intro to inflationary cosmologyphysics.ipm.ac.ir/conferences/ieuc/notes/basset1.pdf · intro to...

“Times are bad. Children no longer obey their parents and everyone is writing a book.”

Cicero, 43 BC

Intro to Inflationary Cosmology Bruce A. Bassett

y gySAAO & UCT

Cosmic Problem 1 : IsotropyCOBE satellite

Size of causal domain atThe formation of the CMB

The 4 LecturesThe 4 Lectures

1 O i f i fl i1. Overview of inflation

2. Structure formation

3. Reheating and Preheating

4. Comparing with observations4. Comparing with observations

Setting the SceneSetting the Scene

• The aims of these lectures – why are we all here?here?

• My recommendations to you

Th h j t• The research project

What is the point of a school?What is the point of a school?

• To learn specific knowledge to enable you to• To learn specific knowledge, to enable you to begin research (in this case in inflation)

• To inspire and moti ate• To inspire and motivate

• Challenge your prior beliefs

• To expand your mind by dealing with complex ideas

What is the point of a school? ‐ IIWhat is the point of a school? II

• Learn to think more critically, objectively andLearn to think more critically, objectively and creatively

• Learn to ask the right questions…g q

• To allow you to see that you can, with work, do good, perhaps even world‐leading, researchp p g

• To help you establish research networkswhich are crucial to success in academia.

My Recommendations IMy Recommendations ‐ I

T l 25 l hi h l• Try to meet at least 25 new people at this school, chat to the lecturers, swap emails, facebook, twitter etc These new friends will help you travel answeretc… These new friends will help you travel, answer questions, help get grants & jobs and be your collaborators

• Sit next to new people every session. Say “hello!” BeSit next to new people every session. Say hello! Be curious and friendly. There is lots of cultural, as well as scientific, knowledge to be gained

My Recommendations ‐ IIMy Recommendations II

• Ask lots of questions There are no stupidAsk lots of questions. There are no stupid questions…don’t worry about your English

• If you prefer write the questions down and giveIf you prefer, write the questions down and give them to the speaker at the end of the lecture

• Lets agree to be very informal and friendly and to learn as much as possible from each other!learn as much as possible from each other!

My Recommendations ‐ IIIMy Recommendations III• Try to guess what is coming next in the lectures…this

ill hi hli h h d d ’ d dwill highlight what you do or don’t understand.

• Ask yourself “What has to happen for me have a really successful school?” How do you make it happen for you?happen for you?

B ti ! Th l t ill t t th i ht• Be proactive! The lectures will not go at the right pace for you, so you need to make up the difference.

The Research ProjectThe Research Project

• We will have a research project, which is open for everyone to p j , p yjoin.

• It will be an opportunity to work on a real research project hi h b bli h d t th dwhich may be published at the end.

• A very good way to learn something is to work with people who already know it…it will also teach team skills, help build a y , presearch network, new collaborations, confidence etc…

• We will introduce it and work on it after the discussion isessions

ReferencesReferences

• I will mostly base my 4 lectures on the review astro‐ph/0507632 (Rev. Mod. Phys)– This will set notation, units etc…– Lots of other good reviews on the arxiv (Brandenberger, …)ots o ot e good e e s o t e a ( a de be ge , )

• Basic Intros: Liddle’s “An Introduction to Modern Cosmology”– Liddle s An Introduction to Modern Cosmology

– My book “Introducing Relativity” (conceptual only)

• Good graduate references are• Kolb and Turner “The Early Universe”• Mukhanov “Physical Foundations of Cosmology”P k W i b t• Peacock, Weinberg, etc…

http://abductit.com/files/articles/3d_art/image_01.jpg

This lectureThis lecture

• The FLRW universe• Problems of the FLRW cosmos• Inflation• How inflation solves the standard problems• Slow‐roll inflation and models of inflation• Quantum fluctuations and galaxies• Reheating after inflationOb i l f i fl i• Observational tests of inflation

• Problems with inflation

Friedmann‐Lemaitre‐Robertson‐lk ( )Walker (FLRW) Geometry

Isotropic and Homogeneous‐ Isotropic and Homogeneous

‐ As a result, the scale factor (size of the universe), onlydepends on time, a = a(t).

Isotropy: observed

NVSSNVSS

sources

http://www.cv.nrao.edu/course/astr534/ExtraGalactic.html

Zoom in of the 15 deg near the North Celestial pole

But homogeneity has NOT yet been proven!proven!

• We could live at the centre of a spherically p ysymmetric (hence isotropic) universe

The Einstein Equations( )(Dynamics)

FLRW DynamicsFLRW Dynamics

Friedmann EquationFriedmann Equation

Acceleration (Raychaudhuri)Equation

H bbl R tHubble Rate

Friedmann Equation RewrittenFriedmann Equation Rewritten


• The FLRW universe• Problems of the standard FLRW cosmos• Inflation• How inflation solves the standard problems• Slow‐roll inflation and models of inflation• Quantum fluctuations and galaxies• Reheating after inflationOb i l f i fl i• Observational tests of inflation


Problems in Standard CosmologyProblems in Standard Cosmology

H i d I h it P bl• Horizon and Inhomogeneity Problem

• Flatness Problem

• Relic problem

• Super‐Hubble Fluctuation problem

COBE satellite

Size of causal domain atThe formation of the CMB

InflationInflation

• Inflation is simply accelerated expansionat o s s p y acce e ated e pa s o

• This requires

• The simplest case is de Sitter expansion [H = constant. How does a(t) behave in this case?]constant. How does a(t) behave in this case?]

Inflationary Solutions to the…Inflationary Solutions to the…

H i d I h it P bl• Horizon and InhomogeneityProblem

• Flatness Problem

• Relic problem

• Super‐Hubble Fluctuation problem

Slow‐roll inflationSlow roll inflation

• How do we violate the strong energyHow do we violate the strong energy condition to get:

• The simplest way is by using scalar fields, p y y g ,which satisfy the generalised Klein‐Gordon eq.

Scalar fields continued…Scalar fields continued…• They behave as perfect fluids in FLRW with:

• Pressure:)(

2

φφ Vp −=&

E d it

)(2

φVp =

2φ&• Energy density: )(2

φφρ V+=

A l ti d• Acceleration needs

Challenge: how do we achieve acceleration for a long period?

Slow‐roll parametersSlow roll parameters

Exercise: Convince yourself that slow‐roll is equivalent to demanding that Each of the slow‐roll parameters is << 1.

Inflationary ‘Prediction’ for the Cosmic Microwave Background Fluctuations

THE CMB

COBE 96)C

lL(l

+1)

L

2 10 100 1000

l

COBEQMASK

)Cl

L(l+1

) L

2 10 100 1000

l

FLATNESS!

COBEQMASKBOOMERanG 00

)Cl

L(l+1

) L

2 10 100 1000

l

COBEQMASKBOOMERanGMAXIMA

)Cl

L(l+1

) L

2 10 100 1000

l

COBEQMASKBOOMERanGMAXIMACBI 03)C

l

CBI 03

L(l+1

) L

2 10 100 1000

l

COBEQMASKBOOMERanGMAXIMACBI 03)C

lDid not showBICEPTOCOACBARCBI 03

WMAP‐5

L(l+1

) ACBARVSASASKATOONARCHEOPSL DASIPYTHONFIRSTenerife

2 10 100 1000

TenerifeOVROSUZIESP

lATCAetc…

So Inflation is looking good…

But so would any other scenario that produces a near scale‐invariant spectrum of adiabatic fluctuations in a nearly flat universe…

Some of my problems with inflationSome of my problems with inflation

• Inflation uses only semi‐classical gravity. Should we really y g y yexpect to solve everything without needing to know the full quantum theory of gravity?

• Does inflation really solve the flatness and horizon problems (and other issues around initial conditions)?

• Is inflation falsifiable, or is there so much freedom in the model‐building we could fit anything?

• There are also lots of technical issues (eta problem etc…)

Simple Model BuildingSimple Model Building

• Chaotic Inflation• Chaotic Inflation

• Small‐field inflation (including old inflation)Small field inflation (including old inflation)

• Hybrid inflationHybrid inflation

• Multiple‐phase inflationp p

• Etc…

HybridInflation

Calculate the critical value, φc

Quantum Fluctuations & Large Scale Structureg

• We want to be able to predict what the CMB andWe want to be able to predict what the CMB and galaxy distribution will look like in any inflationary model

This involves a number of steps:This involves a number of steps:

1 Why and what kind of quantum fluctuations are produced?1. Why and what kind of quantum fluctuations are produced?

2. How do they affect the metric?

3. How do the quantum fluctuations become classical galaxies?3. How do the quantum fluctuations become classical galaxies?

intro to inflationary cosmologyphysics.ipm.ac.ir/conferences/ieuc/notes/basset1.pdf · intro to...

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