The Cosmological Constant and Technical Naturalness

1. The Cosmological Constant and Technical Naturalness Sunny Itzhaki hep-th/0604190+ work to appear

2. The CC problem used to be a simple problem

3. The CC problem used to be a simple problem… to state: Why is the CC vanishing? The CC term is a relevant term that receives large quantum corrections: Lorentz invariance + dim. analysis give g ~ ~ One loop Cut off scale The goal was to find a way to get 0. The CC problem seems to have little to do with particle physics and more to do with deep issues in quantum gravity.

4. Old proposals to solve the CC problem: • 1- Hawking’s wave function of the universe (most likely to have vanishing CC). • 2- Coleman’s wormholes. • … • Particle physics does not help much: • SUSY, that helps in a similar problem with the Higgs mass, gives at best • which is times larger than the total energy density in the universe. ~

5. Now we are trying to explain a small and positive CC • The bad news is that the CC problem evolved into three problems: • 1- Why is the CC so small (in particle physics units)? • 2- If so small why not zero? • 3- Why now? Roughly when galaxies were formed the CC is of the order of the matter energy density in the universe.

6. The bad news is that the CC problem evolved into three problems: • 1- Why is the CC so small (in particle physics units)? • 2- If so small why not zero? • 3- Why now? Roughly when galaxies were formed the CC is of the order of the matter energy density in the universe. • The good news is that we have a scale, to work with. • For example: • 1-(…, Banks, …)

7. CC and Inflation Loop corrections to the CC are within the inflation range In TeV SUSY theories the natural range of the vacuum energy is Gauge mediation models Gravity mediation Which is within the inflation range • This assumption does not solve the CC problem, but if true it changes its nature:

8. The question is now: why is the ratio of the vacuum energy during inflation to the current vacuum energy so large and yet not infinite? Can be Why it is : and not

9. The question is: why is the ratio of the vacuum energy during inflation to the current vacuum energy so large and yet not infinite? Why it is : and not The good thing is that we have to do it only once: Temperature driven phase transitions (like the EW or QCD) will not change the vacuum energy.

10. Out line • Abbott’s model (85). • The empty universe problem. • The hep-th/0604190 model. • The cold universe problem. • Solving the cold universe problem.

11. Abbott’s Model (85) • The action is • Instantons induce a potential: • When we have the symmetry • is technically natural. (similar to the mass of the electron) • Small M is natural. The renormalized CC term

12. Also at the quantum level the potential looks like: • In quantum mechanics the local minima are on equal footing. • Here the situation is more interesting: Hawking temperature in de-Sitter is . • For in effect there are no local minima. • Forwe have tunneling. • The decay rate is Most of the time at small CC.

13. Regardless of we end up with a small CC

14. Regardless of we end up with a small CC BUT we also end up with an empty universe. This is known as the emptiness problem that appears also in other approaches to the CC problem.

15. The hep-th/0604190 model Let’s modify Abbott’s model in the following way: The relaxation action is a simpler version of Abbott’s action where . Much like in Abbott’s case the vacuum energy is reduced slowly. The challenge is to evade the emptiness problem by converting the potential energy into kinetic energy. is designed to fix that while making sure that the vacuum energy at the end of inflation is small.

16. That is makes sure that we have and not

17. We take The potential is designed to have the following properties: and

18. Now the dynamics is more interesting: The effective mass is Slow roll approximation. (This is where it is important that )

19. Now the dynamics is more interesting: The effective mass is There is a phase transition: V For At the critical vacuum energy an instability is developed and acquires an expectation value. The end result is a flat space with plenty of kinetic energy.

20. There are a couple of bounds on the we can get this way: 1- Energy conservation: 2- Vacuum energy can be converted to kinetic energy only when the slow-roll approximation is not valid: In our case (1) and (2) are the same so an upper bound on is

21. What about quantum correction?

22. What about quantum correction? • Claim: • The present value of the vacuum energy • + • Technical naturalness of the model • ___________________________________ • The upper bound on the reheating temperature is at • the TeV scale. • SUSY is broken at around the TeV scale.

23. Let’s consider the simplest potential Quantum corrections to give non-vanishing vacuum energy, , that should be at most .

24. Because of the relevant term it is hard to control these quantum corrections without SUSY. With SUSY we have

25. When SUSY is broken these corrections are enhanced: • Gravity always mediates SUSY breaking • from one sector to the other:

26. So the picture is: Hidden sector TeV SUSY Gravity mediation Gauge mediation sector (N) MSSM

27. So far we talked about: vacuum energy  kinetic energy. Hidden sector TeV SUSY Gravity mediation Gauge mediation sector (N) MSSM

28. So far we talked about: vacuum energykinetic energy. we should have: vacuum energykinetic energySM heat. Hidden sector TeV SUSY Gravity mediation Gauge mediation sector (N) MSSM Re-heating coupling Can we re-heat without spoiling the naturalness of the model?

29. Direct approach: Take We need BUT then:

30. A resolution: Take instead This includes So Looks like the exact same situation/problem as before. But actually

31. So works fine.

32. Conclusion: • We have considered a model that: • Appears to be consistent with basic exp. requirements (TeV SUSY and inflation). • CC is technically natural. • Can the model be embedded in string theory?