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 power

ALAN GUTH (1981) (& Alexei ALAN GUTH (1981) (& Alexei Starobinskii):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): 2

2 2

413

3NGd a

Pa dt c

Inflation in a theorist´s head

Chaotic inflationary model (Linde 1982)

21[ ]

2S g

4d x 2m

RECIPE: TAKE A SCALAR FIELD

˚5˚

PROCESS IT WITH COVARIANT ACTION

KICK IT REAL HARD

WAIT SEC AND WATCH ATTENTIVELY!

37~10

Andrei Linde

SLOW ROLL REGIME: -3710 sec!

22

2

d d= (t) 3H m =0

dt dt

1

2 22 2 2

2Pl

1da 1 d 1H = m

a dt 3M 2 dt 2

,00

Pl

mφH H =

6M ,0 0a a exp(H t)

2 2 20 d a/ dt H a>0 acceleration!

EQUATION OF STATE 22

P (d / dt)w -1+ -1, ( +3P -2 <0)

ρ m / 2

(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 RH = c/H:

FREEZING IN of vacuum fluctuationscorresponds to amplification!

H

HA , R R

2

Amplification of vacuum fluctuations of matter and gravitational potentials in inflation

5

Pl

H TΦ ~10

M T

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 withgaussian 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 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.

sin '0 ( , ) ( ', ) 0 ( )

'

k x xdkx t x t t

k k x x

P

1( ) , 0.96 0.03 t kPs

sn nSPECTRUM:

=1.01 0.02tot crit

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, Berkeley John C. Mather, NASA

COBE Satellite:

FIRAS

DMR

˚12˚

˚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