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Astronomy 182 Origin Evolution of the Universe

Lecture 15

Assignments

For today Essay due on Ferris, Chapter 9 May

23 Final essay due (please discuss your

proposed topic with me in advance) May 30

Final exam in class

Today

Unification in Particle Physics The Inflationary

Scenario

Brief History of Unification

1800s electricity magnetism given a unified

description in Maxwells theory of

Electromagnetism 1960s Electromagnetic weak

interactions unified in electroweak theory

(Glashow, Weinberg, Salam) 1970s Electroweak

strong interactions unified in Grand

Unified Theories 1980s-20?? Unify electroweak,

strong, and gravitational interactions in

Superstring Theory

well-tested

speculative

Higgs field breaks Electroweak Symmetry gives

mass to all particles

Last Undiscovered Ingredient of the

Standard Electroweak Model of Particle Physics

Fermilab or CERN

Beyond the Standard Model

(Bosons integral spin particles)

Electromagnetic

Grand Unified Theories

Electroweak (Standard Model)

Weak

Strong

Grand Unified Theories (GUTs) unify the first 3

3 interactions into a single symmetry, but leave

out gravity

Gravity

String Theory attempted unification of all 4

interactions

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Supersymmetry (SUSY)

Hypothetical symmetry between bosons (particles

with integer spin 0,1,2) and fermions

(particles with half-integer spin). Pros (1)

can help explain why there is such a huge

disparity in energy between the

electroweak and GUT or Planck scale

(2) grand unification of electroweak strong

forces at GUT scale appears more natural

in SUSY theory (running coupling) Puzzle Like

the electroweak symmetry, SUSY must be a broken

symmetry in Nature (we havent discovered

any of the predicted SUSY partner

particles yet). The mechanism of SUSY breaking

remains a mystery (its not due to a Higgs

field).

String Theory

Coupling Constants Of the Different

Interactions Unify at 1015 GeV in theory

w/ Supersymmetry

GeV

Theory of Everything

The Quantum Field Theory marriage of Quantum

Mechanics and (Classical) Fields has

generated an extraordinarily successful model

of Fundamental particles the Standard

(Electroweak) Model and Quantum Chromodynamics

(theory of Strong Interactions). However,

one field has so far resisted Quantization the

gravitational field. We do not yet have a

successful theory that marries Quantum

Mechanics with General Relativity. Quantum

Theory of the Gravitational Field is plagued with

unphysical infinities. As a result, we do

not have a Theory of Everything that unifies

Gravity with the 3 other fundamental

interactions. Superstring Theory is the current

(best) hope for realizing this.

Spacetime Foam

At a lengthscale LPlanck (hG/c3)1/2 10-33 cm,

the Planck length, the quantum fluctuations

of the gravitational field become large,

and the classical picture of a smooth(ly

distorted) spacetime breaks down (and with

it, our notions of space time). These violent

ultra-small-scale fluctuations lead to

infinities in the equations of quantum

gravity.

String Theory

Postulates that all particles are, at the

ultra-microscopic scale, not point-like but

instead are excitations of extended

1-dimensional strings. These strings have a

characteristic lengthscale of the Planck

length. The extended nature of the strings

smooths out the violent Planck-length

fluctuations of the gravitational field and

gets rid of the associated infinities. It turns

out that all the matter and charge carrier

particles can be described in terms of string

vibrational modes. String theory is thus a

candidate Theory of Everything that unifies all

the fundamental interactions in a single

theory.

Photon Gluon

10-31 mm

String

Features of Superstring Theory

Supersymmetry (SUSY) hypothetical symmetry

relating fermions (spin-1/2 particles) with

bosons (integral-spin particles). This

symmetry predicts existence of many new

particles, which may be discovered at

particle accelerators. SUSY is a natural

outcome of String Theory. Extra Dimensions

Superstring Theory naturally lives in 10

spacetime dimensions. Since we only observe

4, the other 6 must be hidden. Two choices

(a) they are very small, of order the

Planck length, or (b) we are confined to only 3

of the 9 space dimensions (3-d membrane).

Symmetry breaking Phase Transitions Cosmology

- As in a Ferromagnet, or as in ice ? water, at a

Temperature - above 100 GeV, the broken Electroweak

symmetry should - be restored the Higgs field is driven to zero

everywhere, and the - W,Z and all other matter particles become

massless. Conversely, - as Universe cools below 100 GeV, the Higgs

field - evolves away from zero to its non-zero

low-Temperature value. - Early Universe may have gone through several such

- Symmetry-breaking Phase Transitions associated

with different - Higgs fields. Depending on the type of

symmetry broken, such - transitions can have interesting consequences

for cosmology - Topological Defects
- Inflation
- Early Universe as a Laboratory for Symmetry

Unification

Potential energy density

High Temp.

High Temperature Symmetry is restored, ?

0. Low Temperature Symmetry is broken ?

or -

Low Temperature

?

Higgs field

Higgs Field

Cosmological effects of Phase Transitions also

depend on the speed of the transition (relative

to the expansion rate) Second order

transitions are fast (the field evolves

continuously from its high-Temperature to

low-Temp. state) First order transitions are

slower field must quantum tunnel through

an energy barrier and can get hung up in the

wrong

(high-Temperature) state

Potential Energy Density

Second-order transition

Low-Temperature state

High-Temperature state

Higgs field value

Cosmological effects of Phase Transitions also

depend on the speed of the transition (relative

to the expansion rate) Second order

transitions are fast (the field evolves

continuously from its high-Temperature to

low-Temp. state) First order transitions are

slower field must quantum tunnel through

an energy barrier and can get hung up in the

wrong

(high-Temperature) state

Potential Energy Density

Low-Temperature state

High-Temperature state

Higgs field value

Inflation

An epoch generally associated with some scalar

field that takes a cosmologically long time

to evolve to its (low-Temperature) ground

state. During this time, the potential energy

density of the Scalar field comes to dominate

over other forms of energy (e.g., in radiation

or massive particles) in the Universe. While the

field is stuck in its high-Temperature

state (or slowly evolving from it), the energy

density of the Universe is approximately

constant (rather than decreasing with time,

as it does during all other epochs). This

implies H constant (approximately) and that the

scale factor grows roughly exponentially in

time. This is the sign of an accelerating

Universe trapped field acts as a (temporary)

cosmological

constant.

The Inflationary Scenario

Theory arose 1980 (Alan Guth) from thinking

about the cosmological consequences of slow

symmetry-breaking Phase Transitions in the

early Universe. Motivations

horizon/homogeneity, flatness, and structure

problems. Why is the Universe homogeneous,

isotropic, and nearly flat? These are not

robust features of the standard cosmology.

How can large-scale structure form without

violating causality?

and Horizons

As the Universe ages, we see more and more

galaxies (other observers) at larger

distances Going back in time, we see a

smaller fraction of the Universe Other

observers were outside our horizon

radius a(t1) Cosmic Scale Factor

radius a(t2)

Horizons the CMB

COBE satellite showed that the Cosmic Microwave

Background radiation is isotropic to 1 part in

105 over the whole sky. This is a puzzle

different regions of the CMB separated by

more than 1 degree or so in angle were, at the

time of Photon decoupling/recombination (105

years after the Big Bang) outside each

others horizon, not yet in causal contact.

Theres no reason these causally disconnected

regions should have been at the same Temperature!

No physical process acting since the Big Bang

could have established this uniformity if it

wasnt there at the beginning. Why then does the

Universe appear isotropic homogeneous on

large scales? HORIZON PROBLEM

CMB Sky Points A and B separated by more than

few degrees were not in causal contact at

decoupling

Horizon of observer B at time of

decoupling

A

B

45o

Big Bang t0

Us, today

Photon Decoupling (Last Scattering

Surface) t 300,000 yr

Structure/Causality Problem

Another symptom of the Horizon problem The

Large-scale structures we see today were, at

early times, larger than the horizon. Thus, the

seeds for structure (density perturbations

which were amplified by gravity into

galaxies, etc) could not have been made

causally unless you wait until very late times

(and we have no theory of how to form seeds at

late times).

Flatness Problem

CMB observations indicate that the observable

Universe (within our present horizon) is nearly

flat ? 1 As the Universe evolves, the spatial

(3D) curvature generally becomes more

important with time Saddle universe (k -1)

rapidly becomes empty Spherical universe (k

1) should recollapse rapidly. Natural timescale

for these rapid events is the Planck time,

tPlanck LPlanck/c 10-43 seconds! But our

Universe still appears almost flat 1017 sec

1060 Planck times after the Big Bang. The

Universe must have been fine tuned to be

very precisely flat at the Planck time for it

still to be roughly flat today.

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Problems of Initial Conditions

Neither flatness nor homogeneity are robust

features of the standard cosmological model

they are unstable conditions. If the early

Universe had been slightly more curved or

inhomogeneous, then it would look much

different today. The present state of the

observable Universe appears to depend

sensitively on the initial state. If we consider

an ensemble of Universes at the Planck

time, only a tiny fraction of them would

evolve to a state that looks like our Universe

today. Our observed Universe is in some (hard

to quantify) sense very improbable.

God may not play dice, but perhaps S/He throws

darts...

Each point in the green dart board represents

the initial condition for a possible Universe

Us, now

today

time

Big Bang t tPlanck

Most Universes look less less like ours does as

they age God must have been extremely lucky or

able to have made our Universe.