Martin L. Perl ( martin@slac.stanford) SLAC National Accelerator Laboratory Holger Mueller

1. Proposed Terrestrial Experiment to Detect the Presence of Dark Energy Using Atom Interferometry Martin L. Perl (martin@slac.stanford.edu) SLAC National Accelerator Laboratory Holger Mueller Physics Department, University California-Berkeley Talk presented at Windows on the Universe, Château Royal de Blois, France,, June 21 -26, 2009

2. The majority of astronomers and physicists accept the reality of dark energy but also believe it can only be studied indirectly through observation of the motions of galaxies [P. J. E. Peebles and B. Ratra, The Cosmological Constant and Dark Energy arXiv:astro-ph/0207347v2, (2002)] This talk opens the experimental question of whether it is possible to directly detect dark energy on earth using atom interferometry through the presence of dark energy density. The possibility of detecting other weak fields is briefly discussed

3. Outline of Presentation • Present beliefs about dark energy. • Comparison of dark energy density • with energy density of weak electric field. • 3. Comparison of dark energy density • with energy density of terrestrial • gravitational field. • 4. Our assumptions about dark energy • and description of the experimental • method. • 5. Remarks on dark matter and zero-point • vacuum energy. • Appendix A: Comparison with other • experimental directions for dark • energy studies.

4. 1. Present beliefs about dark energy

5. Magnitude of dark energy density: Counting mass as energy via E=Mc2 ,the average density of all energy is the critical energy rcrit =9 x10-10 J/m3 rmass» 0.3 x rcrit= 2.7 x10-10 J/m3 rdark energy» 0.7 x rcrit= 6.3 x10-10 J/m3 Use rDE to denote rdark energy

6. rDE » 6.3 x10-10 J/m3 is a very small energy density but as shown in the next section we work with smaller electric field densities in the laboratory Distribution of dark energy density: rDE is taken to be at least approximately uniformly distributed in space

7. 2. Comparison of dark energy density with energy density of weak electric field.

8. rDE» 6.3 ´ 10-10 Joules/m3 Compare to electric field of E=1 volt/m using rE=electric field energy density. Then rE = e0E2/2=4.4 x 10-12 J/m3 This is easily detected and measured. Thus we work with fields whose energy densities are much less than rDE

9. Obvious reasons for ease of working • with electric fields: • There is a qE force on all charged • objects • Electron currents offer manifold, • sensitive, detection methods • Magnetic fields offer manifold, • sensitive, detection methods

10. Obvious reasons for difficulty or • perhaps impossibility of working • with dark energy fields: • Cannot turn dark energy on and off. • Cannot find a zero dark energy field • for reference. • In some hypothesis about • dark energy, it may not exert • a force on any material object • beyond the gravitational force of • its mass equivalent.

11. 3. Comparison of dark energy density with energy density of terrestrial gravitational field

12. rG = gravitational energy density = • rG=g2/(8pGN) • At earth’s surface rG = 5.7´ 10+10 J/m3 • and rDE/ rG ~ 10-20. • The phase change of atoms depends upon the integral of a force over a distance. Hence we are interested in the ratio FDE/FG. • We speculate • FDE/FG ~ (rDE/ rG)1/2 ~ 10-10

13. 4. Our assumptions about dark energy and description of the experimental method

14. Assumptions about dark • energy: • A dark energy force, FDE, exists other • than the gravitational force equivalent • of rDE. • FDE is sufficiently local and rDE is • sufficiently non-uniform so that FDE • changes over distance of the order of • a meter. • FDE acts on atoms

15. Beam Deflector Interference fringes detector Beam source Beam splitter Fig. 1 Conceptual design of atom interferometer • The method: • We use a two beam atom interferometer with arms of unequal length and of extent about 1 meter as shown in Fig. 1

16. The method continued: • To search for FDE the known forces • that change the atomic phase must be nulled out. • The effects of electric and magnetic forces are nulled by shielding. • The effect of the gravitational force is cancelled by the interferometry since gravity is a conserved force. Cancellation by a factor of 10-10 has been demonstrated and we expect to be able to cancel by a factor 10-17

17. Sensitivity: • The sensitivity of the experiment can be as good as • FDE/FG =f ´10-17 • where f=0 if our assumptions are false and f of the order of 0.1 if are assumptions are true

18. Unknown weak fields: • The foregoing discussion applies to any other unknown weak fields.

19. 5. Remarks on dark matter and zero-point vacuum energy.

20. Dark Matter: We have begun to study the effect of dark matter on this experiment. Is it a “bug” in the experiment or an additional feature of the experiment.

21. Zero-Point Vacuum Energy: We have been thinking for time as to whether atomic interferometry can be used to elucidate the maddening infinity problem in zero-point vacuum energy. No progress.

22. Appendix A: Comparison with other experimental directions for dark energy studies.

23. Idea for fitting zero-point vacuum energy to dark energy by looking for a lower frequency cutoff C. Beck et al. [C. Beck and M. C. Mackey, Electromagnetic dark energy,Int. J. Mod. Phys., D17,71(2008); C. Beck and C Jacinto de Matos, arXiv: gr-qc/0709.237v1(2007)] have proposed that the noise spectrum in superconductors will decrease for frequencies above fDE = 4 x 1012 Hz. They propose using Josephson junctions for the test and believe that the same cutoff applies to zero-point energy This idea is criticized by P.Jetzer and N. Straumann [P.Jetzer and N. Straumann Has Dark Energy really been discovered in the Lab? astro-ph/0411034v2, (2004)] We are skeptical.

24. h Idea for looking for effect of dark energy on gravitational inverse square law It is conventional to define a characteristic length, LDE, for dark energy LDE = [ c/ rDE]1/4 = 84 x 10-6 m and to search if the gravitational inverse square law breaks down at distances < LDE = 84 x 10-6 m? No evidence yet for such a breakdown. [D. J. Kapner et al., Phys. Rev. Lett. 98, 021101 (2007)] Also a breakdown could be evidence for a string theory model and have nothing to do with dark ednrgy.

25. h Idea of looking for effect of dark energy on gravitational inverse square law It is conventional to define a characteristic length, LDE, for dark energy LDE = [ c/ rDE]1/4 = 84 x 10-6 m and to search if the gravitational inverse square law breaks down at distances < LDE = 84 x 10-6 m? No evidence yet for such a breakdown. [D. J. Kapner et al., Phys. Rev. Lett. 98, 021101 (2007)] Also a breakdown could be evidence for a string theory model and have nothing to do with dark energy. Also definition of LDE is based on dimensional analysis

26. h Idea for looking for a dark energy particle Does dark energy have a particle nature consistent with our 90 year old understanding of quantum mechanics? Can this be used to detect rDE? Use the relation between a force of range L carried by a particle of mass M: M x L = /c With LDE = 84 x 10-6 m Then MDE = 2.5x10-9 MeV/c2 But if MDE is a conventional particle it will act as matter not as dark energy