inflation: why and how? gert jan hoeve, december 2012
TRANSCRIPT
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’
Why do we have a horizon problem?
• Cosmic Microwave Background radiation originated 500,000 years after the BB.
• No causal correlation possible
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
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