String Theory and Inflation The start of a beautiful relationship C P Burgess Outline 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 Outlook 2 Strings and Inflation String 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 3 Strings and Inflation String 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 4 Strings and Inflation Possible 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 theory 5 mexp 0 000000000 005 mth 0 00000000 Strings and Inflation Gauss 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 6 Strings and Inflation How Long is a String Electromagnetism for r a for r a Effective 4d coupling Q A0 n 1 r Q A0 n a r eff n Gravity GM r n 1 GM h00 n a r h00 a Geff G n a In string theory G and are related to the string coupling and length ls eff 8 ns n n 0 01 a a Geff G 2 ns n n a a 2 s 10 19 fm 2 Strings and Inflation An 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 e 9 Strings and Inflation D Branes Polchinski 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 10 Strings and Inflation Why Do This Good Things Happen if the theory has both strings and Dbranes 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 strongcoupling 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 11 Strings and Inflation Brane 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 12 Strings and Inflation 4D Couplings Revisited The point Being trapped on a p dimensional brane changes how but not G depends on and ls eff l p 3 a a p 3 s p 3 Geff 2 n G l s 2 n ls n a a So if p 3 for example we have Geff n l eff2 s l 2s a Experiments no longer require ls to be so small 13 Strings and Inflation Strings In Your Face Arkani Hamad Dvali Dimopoulos 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 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 15 2 n eff l s l s a l pl Why is the heirarchy a ls so large Strings and Inflation Intermediate Scale Strings CB Ibanez Quevedo Q Can ls and a be similar in size A Yes ls a 0 01 works if I ls lw lp 10 11 fm eff ls 0 01 a 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 l pl l lw l 2 pl 2 s n 2 l s eff a String axions can solve strong CP problem neutrino masses similar to experiments etc 16 Strings and Inflation String Summary String theory is the only known theory where gravity and quantum mechanics co exist at high energies Major Lesson of the 20th Century Relativity and Quantum mechanics are almost inconsistent and so together impose extremely strong self consistency conditions The string length is likely much longer than the Planck length Size Matters much better prospects for comparison with experiments The intermediate scale is well motivated on particle physics grounds ls lw lp 10 11 fm We may all be Brane bound 17 Strings and Inflation Outline 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 Outlook 18 Strings and Inflation Motivations for Inflation The Hot Big Bang Model provides a very successful description of the observed Universe at large Described by expansion of universe R t Requires unnatural initial conditions Flat homogeneous isotropic 19 Strings and Inflation Acausal Correlations Initial correlations cannot be causally understood in the Hot Big Bang since in the past they were not in causal contact with one another Light has not yet had time to travel across the sky