Non-perturbative particle production from SUSY flat directions – a spoiler of delayed thermalisation? Anders Basbøll, University of Aarhus COSMO 2008: Madison, WI based on: AB, D Maybury, F Riva and SM West: Nonperturbative flat direction decay, Phys. Rev. D 76, 065005 (2007) and AB: SUSY Flat Direction Decay – the prospect of particle production and preheating investigated in the unitary gauge, Phys. Rev. D 78 023528 (2008)

(Super)potential and flatness Superpotential (Yukawa couplings same as in SM) Scalar potential: F- and D-term T: symmetry generators Flatness: V=0 All F- and D-terms vanish V=0 only for exact SUSY (unbroken) and no non-renormalisable terms All ~300 flat directions of SUSY are broken by non-renormalisable terms of order n=4 to n=9

Flat direction evolution – from Dine-Randall-Thomas ArXiv:hep-ph/9507453 Flat direction (QLD, example) Flatness easy: Colour, weak charge, hypercharge sum to zero m: dimension with canonical field Equation of motion - with Hubble friction

Evolution during and at end of inflation Potential (n=k*m – k integer in Xk) Last term: non-renormalisable SUSY-breaking c of order unity. Positive sign of c necessary (50%chance? - depends on Kähler potential) With H dominating, induced mass terms and self-couplings dominate over SUSY-breaking terms Minimum at 10^16 GeV?! End of inflation: SUSY mass terms dominate Oscillation around minimum Potential has phase dependent part: Baryon number if B-L not conserved by FD

Consequences of Flat Directions - Allahverdi, Mazumdar hep-ph/0603244v2 and others FD induce masses to inflation decay products: No preheating Energy is stored in the flat direction. Only when the FD decays – Reheating. Reheating temperature 10^3-10^7 GEV This avoids the (lack of) gravitino problem FD itself a candidate for the Inflaton (LLE,UDD) Allahverdi et al. hep-ph/0605035v2 Olive+Peloso hep-ph/0608096: Valid only if decay is nonperturbative SPOILED if FD decays rapidly - likely.

The framework Exitations of fields Lagrangian Exitations must be defined, such that mixed kinetic terms are avoided! Orthogonal transformation to make U-term disappear: ”New” Lagrangian Diagonalisation

Non-perturbative particle production Conformal fields Equation of motion Mass matrix Changing eigenvectors

Multi-field Bogolyubov - Nilles, Peloso and Sorbo ArXiv:0103202 Differential equations generalised Bogolyubov coefficients (in GR: particle production from rapidly changing vacua) Non-diagonal part - not present in single field case Particle number In our framework Rapidly changing eigenSTATES give particles

LLE – in detail VEV's: generic feature: Flatness independent of phase Covariant deriv. Lagrangian F, W: Hypercharge, Weak field strength tensors Mixed kinetic terms – unphysical Goldstones only time derivative of phase - therefore also only 0'th component of Gauge fields matter

Gauging Goldstones away - go to unitary gauge U(1) (hypercharge) transformation with SU(2) (weak charge) transformation P³: 3rd Pauli matrix new VEV's (phase differences gone)

Diagonal Goldstones removed still gives

All Goldstones removed

U-matrix U from Lagrangian Partial integration (Ignoring surface terms)

Mass matrix Notice: block diagonal – split in 2 sectors corresponding to off- [sector 2] and diagonal [sector 1] connection to VEV – generic feature

results – LLE and UDD (seperately) Make transformation eliminating U. J-matrix=0 No preheating! UDD exactly the same. 3 phases, 2 gauged away. J=0, no preheating

QLQLQLE – Fields Squarks with identical SU2-charge chosen ...and 12 fields with no VEV

Mass matrix eigenvalues States 1,2 from diagonal, 3,4 from off-diagonal parts of SU(2) X U(1) States 5-12 diagonal+off-diagonal SU(3)

J – Matrix: Particle production - from 1 flat direction!!! Higgses mix with light states in both diagonal part of SU(2) X U(1) and off-diagonal part of SU(2)

2 Flat directions: UDD+LLE Give VEV's to same fields as before! Now 6 phases – only 4 diagonal generators. However, it is 1 phase for LLE and 1 for UDD that survives. U-matrix block diagonal: Fields and phase of LLE in one block. Fields and phase of UDD in another block. J=0 – no preheating. Very encouraging for the cosmological role of SUSY flat directions!

QLD+LLE – overlapping directions QLD and LLE can co-exist. They can have VEV in the same field. A: relation between VEV's. ”Overlapping field” must have ”pythagoras” size ... and 6 fields with no VEV

Mass matrix Seperated sectors Sector 2 diagonal Sector 1 phases (fields 6,7) have time dependent mass elements

Particle production! 2 terms giving 2 contributions to J NZ= nonzero Notice: J_2 cannot balance this: lower part zero

To be done – and recent papers How much different can VEV's be to get the effects of more directions -how much different from 0 is allowed for A [or log(A)] Investigate which directions will get large VEV's - or make some kind of statistical analysis of probability. Polarisation and numerics: Gümrükçüoğlu et al. arxiv:0805.0273v1 Conserved global charges (NEXT TALK?): Allahverdi et al. arxiv:0802.4430v2

Conclusion SUSY Flat directions can have crucial influence on (p)reheating and offer a very nice explanation of the gravitino problem, baryogenesis and even offer a ”known” particle as a candidate for inflation. Preheating serious threat to this. This deserves further investigation ....... ....and I'm looking for a job!