String Theory and InflationOutlineString Theory: the ideaString Theory: the interactionsPossible DownsidesGauss’ Law in D DimensionsHow Long is a String?An Aside on Magnetic MonopolesD-BranesWhy Do This?Brane vs Bulk States4D Couplings RevisitedSlide 15Intermediate-Scale StringsString SummarySlide 18Motivations for InflationAcausal Correlations?InflationBonus!The Devil is in the Details…Slide 24String Theory and Inflation?Brane InflationThe Brane GasSlide 28OutlookPerhaps a beautiful relationship….….…..and a classic ending.String Theory and InflationThe start of a beautiful relationship?C.P. BurgessStrings and Inflation2Outline•String Theory•A Theory looking for observations.•The D-Brane revolution.•What is the String Scale?•Inflation•Cosmic initial conditions and fluctuations.•Phenomenology looking for a theory.•Inflation in String Theory?•Braneless attempts.•Brane Inflation?•OutlookStrings and Inflation3String Theory: the idea•All matter consists of small one-dimensional objects (strings).•Strings look like particles when not resolved closely enough•All particle types are different normal modes of the string.Strings and Inflation4String Theory: the interactions•All interactions consist of the splitting and joining of these elementary strings.•This is the only known sensible description of the scattering of gravitational waves at very high energies!•Looks like General Relativity plus other interactions at low energies.•No parameters: string length sets units.Strings and Inflation5Possible Downsides•At first sight there appeared to be a number of different kinds of string theories.•Open, closed, heterotic, Type I, Type IIA,...•Predicts we live in 10 spacetime dimensions!•Experimental update: number of (large) dimensions = 4•Very difficult to experimentally test so far.•Strings are so short that once the symmetries and spectrum are gotten right, most of the details are usually also right.•Calculation gets known masses right, but…..•experiment mexp = 0.000000000…………….…005•theory mth = 0.00000000Strings and Inflation6Gauss’ Law in D Dimensions•String properties are inferred from the strength of gravity and electromagnetic interactions in 4 dimensions.•String theory predicts these in 10 dimensions.•The connection depends on the size of the extra dimensions, since Coulomb’s and Newton’s Inverse-Square Laws reflect the spread of flux into space.•Force law falls faster in higher dimensions because there is more space over which to spread flux.Strings and Inflation8How Long is a String? for r « a:for r » a:Effective 4d coupling:Electromagnetism Gravity10nrQA100nrMGhraQAn0raMGhn00effanGeffGan01.0nnsneffaa 21922fm10snnsneffaaGG In string theory G and  are related to the string coupling  and length ls.Strings and Inflation9An Aside on Magnetic Monopoles•Field theories can involve more states than are indicated by the fields they involve.•For example: QED has fields for electrons, positrons and photons, but it can also describe these interacting with very massive magnetic monopoles. •M = /•Monopoles arise as solitons of the other fields, and are not described by fields of their own. •g = 4/eStrings and Inflation10D-Branes•String theory is bigger than previously thought. •Normally, open strings satisfy Neumann boundary conditions, •string ends move at light speed.•Dirichlet boundary conditions also make sense•string ends live on a surface.•This surface is interpreted as a large massive object, a D-brane, in spacetime, much like a monopole.PolchinskiStrings and Inflation11Why Do This?•Good Things Happen if the theory has both strings and D-branes:•Previously-hidden duality symmetries emerge, with all known string theories dual to one another under these symmetries!•Some weakly-interacting string theories are the duals of the strong-coupling limit of others!•Led to discoveries of similar symmetries amongst ordinary particle theories.•Conjecture: all known string theories are different solutions to a more fundamental (11-dimensional) theory (M Theory).Strings and Inflation12Brane vs Bulk States •Important Brane Facts:•At low energies some states are trapped to live near the Brane•eg: Open strings terminating on a Brane.•Other states - Bulk states - can ramble: •eg: Closed strings, including gravitons.•Trapping is not really so weird.•Similar to the trapping of ‘zero modes’ on defects like vortices and domain walls in solids.•Brane-World Scenario: All known particles are so trapped.Strings and Inflation134D Couplings Revisited•The point: Being trapped on a p-dimensional brane changes how  (but not G) depends on  and ls effap 3lsp 3ap 3 GeffGan2lsnanls2So if p=3 (for example) we haveExperiments no longer require ls to be so small! Geffeff2lsanls2Strings and Inflation15Strings In Your Face•Could strings be as big as they can be: ls = lw? •Non-gravitational physics is characterized by the weak scale:GF = lw2 = (10-3 fm)2•If so, strings may be experimentally discovered ‘tomorrow’! •If so, does this explain why lw is so much larger than lp = 10-19 fm?•ie: Why is gravity so weak? Why are stars so big?Why is the heirarchy a/ls so large? a efflslpl2 / nlsArkani-Hamad, Dvali & Dimopoulos•Gravity would be weak because the extra dimensions are large:If n = 2 then ls = lw requires a ~ 0.1 mm!! If n = 6 then ls = lw requires a ~ 105 fm,Strings and Inflation16Intermediate-Scale Strings•Q: Can ls and a be similar in size?•A: Yes. ls / a = 0.01 works if:•I: ls = √(lw lp) =10-11 fm. • lw = ls2 / lp naturally arises if supersymmetry breaks on another brane, and is transmitted to our brane by gravity.•II: n = 6 extra dimensions.•No heirarchy need be dialed in.•Other nice things also happen if so:String axions can solve strong CP problem, neutrino masses similar to experiments, etc lpllwlpl2ls2eff2lsan efflsa0.01CB, Ibanez & QuevedoStrings and Inflation17String Summary•String theory is the only known theory where gravity and quantum mechanics co-exist at high energies.•Major Lesson of the 20th