1 Cosmic Inflation Tomislav Prokopec ITP UU WMAP

˚ 1˚ Cosmic Inflation Tomislav Prokopec (ITP, UU) WMAP 3 y 2006 Utrecht Summer School, 28 Aug 2009

˚ 2˚ Big Bang

˚ 3˚ Roadmap to Inflation NOT WHAT WE MEAN: Inflation is a rise in the general level of prices, as measured against some baseline of purchasing power Massive objects attract each other gravitationally. Therefore, a 13. 7 billion old universe should appear very wrinkled & clumpy ALAN GUTH (1981) (& Alexei Starobinskii): realised that a period of an accelerated expansion in an early Universe (@ ~10^-36 s) can smooth out the initial wrinkles: GRAVITY EFFECTIVELY REPULSIVE FORCE SDSS galaxy catalogue (2004) How to get repulsive GRAVITY in Lab? We need a ‘matter’ with positive energy (ρ>0) and negative pressure (P<0) (w. r. t. vacuum) Alchemist Laboratory (Hamburg 1595) ρ>0, P<0 (ρ+3 P<0)

˚ 4˚ Inflation in Lab? How to get repulsive GRAVITY in Lab? WORK: δW=-Fδs= PδV<0 Alchemist Laboratory (Hamburg 1595) work done on the system (rubber, chewing gum, iron) Q: But, who pulls the Piston (in the Universe)? A: Gravity itself (if filled e. g. with repulsive scalar matter)? Friedmann equation (FLRW): ACTIVE GRAVITATIONAL ENERGY (MASS): active= +3 P<0 sources the Newtonian Force in Einstein’s theory the Universe expands in an accelerated fashion

Inflation in a theorist´s head RECIPE: ˚ 5˚ TAKE A SCALAR FIELD PROCESS IT WITH COVARIANT ACTION KICK IT REAL HARD WAIT SEC AND WATCH ATTENTIVELY! Andrei Linde SLOW ROLL REGIME: Chaotic inflationary model (Linde 1982) (exponentially expanding universe) EQUATION OF STATE

Inflatiomatica Inflation solves many cosmologist’s headaches (1) Homogeneity and isotropy problem (Einstein’s cosmological principle, 1930 s) 2 d. F galaxy survey (2) flatness problem (curvature radius > 30 Gpc) (3) causality problem (CMB sky: ~4000 domains) (4) Size & age problem (13. 7 billion years) (5) Cosmological relics (monopoles, strings, . . ) (6) Seeds formation of stars, galaxies & large scale structure by creating cosmological perturbations: primordial gravitational potentials CLOSE OPEN FLAT ˚ 6˚

Cosmological perturbations ˚ 7˚ Amplification of vacuum fluctuations of matter and gravitational potentials in inflation The amplitude of vacuum fluctuations of a field is expected to decrease as A ~1/R, where R is the size (wavelength) of the fluctuation. During inflation however, the amplitude A stops decreasing as wavelengths grow larger than the Hubble radius RH = c/H: Hubble parameter H=(1/a)da/dt measures the expansion rate. FREEZING IN of vacuum fluctuations corresponds to amplification! CURVATURE PERTURBATION (gravitational potential):

Evolution of scales in the Universe ˚ 8˚ During inflation space (& particle’s wavelenghts) get stretched enormously: small scales during inflation can correspond to astronomical scales today STANDARD ‘WISDOM’: Primordial gravitational potentials appear as stochastic random field with gaussian distributed amplitude and random phases (in momentum space) (this is used in studies of large scale structure & CMB and tests inflation)

Evidence for inflation ˚ 9˚ "Relevant evidence" means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence. (1) Nearly scale invariant and gaussian power spectrum of cosmological perturbations ☺Predicted by inflation (Chibisov, Mukhanov, 1981) SPECTRUM: (2) Spatial sections appear flat (curvature radius > 25 Gpc) WMAP 3 y scalar CMBR spectrum TOTAL ENERGY DENSITY CONSISTENT WITH CRITICAL CLOSE (3) IN FUTURE we hope to detect primordial gravitational waves (Planck) OPEN NB: NO DIRECT EVIDENCE AT THIS MOMENT FLAT

˚ 10˚ CMB spectrum WMAP 3 y scalar CMBR spectrum

2006 Nobel Laureates George Smoot(h), LBL, Berkeley ˚ 11˚ John C. Mather, NASA COBE Satellite: FIRAS DMR

Geometry and the fate of the Universe Measuring the energy (mass) content of the Universe, determines its fate: Dominant energy components are: DARK MATTER: 21% of crit. DARK ENERGY: 75% of crit. BARYONIC MATTER: ~5% - Visible matter (stars, . . ) Neutrinos, photons, . . : <1% NB: crit. -> FLAT universe size a of Universe ˚ 13˚

˚ 14˚ Geometry and temperature fluctuations in CMBR The largest triangle in the Universe is FLAT (flat spatial sections: sum angles=180°) Last scattering surface Temperature fluctuations in primordial photons (CMBR, WMAP satellite 2006)

˚ 15˚ “The great bird will take its first flight from mount Ceceri which will fill the Universe with amazement. ” Leonardo da Vinci