1. A MANIFESTLY LOCAL T HEORY OF V ACUUM E NERGY S EQUESTERING George Zahariade UC Davis

2. O UTLINE Cosmological constant problem Prelim: CC problem in Unimodular Gravity Original vacuum energy sequestering proposal (Kaloper, Padilla 2013-2015) arXiv:1309.6562 arXiv:1406.0711 arXiv:1409.7073 Localized sequestering model (Kaloper, Padilla, Stefanyszyn, Zahariade 2015) arXiv:1505.01492

3. T HE COSMOLOGICAL CONSTANT PROBLEM Of vacuum energy, phase transitions, bubbles and radiative corrections

4. T HE COSMOLOGICAL CONSTANT Einstein-Hilbert action Cosmological observations: accelerated expansion of the universe Main energy component of the universe What is it?

5. V ACUUM ENERGY Equivalence principle: ALL energy gravitates Two contributions Classical minimum of the potential Zero-point energy of quantum fluctuations Vacuum energy and the cosmological constant Problem: high accuracy cancellation!!!

6. C OSMOLOGICAL CONSTANT PROBLEM ( S ) Classical cosmological constant problem Phase transitions: classical component of Λ cancellation before XOR after Quantum mechanical cosmological constant problem Quantum corrections: zero-point energy component computed in QFT in the locally flat frame (Zel’dovich) Quantum matter Classical gravity e.g. scalar λφ 4 theory Radiative instability / non-naturalness

7. P ROBLEMS TO SOLVING THE PROBLEM Radiative instability = knwoledge of the UV details of the theory Supersymmetry: not enough supersymmetry in the world… Technically natural value of Λ~ ( M SUSY ) 4 too big No-Go theorem (Weinberg 1989) No local self adjustment mechanisms for Poincaré invariant vacua Would imposing global constraints help?

8. A PEAK AT U NIMODULAR G RAVITY Or the Cosmological Constant problem in GR revisited...

9. T HE M ODEL Henneaux-Teitelboim (1989): unimodular gravity Diffeomorphism invariance recovered Key point: New volume form New gauge symmetry

10. E QUATIONS OF M OTION Einstein equations Λ variation A variation Global variable Λ Cosmological constant: constant of motion set by the boundary conditions and potentially small Do matter sector quantum corrections spoil this small cosmological constant configuration?

11. R ADIATIVE C ORRECTIONS Background solution of the EOMs QFT in the locally flat frame Einstein box EOM decomposition Scalar curvature sector unstable...

12. O RIGINAL SEQUESTERING MECHANISM GR with global constraints (at the price of a not so local action)

13. (G LOBAL ) S EQUESTERING ACTION Idea: couple matter sector scales and cosmological constant Action Matter couples to Λ, λ: global variables σ smooth odd function: determined phenomenologically μ mass scale ~ M P

14. F IELD E QUATIONS AND V ACUUM ENERGY SEQUESTERING Einstein equations Global equations Key equation:

15. D ISCUSSION Classical and (matter sector) quantum contributions to Λ cancel to all loop orders! Residual cosmological constant (radiatively stable) BUT given by a 4-volume average Non-zero mass gap: finite volume universe Weinberg No-Go evaded: global constraints decouple cosmological constant from matter mass scales BUT non-local action (although GR recovered locally)

16. L OCALIZED SEQUESTERING MECHANISM Or how to enforce global constraints with local degrees of freedom?

17. (L OCAL ) S EQUESTERING ACTION Idea: work in Jordan frame and couple the two “eventually global” variables using HT trick Action Λ,κ: local fields F = dA, H = dB : 4-forms σ,τ: smooth functions determined phenomenologically μ mass scale ~ M P

18. F IELD EQUATIONS Einstein equations Variation of F and H Variation of Λ and κ 2

19. V ACUUM ENERGY SEQUESTERING Cosmological constant equation Key equation New residual cosmological constant component

20. R ADIATIVE C ORRECTIONS Background solution of the EOMs QFT in the locally flat frame Einstein box Quantum corrections renormalize κ 2 Radiatively stable if M UV ~ κ 2 ~ μ

21. R ADIATIVE CORRECTIONS Vacuum energy loops? Decomposition of the EOMs Form sector Cosmological constant sector Curvature sector

22. D ISCUSSION σ,τ smooth: quantum corrections give at most O(1) corrections as long as κ ~ M P Form sector insensitive to UV details Volume integrals: IR quantities New residual cosmological constant component also radiatively stable GR recovered locally (globally, different theories) Weinberg No-Go evaded: equivalence principle violated, vacuum energy sector non-gravitating

23. C ONCLUSION Vacuum energy sequestering: mechanism for cancelling matter loop corrections exhaustively via global constraints Residual cosmological constant radiatively stable Original scenario: non-local action Localization via the unimodular HT trick NB: graviton loops not included

24. T HANK YOU FOR YOUR ATTENTION