1. Time dependence of SM parameters

2. Outline Dirac´s hypothesis SM parameters Experimental access to time dependence  laboratory measurements  Quasar absorption spectra  Oklo natural nuclear reactor  Big-Bang Nucleosynthesis

3. Dirac´s hypothesis 1937 after the publication of Hubble´s law. Dirac was convinced that “relativity will play only a subsidiary role in the subject of cosmology” Extrapolating Hubble´s law he concluded that the universe is some Ga old. Searching for a new fundamental law he tried to connect cosmology with Atomic theory Constructed out of atomic “constants” and cosmological quantities something with Unit time and divided with Hubble constant to make it dimensionless again:

4. Dirac´s hypothesis relative strength of electric to gravitational force: Size of Universe compared to an electron: Number of particles in the universe:

5. Dirac´s hypothesis If this are fundamental relations and for example the ratio which is nowadays of order one is constant. With: Some of other constants not constant For example:

6. Standard model parameters Quark masses Lepton masses + Other parameters related to Symmetry breaking Strong Coupling, CKM Matrix, etc. Electroweak coupling

7. SM parameters In principle different couplings can vary differently with time But GUT theories offer connection between couplings: SM MSSM

8. Experimental access to time dependence The shorter the observed time scale is, the more accurate the measurement has to be! Laboratory experiments (a) Oklo (1Ga) QSO (5Ga) BBN (16Ga)

9. Laboratory experiments Frequency of atomic clocks depends on alpha. But different clocks -> different alpha dependence: 00.15 today: next year: 00.16

10. Oklo Natural nuclear fission reactor in West Afrika. Uranium composition indicates that it was active 1.7 Ga ago, using surface and groundwaters to moderate and reflect neutrons Absence of indicates that stopped at least 0.1 Ga ago

11. Oklo The Oklo abundance of is lower than what is found elsewhere, which is due to neutron capture. Capture cross-section depends on alpha (very narrow peak) and other constants. -Shlyakhther -Damour, Dyson

12. QSO Constraints QSO (Quasi stellar object) is a extremely large black hole in centre of galaxies. When matter falls in light of all wavelengths is emitted So brilliant, that can be observed at large distances On way to earth light passes through absorbing gas clouds Study fine structure splitting:

13. QSO constraints Red shift with

14. QSO constraints More sophisticated analysis taking into account Many electron effects different transition lines like spin orbit coupling different elements for line fitting (Mg, Al, Fe...) and statistics from 49 Quasar absorption systems... for 0.5<z<3.5 Murphy et al. Webb et al.

15. QSO constraints

16. BBN (Big-Bang Nucleosynthesis) Question: “Where do heavy nuclei come from?” 1942 Gamow idea taking BBN as origin for heavy nuclei 1957 Hoyle, Margaret, Burbidge, Fowler show that all elements beyond 4 He can be made by stars 1964 Hoyle and Tayler show abundance of 4 He (around 25%) and suggest BBN Several models follow until around 1982 all primordial abundances of all four light elements are predicted in agreement with measurement by hot big-bang model.

17. BBN Light elements that had to be explained are: BBN takes place in non equilibrium during a few minutes in an expanding, radiation- dominated plasma. Compare stellar nucleosynthesis takes place over billions of years Assume general relativity, standard model -> dozen of cross sections -> calculate (All astrophysical processes except BBN destroy D)

18. BBN Statistical equilibrium-> formation of light nuclei Coulomb barriers and stability gaps at masses five and eight work against formation of larger nuclei

19. BBN yields of primordial nucleosynthesis with 2 sigma theoretical errors as function of baryon density:

20. BBN Further implications from BBN: (More neutrinos -> more 4 He produced)

21. BBN Back to variation of SM parameters: Concordance of BBN rests on balance between interaction rate and expansions rate Gives constraints on variation of almost all participating parameters like: -Particle types -Particle masses -Particle interactions

22. BBN Especially D production rates seem to be very sensitive to the change of this gives bounds on: But this is strongly dependent on the used (simplified) model Flambaum,Shuryak Beane and Savage worked with an effective field theory (without s-quarks) and could not derive bounds on change of quark mass ratios.

23. Summary Time dependence of fundamental constants is still a riddle for theorists and a task for experimentalists. Time will reveal the existence of time dependence..