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The Nuts and Bolts of Inflation Richard Barrett 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 Seminar Glasgow 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-one’s seen it) Dark Energy Seminar Glasgow 29/11/2003 Inflation Why was inflation ‘invented’? Inflation invented by Alan Guth in 1981 to solve some serious problems with ‘standard’ cosmology: • The horizon problem • The flatness problem Happens in the very early universe Now known to be important at the present epoch Dark Energy Seminar Glasgow 29/11/2003 Inflation The horizon problem How do we explain the isotropy of the CMBR, when opposite sides of the sky were ‘causally disconnected’ when the CMBR photons were emitted? Dark Energy Seminar Glasgow 29/11/2003 From Guth (1997) time Our world line Now Our past light cone A Big Bang B CMBR space 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 Seminar Glasgow 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 Dark Energy Seminar Glasgow 29/11/2003 Solution (first proposed by Alan Guth in 1981) is… INFLATION …a period of accelerated expansion in the very early universe. Inflationary solution to the Horizon Problem Limit of observable Universe today INFLATION Small, causally connected region From Guth (1997) Inflationary solution to the Flatness Problem From Guth (1997) 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 Seminar Glasgow 29/11/2003 Inflation More mass (density) = more spacetime curvature: Flat space Dark Energy Seminar The sun Neutron star Black hole Glasgow 29/11/2003 Inflation More curvature means stronger attraction: Dark Energy Seminar Glasgow 29/11/2003 Inflation Basic gravity physics: the EP The Equivalence Principle (EP) says • 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 Dark Energy Seminar Glasgow 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 Seminar Glasgow 29/11/2003 Inflation Gas elements Forces No net force Net force = Pressure Position Dark Energy Seminar Position Glasgow 29/11/2003 Inflation Basic gravity physics: pressure • In a homogeneous universe pressure is the same everywhere pressure doesn’t push matter at all Can’t make matter expand using pressure Dark Energy Seminar Glasgow 29/11/2003 Inflation Basic gravity physics: pressure Does pressure have any effect? • Pressure = Energy • Energy = Mass (E = mc2 ) • Mass generates gravity that’s attractive • So: pressure makes matter attract itself High pressure slows the expansion of the universe Dark Energy Seminar Glasgow 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 mv2) • Also works for photons, by special relativity (E = cp) Dark Energy Seminar Glasgow 29/11/2003 Inflation Inflating the universe • What if we could make matter (‘gas’) with negative pressure? • Would generate gravity that’s repulsive • Universe would expand even faster INFLATION Dark Energy Seminar Glasgow 29/11/2003 Inflation Inflating the universe • Not possible with ‘normal’ matter • Need something a bit exotic A SCALAR FIELD (Physically scalar field isn’t 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 Seminar Glasgow 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 Seminar Glasgow 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 Tab • Einstein’s equations are Gab = 8Tab (CURVATURE = MATTER DENSITY) • Tab has the same form for gases and scalar fields • Scalar fields are only like gases in terms of their gravity Dark Energy Seminar Glasgow 29/11/2003 Inflation Normal gas: Tab = (+p)uaub + pgab Scalar field: Tab = a b Energy part - [a a/2 + V()]gab Pressure 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 Seminar Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 29/11/2003 Inflation Spontaneous Symmetry Breaking • V() has a minimum at = 0 before SSB • V() has a minimum at > 0 after SSB • quantum tunnels from 0 to the new minimum Original inflation Dark Energy Seminar Slow-roll inflation Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 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 Seminar Glasgow 29/11/2003 Inflation Branes and inflation Brane cosmology simulation Dark Energy Seminar Glasgow 29/11/2003
