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

Big Bang ˚ 2˚

Roadmap to Inflation ˚ 3˚ Alchemist Laboratory (Hamburg 1595) Massive objects attract each other gravitationally. Therefore, a 13.7 billion old universe should appear very wrinkled & clumpy NOT WHAT WE MEAN: Inflation is a rise in the general level of prices, as measured against some baseline of purchasing powerpurchasing power ALAN GUTH (1981) (& Alexei Starobinskii): 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 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) ρ>0, P<0 (ρ+3P<0) SDSS galaxy catalogue (2004)

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

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

Inflatiomatica ˚ 6˚ 2dF galaxy survey Inflation solves many cosmologist’s headaches (1) Homogeneity and isotropy problem (Einstein’s cosmological principle, 1930s) (2) flatness problem (curvature radius > 30 Gpc) (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  (3) causality problem (CMB sky: ~4000 domains)

˚ 7˚ Cosmological perturbations Hubble parameter H=(1/a)da/dt measures the expansion rate. 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 R H = c/H: FREEZING IN of vacuum fluctuations corresponds to amplification! Amplification of vacuum fluctuations of matter and gravitational potentials in inflation  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 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) STANDARD ‘WISDOM’:

Evidence for inflation ˚ 9˚ WMAP 3y scalar CMBR spectrum (1) Nearly scale invariant and gaussian power spectrum of cosmological perturbations (2) Spatial sections appear flat (curvature radius > 25 Gpc) CLOSE  OPEN  FLAT  "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. SPECTRUM:  TOTAL ENERGY DENSITY CONSISTENT WITH CRITICAL (3) IN FUTURE we hope to detect primordial gravitational waves (Planck) NB: NO DIRECT EVIDENCE AT THIS MOMENT ☺Predicted by inflation (Chibisov, Mukhanov, 1981)

CMB spectrum WMAP 3y scalar CMBR spectrum ˚10˚

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

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

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

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