The Accelerating Universe,Inflation, & the Dark Energy

33
Ta-Pei Cheng Univ of Missouri - St. Louis Material based on the book Relativity, Gravitation & Cosmology: A basic Introduction(Oxford, 2005)

description

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

Transcript of The Accelerating Universe,Inflation, & the Dark Energy

Page 1: The Accelerating Universe,Inflation, & the Dark Energy

Ta-Pei ChengUniv of Missouri - St. Louis

Material based on the book

“Relativity, Gravitation & Cosmology: A basic Introduction”

(Oxford, 2005)

Page 2: The Accelerating Universe,Inflation, & the Dark Energy

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”

Page 3: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 4: The Accelerating Universe,Inflation, & the Dark Energy

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)

Page 5: The Accelerating Universe,Inflation, & the Dark Energy

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?

Page 6: The Accelerating Universe,Inflation, & the Dark Energy

This requires a GR concept:

“The Dark Energy”

GENERAL RELATIVITY is the framework for COSMOLOGY

Talk’s message

Page 7: The Accelerating Universe,Inflation, & the Dark Energy

• 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.

Page 8: The Accelerating Universe,Inflation, & the Dark Energy

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)

Page 9: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 10: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 11: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 12: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 13: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 14: The Accelerating Universe,Inflation, & the Dark Energy

(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

Page 15: The Accelerating Universe,Inflation, & the Dark Energy

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)

Page 16: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 17: The Accelerating Universe,Inflation, & the Dark Energy

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)

Page 18: The Accelerating Universe,Inflation, & the Dark Energy

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…

Page 19: The Accelerating Universe,Inflation, & the Dark Energy

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?

Page 20: The Accelerating Universe,Inflation, & the Dark Energy

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

….

Page 21: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 22: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 23: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 24: The Accelerating Universe,Inflation, & the Dark Energy

M+ 0.3

Omega plot

► t0 ≈ 14 Gyr

Distant SNe ≈25% less luminous than expected

Page 25: The Accelerating Universe,Inflation, & the Dark Energy

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.

Page 26: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 27: The Accelerating Universe,Inflation, & the Dark Energy

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)

Page 28: The Accelerating Universe,Inflation, & the Dark Energy

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”.

Page 29: The Accelerating Universe,Inflation, & the 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

Page 30: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 31: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 32: The Accelerating Universe,Inflation, & the Dark Energy

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

Page 33: The Accelerating Universe,Inflation, & the Dark Energy

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?