Challenging the Challenging the Cosmological Constant Cosmological Constant Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis Based on: arXiv:0706.1977/ [astro-ph]
Overview Overview Dark thoughts Dark thoughts Where fields hide Where fields hide Environmental mass effects and chameleonic behavior Environmental mass effects and chameleonic behavior Changeling Changeling A chameleon that actually may A chameleon that actually may work work as quintessence as quintessence Summary Summary
The concert of Cosmos? The concert of Cosmos? Einstein Einstein’ ’s GR: a beautiful theoretical framework for s GR: a beautiful theoretical framework for gravity and cosmology, consistent with numerous gravity and cosmology, consistent with numerous experiments and observations: experiments and observations: Solar system tests of GR Solar system tests of GR New tests? New tests? Sub-millimeter (non)deviations from Newton Sub-millimeter (non)deviations from Newton’ ’s law s law New tests? New tests? Concordance Cosmology! Concordance Cosmology! Or, Dark Discords? Or, Dark Discords? How well do we How well do we REALLY REALLY know gravity? know gravity? Hands-on observational tests confirm GR at scales between Hands-on observational tests confirm GR at scales between roughly 0.1 mm 0.1 mm and - say - about and - say - about 100 100 MPc MPc; ; are we are we certain certain roughly that GR remains valid at shorter that GR remains valid at shorter and and longer longer distances? distances?
Cosmic coincidences? Cosmic coincidences? We have ideas for explaining the near identities of some relic We have ideas for explaining the near identities of some relic abundances, such as dark matter, baryon, photon and neutrino dark matter, baryon, photon and neutrino : : abundances, such as inflation+reheating, with Universe in thermal equilibrium (like it inflation+reheating, with Universe in thermal equilibrium (like it or not, at least it works)… … or not, at least it works) However there’ However there ’s much we do not understand: s much we do not understand: DARK E ENERGY DARK E ENERGY The situation with cosmological constant is The situation with cosmological constant is desperate desperate (by (by 60 orders of magnitude!) 60 orders of magnitude!) → → desperate measures required? desperate measures required?
Blessings of the dark curse Blessings of the dark curse How do we get small Λ ? Is it anthropic anthropic? Is it even ? Is it even Λ ? Or How do we get small Λ ? Is it Λ ? Or • • do we need some really weird really weird new physics? new physics? do we need some Age of discovery: the dichotomy between observations Age of discovery: the dichotomy between observations • • and theoretical thought forces a crisis upon us! and theoretical thought forces a crisis upon us! A possible strategy: find all that needs explaining, and A possible strategy: find all that needs explaining, and • • be careful about dismissals based on current theoretical be careful about dismissals based on current theoretical prejudice (learning to be humble from the story of Λ … …) ) prejudice (learning to be humble from the story of Λ Ultimately, perhaps both cosmological observations and observations and Ultimately, perhaps both cosmological • • LHC should be viewed as tests of naturalness naturalness … … LHC should be viewed as tests of
Alternatively: we may seek non-standard dynamics with new degrees of freedom…
Dark Energy in the lab? Dark Energy in the lab? The issue: The issue: measuring measuring Λ the same as measuring the Λ the same as measuring the absolute zero point of energy. absolute zero point of energy. Only gravity can see it, at relevant scales Only gravity can see it, at relevant scales Gravity is weak: we can see a tidal effect, Gravity is weak: we can see a tidal effect, ~ H ~ H 2 2 r t r t Too small to care unless we have really large scale Too small to care unless we have really large scale exps exps (like (like Sne Sne!) !) Non-gravitational physics cannot directly see Non-gravitational physics cannot directly see Λ Λ . . An exception: quintessence fields might bring along new couplings An exception: quintessence fields might bring along new couplings Quintessence fields constrained by gravity experiments. Quintessence fields constrained by gravity experiments. How to evade such no go theorems? How to evade such no go theorems? Environmental chameleon masses, similar to effective Environmental chameleon masses, similar to effective masses of electrons in crystals, dressed by phonons. masses of electrons in crystals, dressed by phonons. Ordinary matter plays Ordinary matter plays the role of phonons the role of phonons… … Damour, Polyakov Khoury, Weltman
Chameleon Chameleon Consider a scalar Consider a scalar with (almost) with (almost) gravitational couplings to matter: gravitational couplings to matter: In presence of matter stress energy, it’ ’s effective potential is s effective potential is In presence of matter stress energy, it It’ It ’s minimum and mass at the minimum are s minimum and mass at the minimum are A good approximation for time scales τ « 1/ Η A good approximation for time scales τ « 1/ Η What happens when the field sits in this environmental minimum? the field sits in this environmental minimum? What happens when In the lab? In the lab? Cosmologically? Cosmologically?
Lab phenomenology Lab phenomenology We must pass the current laboratory bounds on sub-mm corrections bounds on sub-mm corrections We must pass the current laboratory to Newton’ to Newton ’s s law. The thin shell effect for the chameleons helps, law. The thin shell effect for the chameleons helps, since it suppresses the extra force by since it suppresses the extra force by R is the size of the object. For gravitational couplings this where R is the size of the object. For gravitational couplings this where still yields still yields Khoury, Weltman
Cosmology Cosmology FRW equations: FRW equations: Can check: in a matter dominated universe, if the field Can check: in a matter dominated universe, if the field sits in the minimum, the universe does not does not accelerate! accelerate! sits in the minimum, the universe For acceleration we must have generalized slow roll: For acceleration we must have generalized slow roll:
Cosmic phenomenology Cosmic phenomenology When When we can check that we can check that This shows that unless we put dark energy by hand This shows that unless we put dark energy by hand chameleon WILL chameleon WILL NOT NOT lead to accelerating universe! lead to accelerating universe! Thus we Thus we MUST HAVE MUST HAVE slow roll! slow roll!
Failure? Failure? Use the change of environment energy density between the lab and Use the change of environment energy density between the lab and the outer limits to get a huge variation in the mass; for the outer limits to get a huge variation in the mass; for one finds γ < 1 < 1 for any n, and for any n, and one finds γ Between the Earth, where , and the outer , and the outer Between the Earth, where limits, the mass can change by at most a factor limits, the mass can change by at most a factor of of So for any γ < 1 , and any integer n n , , a chameleon which obeys the a chameleon which obeys the So for any γ < 1 , and any integer lab bounds CANNOT lab bounds CANNOT yield cosmic acceleration by itself! yield cosmic acceleration by itself!
Log changeling Log changeling An exception: The log potential, where the mass scales linearly The log potential, where the mass scales linearly An exception: with density: with density: In more detail: In more detail: where the scales are chosen where the scales are chosen as is usual in quintessence models as is usual in quintessence models Rationale: we are NOT Rationale: we are NOT solving the cosmological constant problem! solving the cosmological constant problem! We are merely looking at possible signatures of such solutions. Yet, looking at possible signatures of such solutions. Yet, We are merely this may only require tunings in the gravitational sector… … this may only require tunings in the gravitational sector Now Now we look at cosmic history we look at cosmic history… …
Effective potential potential Effective
Early universe evolution I Early universe evolution I During inflation, the field is fixed: inflation, the field is fixed: During yields yields So the field is essentially decoupled! So the field is essentially decoupled! After inflation ends, at reheating After inflation ends, at reheating A huge number: we can ignore any non-relativistic matter density. A huge number: we can ignore any non-relativistic matter density. During the radiation era the potential is just a pure, tiny log - so the potential is just a pure, tiny log - so the During the radiation era the field will move like a free field! field will move like a free field!
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