Intro to Inflationary Cosmology

Times are bad. Children no longer obey their parents and everyone is writing a book. Cicero, 43 BC Bruce A. Bassett Intro to Inflationary Cosmology SAAO & UCT

Cosmic Problem 1 : Isotropy COBE satellite Size of causal domain at The formation of the CMB

The 4 Lectures 1. Overview of inflation i 2. Structure formation 3. Reheating and Preheating 4. Comparing with observations

Setting the Scene The aims of these lectures why are we all here? My recommendations to you The research project

What is the point of a school? To learn specific knowledge, to enable you to begin research (in this case in inflation) To inspire and motivate Challenge your prior beliefs To expand your mind by dealing with complex ideas

What is the point of a school? II Learn to think more critically, objectively and creatively Learn to ask the right questions To allow you to see that you can, with work, do good, perhaps p even world leading, research To help you establish research networkswhich are crucial to success in academia.

My Recommendations I 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, answer questions, help get grants & jobs and be your collaborators Sit next to new people every session. Say hello! Be Sit 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 II Ask lots of questions. There are no stupid questions don t worry about your English If 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 learnas as much as possible from each other!

My Recommendations III Try to guess what is coming next in the lectures this will highlight hli h what you do or don t understand. d Ask yourself What has to happen for me have a really successful school? How do you make it 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 Project We will have a research project, which is open for everyone to join. It will be an opportunity to work on a real research project which h 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 research network, new collaborations, confidence etc We will introduce it and work on it after the discussion sessions

References 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 e son the ea arxiv (Brandenberger, ) Basic Intros: 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 Peacock, Weinberg, Wib etc

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This 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 inflation Observational tests of inflation i Problems with inflation

Friedmann Lemaitre Robertson Walker (FLRW) Geometry Isotropic and Homogeneous As a result, the scale factor (size of the universe), only depends on time, a = a(t).

Isotropy: observed NVSS 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! We could live at the centre of a spherically symmetric (hence isotropic) universe

The Einstein Equations (Dynamics)

FLRW Dynamics Friedmann Equation Acceleration (Raychaudhuri) Equation Hubble Rt Rate

Friedmann Equation Rewritten

This lecture 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 inflation Observational tests of inflation i Problems with inflation

Problems in Standard Cosmology Horizon and Inhomogeneity Problem Flatness Problem Relic problem Super Hubble Fluctuation problem

Size of causal domain at The formation of the CMB COBE satellite

Inflation Inflation is simply pyaccelerated e ated expansion epaso This requires The simplest case is de Sitter expansion [H = constant. How doesa(t) behaveinthiscase?]

Inflationary Solutions to the Horizon and InhomogeneityProblem Flatness Problem Relic problem Super Hubble Fluctuation problem

Slow roll inflation How 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 They behave as perfect fluids in FLRW with: Pressure: 2 φ p = & VV 2 ( φ ) Energy density: &2 φ ρ = + V ( φ) 2 Acceleration needs

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

Slow 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 L(l+1) C l 2 10 100 1000 l

COBE QMASK L(l+1) C l 2 10 100 1000 l

FLATNESS! COBE QMASK BOOMERanG 00 L(l+1) C l 2 10 100 1000 l

L(l+1) C l COBE QMASK BOOMERanG MAXIMA 2 10 100 1000 l

C l L(l+1) COBE QMASK BOOMERanG MAXIMA CBI 03 2 10 100 1000 l

C l L (l+1) l COBE QMASK BOOMERanG MAXIMA CBI 03 WMAP 5 2 10 100 1000 Did not show BICEP TOCO ACBAR VSA SASKATOON ARCHEOPS DASI PYTHON FIRS Tenerife OVRO SUZIE SP ATCA etc

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 inflation Inflation uses only semi classical gravity. Should we really expect 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 Building Chaotic Inflation Small field inflation (including old inflation) Hybrid inflation Multiple phase p inflation Etc

Hybrid Inflation Calculate the critical value, φ c

Quantum Fluctuations & Large Scale Structure We 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: 1. Whyand what kind of quantum fluctuations are produced? 2. How do they affect the metric? 3. How do the quantum fluctuations become classical galaxies?