Inflation: why and how?

Gert Jan Hoeve, December 2012

Problems with the Hot Big Bang

• Flatness– |Ω-1|<1016 at nucleosythesis

• Unwanted relics• Horizon problem– Homogeneity over parts of space that are

presumably not causally correlated.

• Baryogenesis– Conventional theories of symmetry

breaking are insufficient for the observed ammount of baryons

The solution: inflation

d2a/dt2 >> 0 or equivalently,

-(dH/dt)/H2 >> 1

Between Planck time (10-43) and GUT decoupling (10-35)

Alan Guth, 1981

Picture: Wikipedia

How does cosmic inflation solve the flatness problem?

• Ω is pushed towards 1 during inflation

• ‘Stretching’

Unwanted relics: magnetic monopoles

• Abundant at high temperature• Slow decay

Why do we have a horizon problem?

• Cosmic Microwave Background radiation originated 500,000 years after the BB.

• No causal correlation possible

Inflation solves the horizon problem:

Picture: one minute astronomer

How much inflation do we need?

Inflation ends at t0 = 10-35 s, we are at t1 = 1017 s

In radiation dominated universe |Ω-1|proportional to time

|Ωnow-1| ≤ 10-2 |ΩGUT-1|≤ 10-54

Recall |Ω-1|=|k|/(Ha)2

During inflation H=constant, so |Ω-1|proportional to 1/a2

Total expansion > ~ 1027

Baryogenesis

• Three conditions (Sakharov’s conditions)– Baryon number violating interactions• obvious

– C violation and CP violation• Because any B-violating interaction would

be mirrored by a complementary interaction

– Thermal non-equilibrium (or CPT violation)• Otherwise the backwards reaction would be

equilly strong

B-violating interactions

• Standard model: sphalerons• Difference leptonnumber and baryonnumer conserved

• Example: (u+u+d)+(c+c+s)+(t+t+b) e++μ++τ+

C and CP violation

• B-violating process must outrate symmetric process

• Both symmetries must be violated

Thermal non-equilibrium at baryogenesis

• Phase transition bubbles• Thermal energy gradient at bubble

edge• Local breakdown of time symmetry

How did inflation arise?

Scalar field V(φ) causes spontaneous symmetry breakingFirst or second order phase transition?

B. Clauwens , R. Jeanerot, D-term inflation after spontaneous symmetry breakingH. Bohringer

Original model (Guth, 1981)

• False/real vacuum• First order phase

transition• Reheating

problems

Slow-roll inflation (Linde, 1982)

• d2φ/dt2 + 3H dφ/dt = -dV(φ)/dφ• Friedman H2 = (1/2 dφ/dt +V(φ))/3 –

k/a2

• Inflation decays as slope increases• H= (da/dt)/a

Quintessential scalar field

• 5th fundamental force

• Continueous decaying scalar field

• Could explain inflation and dark energy at the same time!

M. Trodden, Baryogenesis and the new cosmology, 2002

Conclusion

Cosmological inflation is a viable hypothesis, but in desperate need of a more solid foundation (and experimental confirmation) from the realm of particle physics.