The physics of inflation and dark energy

2.6 Acceleration in scalar field models

Hubble “drag”Potential

V() 03 , VH

)(´)( 221 V

• Canonical scalar fields:

If the kinetic energy => slow roll :

)(´)( 221 Vp

energy is << than the potential

1w)(´)(

)(´)(w r. s.

221

221

V

Vp

constant)( V

)( Vp

With slow-roll, works like a "time-

dependent" V

Equation of motionsmall

The physics of inflation and dark energy

2.7 Starting and stopping a slow-rolling scalar field

V()

! Hard to turn on at right time !

• Inflation is easy to start : just prepare the scalar field somewhere, and "let it

roll". If its energy is not negligible,

then it will quickly dominate, and the slow-rolling scalar field will cause spacetime to inflate.

-domination begins "here"when z~1 , 0 = (2.3x10 - 3 eV) 4

V()

begins ?

reheating?

not here

ends

• But... not so good for dark energy:

since is nearly constant, there is

usually a fine tuning problem with the

the scalar field (as happens with

=> it is very hard to adjust and V()

such that dominates the energy

density at just the right time (z~1) !

The physics of inflation and dark energy

2.8 Dark energy - a theorist´s viewpoint

• Tracking dark energy w = w(t)

w = -1

• Cosmological Constant w = - 1

wX = const.

• “Barotropic” dark energy wX = const.

Fine tuning

Fine tuning

Coincidence

Problem!!!

Coincidence

Problem!!!

Self-adjusting (?)

1+z = a0/a

radiation=>matter

K-essence

today

The physics of inflation and dark energy

•V()=m4 exp[-] Wetterich 1988

•V()=m4+ - Ratra & Peebles 1988

•V()=m4 [cos()+1] Frieman et al 1995

•V()=m4 cosh[] Chimento & Jakubi 1996

•V()=m4+ - exp[] Binétruy 1998, Martin et al 1998

•V()=m4 exp[] Steinhardt et al 1998

•V()=m4 [ 1-(exp[-] Albrecht & Skordis 1995

•V()=whatever many many authors

0.7~ΩΩ if eV 10 2~m Typically, Λ3-

• = (´)2/(1+a´+b´) (K-essence) Armendáriz-Picón et al 2001

• = V()/[1-(dµ)2] (Tachyon) Sen 2002, Padmanabhan 2002

• p= -A/ (Chaplygin gas) Kamenshchick et al. 2001, ...

• ??? (Branes) many many many many many

Canonical ("honest-to-God") scalar fields:

Other models:

2.9 The modelling battlefield

Very common: attractor behavior for the background (Ferreira & Joyce 1998,Brax et al. 2000) and for the perturbations (Abramo & Finelli 2000)

=> results independent of the initial conditions!

The physics of inflation and dark energy

Dark energy models - pro´s and con´s

•Scalar field , w=w(t)

•“Barotropic”, wX=const.

(Ex: , w = - 1)

Pro:

•Easy to parametrize•Cosmolog. quantities are simple expressions•Observations so far only

sensitive to w, not dw/dt

Con:

•Fine tuning•No good motivation

(except for pure )

•Easy to model•(Maybe) physically well-motivated•Fair hope of explaining

coincidence problem.

•Still, some fine tuning!•Often not really well-motivated at all•Can´t resolve time

dependence of w

•Other models: K-essence, "rolling tachyon", Chaplygin gas, "vacuum metamorphosis", ... ?

???

???

The physics of inflation and dark energy

3. Inflation´s greatest achievement:

particle creation and the origin of everything

QUANTUM MECHANICS:

" E t > h/2"

The vacuum is filled with virtual

pairs of particles, which exist for

very brief moments, before being

annihilated back to nothingness.

The physics of inflation and dark energy

3.1 Virtual pairs and particle creation

2π

hΔtΔE

2π

hΔtΔE

Right here, right now:

The physics of inflation and dark energy

3.2 Virtual pairs in an accelerating background

Horizon H-1

Inflation (acceleration) converts virtual pairs into

real pairs

accelerated expansion rips pairs apart

The physics of inflation and dark energy

3.3 From quantum fluctuations to galaxies

10-35 s 10-33 s 3. 105 y 1.5 1010 y

quantum

fluctuationclassic

al

fluctuationdensity

and

temperature

perturbatio

n

Andromeda

That´s us

(Adapated from Lineweaver 1997)

The physics of inflation and dark energy

Past light cone of an astronomer on Earth:

The physics of inflation and dark energy

CMB sky

CMB deconstructed

The physics of inflation and dark energy

Conclusions

•There is an impressive amount of observational evidence suggesting that the Universe has suffered two phases of acceleration: one in the very early Universe (inflation, t~10-35 s), and the other right about now (Dark energy age, t~1010 years);

•The two phases appear to be completely unrelated: what works for one, does not seem to work for the other;

•Inflation will never be "confirmed": either the evidence will be consistent with it, or not. Must learn to live with that...

•The physics of inflation use, in a very deep way, both Quantum Mechanics and General Relativity - and the consequences are fully consistent with observations!

•The evidence for dark energy is persuasive and growing, but is still shaky. The case is not as solid as for inflation (yet);

•At present, nearly all dark energy models are contrived, fine-tuned and degenerate - in short, bad and ugly;