 DU > 0 Energy conservation ? 1st law: DU= pDV but we have DU= uDV Hence, just the required negative pressure of p = -uIs this physically sensible? L constant energy per unit volume, indept of V change System can lower its energy by volume contraction ( pulls in the piston)
repulsive forceNegative pressure = source of gravitational repulsion
biggest blunder (r, p) attraction + (rL, pL) repulsion
But the original proof of stability of the solution is incorrect then came Hubbles discovery...
George Gamow (1904-1968) in My World Line p.44 Thus, Einsteins 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 Gamows opinion ...But, no known physics ( L = 0)
a key ingredient of modern cosmology: inflationary epoch & dark energy in the acc U
CC-2Its discovery should be regarded as one of Einsteins great achievements
Time evolution of the universe w/o
Cosmic expansion requires fine-tuned initial conditions Horizon problem: Far apart regions, outside each others horizons, are correlated. How?Must postulate the existence, at the very beginning, of all energy and particlesRequires a theory of the Big Bang itself . so as to leave behind just the right conditions for subsequent expansion.Flatness problem: [W0]obs= O(1) an extremely flat universe W = 1.000000
Inflationary Cosmology Alan Guth (1980) used particle physics ideas (SSB, false vac) to formulate a cosmological theory with a large effective cosmological constantSelf-reinforcing nature of L bring about an exponential expansion, reaching superluminary rateSolving 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 spaceLeff= 0 after the inflationary epoch?
CMB picA firm prediction of inflationary cosmology: a flat universe1st evidence came in mid-1990s from CMB temperature anisotropyBut a L = 0 flat universe has problems .
puzzle 1A flat universe must have = 1 (i.e., = c) Yet observation showing lum 0.005 even with dark matter dark +lum M still M 0.3 only
The age of a flat universe t0 = H0-1 < 10 Gyr Yet some stars (e.g., globular clusters, quasars..) are estimated to be as old as 12.5 Gyr
L 0 again to the rescue?The vacuum energy rL is the missing energy matter energy + dark energy = total energy W = W M + WL = 1 ? Possibility to solve the missing energy problemAn accelerating expansion the expansion was slower in the past a longer age for the universe Possibility to solve the cosmic age problem
WM+ WL 0.3 + 0.7 = 1Omega plot t0 14 Gyr0.7 +0.3 =1
The smoking-gun evidence of an acc univMundane 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 (a0): WL ~ a0 vs. Wmat ~ 1/a3 , Wrad ~ 1/a4 Acceleration must be preceded by deceleration Dimming followed by brightening for even higher redshift
Signal dimmer than expected may be NOT due to SNe farther sway than expected?vs.
Bulge in HubbleSuch a bulge cannot be mimicked by any mundane causesthe cosmic expansion slowed down before it eventually sped up
Evidence for deceleration to acceleration transitionAlso, more recent observations by Hubble ST
Dark Energy negative eqn-of-state energyL with w = -1 is the simplest example of dark energyEqn of state: p = wu with w < 0 so as to obtain gravitational repulsionThe name dark energy is neither descriptive nor accurate !For example, black holes, neutrinos, are all dark, but they are NOT counted as dark energy.
but understanding?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
Quantum Mechanical Vacuum Energy as the dark energyField = collection of simple harmonic oscillatorsQuantized SHO energy spectrum:
Zero-point energy: quantum vacuum nothingness (quantum fluctuation: creation, annihilation of virtual particles)
Quantum vacuum energy has a constant energy density:
Zero-pt energy crucial in many QM applications, e.g., the Casimir Effect, a macroscopic phenomenon. negative pressure
The size of quantum vac energy density
Thus the quantum vac density is more than 120 orders of magnitude too large
Namely, need a theory to explain why
Yet, 121st 0
Summery-1A key concept in modern cosmology: The Cosmological Constant ~ constant energy density, negative pressureA 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 expansionA small L, the dark energy, fits snugly with the inflation cosmology prediction of a flat universe solving the missing energy and cosmic age problems
Summery-2A concordant cosmological picture : A flat universe (with WL+ WM= W = 1) dominated