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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. - PowerPoint PPT Presentation
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Ta-Pei ChengUniv of Missouri - St. Louis
Material based on the book
“Relativity, Gravitation & Cosmology: A basic Introduction”
(Oxford, 2005)
Hubble diagram
(recession velocity) red-shift z
Red shift z =
H0Δr=cz
AccU basics
H0 = H(t0)
H0-1 15 Gyr
Hubble time tH
“Expansion of the space itself”
Exp rate H indept of Δr and z : the same relation for all galaxies
Luminosity (Distance r )
“Standard candle”
past
now
(recession velocity) red-shift z
Luminosity (Distance r )
COASTING
Decelerating universe
?
The universe has matter / energy;
their mutual gravitational attraction
would cause the expansion to slow down
AccU basics
H larger in the past: for a fixed z=HΔr
Δr must be smaller -- the Hubble curve bends
downward
Looking further out into space
further back into time
Involves catching the light of exploding stars emitted billions of years ago
… and their intrinsic luminosity understood
AccU basics
past
Luminosity (Distance r )
(recession velocity) red-shift z
past
now
SNe further away. They are dimmer than expected
Accelerating universe
Surprising discovery
Hubble curve bends upward !
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)
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.)
Accelerated expansion =
gravitational repulsion?
Distant SNe ≈25% less luminous than expected
Why accepted so quickly?
This requires a GR concept:
“The Dark Energy”
GENERAL RELATIVITY is the framework for COSMOLOGY
Talk’s message
• Einstein: Gravitation field = curved spacetime, Spacetime tells matter how to move
Matter tells spacetime how to curve
GR = Gravitational field theory source particle field test particle
GR field eqn
Field eq eq motion
•Field equation: (Electromagnetism: Maxwell’s eqn) GR: Einstein’s eqn G = gN T math
property
geometry matter/energy
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.
Homogeneous & isotropic universe
Geometric side has 2 unknowns (k, a): G = gN T
1. Curvature signature k = 0, +1, -1 (flat, closed, open u)
2. Scale factor a(t) ≠ constant → expanding universe
Mass/energy side has 2 unknowns (ρ, p) for an ideal fluid.
Einstein eq in cosmology:
Ω = ρ/ρc critical density ρc= 3H2/8πgN with H=å/a
)1(2 a
k
Geometry and mass/energy content determine each other e.g., a flat universe (k = 0) (Ω =1)
GR 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
]0[]0[ paa
Any addition to the Einstein eq G = gNT must be symmetric, rank-2, zero-divergence
Simplest possibility: the metric tensor g itself
G - g = gNT
CC intro 1
not to contradict the Newton’s law: the new term must be extremely small on normal scales
but, relevant on the cosmic dimension
For easier physical interpretation of CC intro 1
Move it, from the geometry side, to the energy side
G - g = gNT
G = gNT+ gN-1 g )= gNT+ T)
“the energy-momentum tensor of the vacuum”
Interpreting T in terms of (Λp
Energy density uΛ≡ ρΛc2 =Λ/gΛ = constant
Pressure pΛ = -uΛ = negative
Cosmo constant = constant energy density and negative pressure
neg pressure
V > 0 U > 0 … Energy conservation ? 1st law: U= –pV but we have U= uV
Hence, just the required negative pressure of p = -u
Is this physically sensible? constant energy per unit volume, indept of V
change System can lower its
energy by volume contraction (… pulls in the piston)
Negative pressure pulls in the piston
repulsive force
General (p) gNp/c2)
not only mass, but also pressure = source of gravity
Negative pressure (opposite sign) = repulsionA B
Negative pressure = source of gravitational repulsion
2 -, - r2,
(- =) F = + r instead of the familiar –1/r2 force
a repulsive force that increases with distance
…can be relevant on the cosmic scale
(p) attraction +
(p) repulsion
biggest blunder
The biggest blunder of my life
But the original proof of stability of the solution is incorrect…
then came Hubble’s discovery...
the geometry of a closed universe
Static Solution
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 rears its ugly head again and again and again.
“blunder” - perhaps reflecting more of Gamow’s opinion ...
But, no known physics ( = 0)
a key ingredient of modern cosmology: inflationary epoch & dark energy in the acc U
CC-2
Its discovery should be regarded as one of Einstein’s great achievements
Time evolution of the universe w/o Λ
a(t)
t
tH
⅔tH0
diff curve diff t=0 origin
k = 1 closed univ
k = flat univ
empty
univ
decelerating universe
t00 0NOW
accelerating universe
• Discovery of 2.7o CMB
• Light nuclear element abundance (BB nucleosynthesis)
Cosmic expansion requires
fine-tuned initial conditions
• 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.
• Flatness problem: [obs= O(1) → an extremely flat universe = 1.000000…
Inflationary Cosmology Alan Guth (1980) used particle physics ideas (SSB, “false vac”) to
formulate a cosmological theory with a large effective cosmological constant
Self-reinforcing nature of 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
eff= 0 after the inflationary epoch?
CMB pic A firm prediction of inflationary cosmology: a flat universe1st evidence came in mid-1990’s from
CMB temperature anisotropyCMB = 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 K, 1st detected by COBE satellite
Finally BOOMERANG and MAXIMA balloon borne detectors had the angular resolution… more recently WMAP confirmed..
But a 0 flat universe has problems
….
A flat universe must have Ω = 1 (i.e., ρ = ρc)
Yet observation showing Ωlum ≈ 0.005
even with dark matter Ωdark +Ωlum ≡ΩM
still … ΩM ≈ 0.3 only
puzzle 1
A missing energy problem
puzzle 2
The age of a flat universe t0 = ⅔H0
-1 < 10 Gyr
Yet some stars (e.g., globular clusters, quasars..) are estimated to be as old as 12.5 Gyr
A cosmic age problem
again to the rescue?
The vacuum energy is the missing energy matter energy + dark energy = total energy = M + = 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
M+ 0.3
Omega plot
► t0 ≈ 14 Gyr
Distant SNe ≈25% less luminous than expected
The “smoking-gun evidence” of an acc univ
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):
~ a0 vs. mat~ 1/a3 , rad~ 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.
k = 1,
k =
a(t)em
pty univ
decelerating universe
accelerating universe
t0
NOW
k =
tH
0⅔tH
Such a bulge cannot be mimicked by any
mundane causes
(dec) → (acc) transition shows up as
the cosmic expansion slowed down before it eventually sped up
Evidence for deceleration to acceleration transition
Also, more recent observations by Hubble ST
Continuing
dimming
↑ z = 1.7
•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)
Dark Energy ≡ negative eqn-of-state energy
with w = -1 is thesimplest example of dark energy
Eqn of state: p = wu with w < 0 so as to obtain gravitational repulsion
The 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 = ? ≈ 0.3 (vs. ≈ 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 = ?
≈ 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 energy
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)
,...2,1,0
)21(
i
iii
n
nU
constant
const)(
21
00
3
33
0
uVU
Vph
pxdd
U ii
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
?)(
)( *03
4*
42223
20
*
puc
cp
cmcpdpp
V
U p
quantum gravity = quantized spacetime
)10()(
w/)(identify
),,(),,(
275*
*
eVOgccp
energyPlanckcp
tlmgc
NPlanck
PlanckN
Thus the quantum vac density is more than 120 orders of magnitude too large
120
4
3
270 10
10
10
)(
obsu
u
3
432
)(
)10()()(
c
eVcOu cobs
Tiny but non-zero!
Namely, need a theory to explain why
vacquu )(.....0000.0 0120
Yet, 121st ≠ 03
427
0 )(
)10(
c
eVu
A key concept in modern cosmology: The Cosmological Constant
~ constant energy density, negative pressure
A large 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 the dark energy,fits snugly with the inflation cosmology prediction of a flat universe solving the missing energy and cosmic age problems
A concordant cosmological picture : A flat universe (with
dominated by dark energy
(by dark matter M > (lum ≈
0.005) If the dark energy density does not change with time, the expansion will go faster,
faster foreverRequires new physics to understand its main ingredients:
What is the dark matter?
What is the dark energy?