Constraints on the very early universe from thermal WIMP Dark Matter

1. Constraints on the very early universe from thermal WIMP Dark Matter Mitsuru Kakizaki (Bonn Univ.) July 27, 2007 @ Karlsruhe Univ. • In collaboration with • Manuel Drees • Hoernisa Iminniyaz • Refs: • PRD73 (2006) 123502 [hep-ph/0603165] • arXiv:0704.1590 [hep-ph]

2. 1. Motivation • Observations of • cosmic microwave background • structure of the universe • etc. [http://map.gsfc.nasa.gov] Non-baryonic cold dark matter (CDM): • Neutral, stable (long-lived) weakly interacting massive particles (WIMPs) are good candidates for CDM • Neutralino (LSP); 1st KK mode of the B boson (LKP); etc. When WIMPs were in full thermal eq., the relic abundance naturally falls around the observed CDM abundacne: Mitsuru Kakizaki

3. Investigation of early universe using CDM abundance e.g. SUSY • The relic abundance of thermal WIMPs is determined by the Boltzmann equation: WMAP and the maximal temperature of RD epoch • The (effective) cross section can be determined from collider and DM detection experiments We can test the standard CDM scenario and investigate the conditions of very early universe: [From Ellis et al.,PLB565 (2003) 176] • Standard scenario: • Non-standard scenarios: • Low reheat temperature • Entropy production • Modified Hubble parameter • Non-thermal production [Scherrer et al., PRD(1985); Salati,PLB(2003); Fernengo et al., PRD(2003); Chung et al., PRD (1999); …] • was in chemical eq. is independent of ( : Rel. dof) Mitsuru Kakizaki

4. Outline This work • We provide an approximate analytic treatment that is applicable to low-maximal-temperature scenarios • Based on the assumption of CDM = thermal WIMP • we derive the lower bound on the maximal temperature of RD epoch • we constrain possible modifications of the Hubble parameter Motivation Standard calculation of WIMP relic abundance Low-temperature scenario Constrains on the very early universe from WIMP dark matter Summary Mitsuru Kakizaki

5. 2. Standard calculation of the WIMP relic abundance Co-moving number density [Scherrer, Turner, PRD33(1986)] Decoupling • Conventional assumptions for : • , single production of is forbidden Increasing Thermal equilibrium • Thermal equilibrium was maintained • For adiabatic expansion the Boltzmann eq. is • During the RD epoch, and decoupled when they were non-relativistic: Mitsuru Kakizaki

6. 3. Low-temperature scenario • : The maixmal temperature of the RD epoch The initial abundance is assumed to be negligible: • Zeroth order approximation: annihilation is negligible: The solution is proportional to the cross section: At late times, This solution should be smoothly connected to the standard result Mitsuru Kakizaki

7. First order approximation • Add a correction term describing annihilation to : • As long as , the evolution equation for is The solution is proportional to At late times, • soon dominates over for not very small cross section fails to track the exact solution Mitsuru Kakizaki

8. Re-summed ansatz • It is noticed that For large cross section, should be • This observation suggests the re-summed ansats: • For , Standard formula At late times, • In the case where production is negligible but the initial abundance is sizable, is exact Mitsuru Kakizaki

9. Evolution of solutions : Exact result, : Re-summed ansatz, • The re-summed ansatz describes the full temperature dependence of the abundance when equilibrium is not reached • For larger cross section the deviation becomes sizable for , but the deviation becomes smaller for Mitsuru Kakizaki

10. 4. Constrains on the very early universe from WIMP DM • Out-of-equilibrium case: ; Equilibrium case: ; Independent of • Thermal relic abundance in the RD universe: Assumption that , Lower bound on the maximal temperature: Mitsuru Kakizaki

11. Modified expansion rate • Various cosmological models predict a non-standard early expansion Predicted WIMP relic abundances are also changed • When WIMPs were in full thermal equilibrium, in terms of the modification parameter the relic abundance is This formula is capable of predicting the final relic density correctly If , and we recover the standard formula This formula is capable of predicting the final relic density correctly Mitsuru Kakizaki

12. Constrains on modifications of the Hubble parameter • In terms of,we need to know only for This suggests a parameterization of in powers of : [Olive et al., AP(1999); Lisi et al., PRD(1999); Cyburt et al., AP(2005)] subject to the BBN limit: Maximal temperature where the parametrization is valid • Once we know , we can constrain : Tuning depends on all Larger allowed region for Mitsuru Kakizaki

13. 5. Summary • Using the CDM relic density we can examine very early universe around (well before BBN ) • The relic density of thermal WIMPs depends on the maximal temperature and on the Hubble parameter • We derived approximate solutions for the number density which accurately reproduce exact results when full thermal equilibrium is not achieved • By applying , we found the lower bound on the maximal temperature: • The sensitivity of on is weak because depends on all Mitsuru Kakizaki

14. Backup slides Mitsuru Kakizaki

15. Semi-analytic solution • has a maximum (left) • New semi-analytic solution can be constructed: (right) For , use ; for , use The semi-analytic solution reproduces the correct final relic density to an accuracy of a few percent Mitsuru Kakizaki