Transcript The Cosmology of the Nonsymmetric Theory of Gravitation (NGT)

˚ 1˚
Cosmic Inflation
Tomislav Prokopec (ITP, UU)
WMAP 3y 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+3P<0)
˚ 4˚
Inflation in Lab?
How to get repulsive GRAVITY in Lab?
Alchemist Laboratory
(Hamburg 1595)
WORK: δW=-Fδs= PδV<0  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)?
2
4 GN
1
d
a
Friedmann equation (FLRW):

  3P 
2
2 
a dt
3c
ACTIVE GRAVITATIONAL ENERGY (MASS): active=+3P<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
S[ ]   d4 x  g
 KICK IT REAL HARD
1
    m 2  2 

2
 WAIT ~ 1037 SEC AND WATCH
ATTENTIVELY!
Andrei Linde


SLOW 10-37 sec! ROLL REGIME:
d2
d
 = (t)  2  3H  m2 = 0
dt
dt
2
2
1  1  d  1 2 2 
 1 da 
H 
 = 3M2  2  dt   2 m  
a
dt


 
Pl 

2
 H  H0 =
mφ0
6MPl
,
a  a0 exp(H0 t),
Chaotic inflationary model (Linde 1982)
(exponentially expanding universe)
 d2 a/dt2  H02a > 0  acceleration!
P
ρ
EQUATION OF STATE w   -1 +
(d /dt)
 -1, (  +3P  -2  < 0)
m2 2/2
Inflatiomatica
Inflation solves many cosmologist’s
headaches
(1) Homogeneity and isotropy problem
(Einstein’s cosmological principle, 1930s)
2dF 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:
H
A
,
2
R  RH
Hubble parameter H=(1/a)da/dt
measures the expansion rate.
FREEZING IN of vacuum fluctuations
corresponds to amplification!
CURVATURE PERTURBATION
(gravitational potential):
Φ
H
T

~ 105
MPl
T
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:
P (t )  k ns 1 , ns  0.96  0.03
0 ( x , t )( x ', t ) 0  
sin  k x  x '
dk
P (t )
k
k xx'

(2) Spatial sections appear flat
(curvature radius > 25 Gpc)
WMAP 3y scalar CMBR spectrum
 TOTAL ENERGY DENSITY CONSISTENT WITH CRITICAL
tot = 1.01  0.02 crit
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 3y scalar
CMBR spectrum
2006 Nobel Laureates
George Smoot(h), LBL, Berkeley
˚11˚
John C. Mather, NASA
COBE Satellite:
FIRAS
DMR
˚12˚
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