The Nuts and Bolts of Inflation Richard Barrett

Dark Energy SeminarGlasgow 29/11/2003 Inflation What is inflation? What is dark energy? Why was inflation invented? Some basic gravity physics The physics of inflation Sources of dark energy Branes and inflation

Dark Energy SeminarGlasgow 29/11/2003 Inflation Inflation is Any time when expansion of universe accelerates Originally meant inflation in the very early universe but now applies also to current inflationary epoch Both caused by same thing (scalar fields) The scalar field causing inflation now is called dark energy (because no-ones seen it)

Dark Energy SeminarGlasgow 29/11/2003 Inflation Why was inflation invented? The horizon problem The flatness problem Inflation invented by Alan Guth in 1981 to solve some serious problems with standard cosmology: Now known to be important at the present epoch Happens in the very early universe

Dark Energy SeminarGlasgow 29/11/2003 Inflation How do we explain the isotropy of the CMBR, when opposite sides of the sky were causally disconnected when the CMBR photons were emitted? The horizon problem

From Guth (1997)

CMBR Big Bang time space Our world line Now A B Our past light cone

Dark Energy SeminarGlasgow 29/11/2003 Inflation The flatness problem In standard cosmology: =1 means universe is flat If 1, moves quickly away from 1 after big bang Today universe is close to flat

Dark Energy SeminarGlasgow 29/11/2003 Inflation Present day closeness of matter density to the critical density appears to require an incredible degree of fine tuning in the very early universe. This is the FLATNESS PROBLEM

Solution (first proposed by Alan Guth in 1981) is… INFLATION …a period of accelerated expansion in the very early universe.

Small, causally connected region Limit of observable Universe today INFLATION Inflationary solution to the Horizon Problem From Guth (1997)

Inflationary solution to the Flatness Problem From Guth (1997)

Dark Energy SeminarGlasgow 29/11/2003 Inflation Basic gravity physics: matter and gravity No force field for gravity: matter falls freely through (curved) spacetime BUT: matter generates the curvature Normal matter always makes curvature that causes two objects to move towards each other gravity is always attractive

Dark Energy SeminarGlasgow 29/11/2003 Inflation More mass (density) = more spacetime curvature: Black holeThe sunNeutron starFlat space

Dark Energy SeminarGlasgow 29/11/2003 Inflation More curvature means stronger attraction:

Dark Energy SeminarGlasgow 29/11/2003 Inflation Basic gravity physics: the EP All matter moves in the same way under gravity (because gravity is just the shape of spacetime) So, if some matter generates gravity, all other matter feels it The Equivalence Principle (EP) says

Dark Energy SeminarGlasgow 29/11/2003 Inflation Basic gravity physics: pressure Normal cosmic matter is a gas with pressure (just like air pressure on earth): the gas pushes on itself Only pressure gradients give a net force on gas

Dark Energy SeminarGlasgow 29/11/2003 Inflation Gas elements No net forceNet force = Forces Pressure Position

Dark Energy SeminarGlasgow 29/11/2003 Inflation Basic gravity physics: pressure In a homogeneous universe pressure is the same everywhere pressure doesnt push matter at all Cant make matter expand using pressure

Dark Energy SeminarGlasgow 29/11/2003 Inflation Pressure = EnergyPressure Energy = Mass (E = mc 2 ) Mass generates gravity thats attractive So: pressure makes matter attract itself Basic gravity physics: pressure Does pressure have any effect? High pressure slows the expansion of the universe

Dark Energy SeminarGlasgow 29/11/2003 Inflation Gas particles move (they have momentum) Momentum transferred to walls gives force BUT: Moving particles have kinetic energy too (E = 1/2 mv 2 ) Also works for photons, by special relativity (E = cp)

Dark Energy SeminarGlasgow 29/11/2003 Inflation Inflating the universe What if we could make matter (gas) with negative pressure? Would generate gravity thats repulsive Universe would expand even faster INFLATION

Dark Energy SeminarGlasgow 29/11/2003 Inflation Inflating the universe Not possible with normal matter Need something a bit exotic A SCALAR FIELD (Physically scalar field isnt really like a gas, it only makes curvature in the same way as a gas, but like a gas with negative pressure would)

Dark Energy SeminarGlasgow 29/11/2003 Inflation The physics of inflation Field means something that is distributed smoothly through space (like electric field), rather than made of particles Scalar just means the value of the field at any point is just a number (in contrast, the electric field is like an arrow at each point) Call this value. can vary from place to place and from time to time: = (x,t)

Dark Energy SeminarGlasgow 29/11/2003 Inflation The physics of inflation How does a scalar field generate curvature (gravity)? All matter generates gravity through its stress-energy tensor T ab Einsteins equations are G ab = 8 T ab (CURVATURE = MATTER DENSITY) T ab has the same form for gases and scalar fields Scalar fields are only like gases in terms of their gravity

Dark Energy SeminarGlasgow 29/11/2003 Inflation Scalar field:T ab = a b - [ a a /2 + V( )]g ab Normal gas:T ab = ( +p)u a u b + pg ab Energy partPressure part The important bit is V( ), the scalar potential. Its value at any point just depends on It does exactly what pressure p does for gases For gases p must be positive, BUT: V( ) can have any value at all We get negative pressures with the right V( )

Dark Energy SeminarGlasgow 29/11/2003 Inflation The physics of inflation To get inflation we need V( ) to be large. How can this happen? Spontaneous Symmetry Breaking (in the very early universe) Scalar fields (dilatons) predicted by string theory can have inflationary potentials

Dark Energy SeminarGlasgow 29/11/2003 Inflation Spontaneous Symmetry Breaking At high energies (early universe) laws of physics have high symmetry At lower energies the preferred state has less symmetry Some scalar field that previously was at the minimum of V( ) is now not at the minimum The scalar field has vacuum energy, V( ) > 0 moves to the new minimum and symmetry is broken This is a phase transition Inflation occurs

Dark Energy SeminarGlasgow 29/11/2003 Inflation Spontaneous Symmetry Breaking Original inflationSlow-roll inflation V( ) has a minimum at = 0 before SSB V( ) has a minimum at > 0 after SSB quantum tunnels from 0 to the new minimum

Dark Energy SeminarGlasgow 29/11/2003 Inflation The cosmological constant Original explanation of inflation was in term of the cosmological constant This is just like a scalar field = that is constant everywhere at all times Gives pressure p = -

Dark Energy SeminarGlasgow 29/11/2003 Inflation Sources of dark energy Observational evidence (SNIa, CMBR, SDSS, ) provides a consistent picture: the expansion is accelerating We must have a scalar field in action This is the mysterious dark energy Where does it come from?

Dark Energy SeminarGlasgow 29/11/2003 Inflation Sources of dark energy Spontaneous symmetry breaking phase transition (like in the early universe)? String theory: all predict a scalar field (the dilaton) in the low-energy limit that could act as an inflaton Branes: string theory also suggests that our universe is a brane in a higher dimensional space, and that a scalar field that could cause inflation

Dark Energy SeminarGlasgow 29/11/2003 Inflation Branes and inflation String theories predict universe actually has 4 space dimensions Our universe is a 3D brane moving in this 4D bulk (a 3D sheet floating in 4D space) Gravity propagates in the bulk (4D), other forces only on the brane The inflaton scalar field comes from the part of gravity propagating through the bulk

Dark Energy SeminarGlasgow 29/11/2003 Inflation A brane is soliton (a stable solution of the string theory equations where matter and the nongravitational fields are nonzero only in a very thin layer) All the physics that we are familiar with happens on this brane

Dark Energy SeminarGlasgow 29/11/2003 Inflation Branes and inflation In one string theory the universe is a 4D bulk with a 3D brane at each end: One brane is the real universe, the other a mirror world We are aware of the mirror world only through its gravity This gravity looks like a scalar field to us The two branes can get closer together (and even cross over) This gives rise to the cyclic model of Steinhardt and Turok

Dark Energy SeminarGlasgow 29/11/2003 Inflation Branes and inflation Brane cosmology simulation