Challenging the Cosmological Constant

We outline a dynamical dark energy scenario whose signatures may be simultaneously tested by astronomical observations and laboratory experiments. The dark energy is a field with slightly sub-gravitational couplings to matter, a logarithmic self-interaction potential with a scale tuned to ∼ 10 eV, as is usual in quintessence models, and an effective mass mφ influenced by the environmental energy density. Its forces may be suppressed just below the current bounds by the chameleon-like mimicry, whereby only outer layers of mass distributions, of thickness 1/mφ, give off appreciable long range forces. After inflation and reheating, the field is relativistic, and attains a Planckian expectation value before Hubble friction freezes it. This can make gravity in space slightly stronger than on Earth. During the matter era, interactions with nonrelativistic matter dig a minimum close to the Planck scale. However, due to its sub-gravitational matter couplings the field will linger away from this minimum until the matter energy density dips below ∼ 10 eV. Then it starts to roll to the minimum, driving a period of cosmic acceleration. Among the signatures of this scenario may be dark energy equation of state w 6= −1, stronger gravity in dilute mediums, that may influence BBN and appear as an excess of dark matter, and sub-millimeter corrections to Newton’s law, close to the present laboratory limits. [email protected] Understanding cosmic acceleration is the deepest problem of modern cosmology. It has profound implications both for fundamental physics and for the fate of the universe [1]. A range of ideas have been pursued to explain the acceleration, and to date in all of them, one is forced to fine tune some dimensional scales to accommodate cosmic acceleration now. This yields the ‘Why Now’ problem, which may be taken as a clue that we are missing something important in the formulation of the problem [2]. To compound the puzzle, to date we have noted other curious coincidences, such as the near matches between the scale of the cosmological constant, the dark matter density, the neutrino mass, and the laboratory limits on gravitational force, which are all controlled by a length scale of about a millimeter. While these may simply be numerical accidents, it is interesting to probe for deeper connections between them. We can pursue this by formulating models where cosmic acceleration has other direct observable consequences, as exemplified in [3]-[7]. The main problem in building such models is the range of mass scales which one needs for nontrivial dynamics. For example, to have a dynamical dark energy instead of the cosmological constant one needs ultralight degrees of freedom, say scalars, with masses mφ < ∼ H0 ∼ 10eV. These must couple to matter significantly more weakly than gravity to avoid conflicts with Solar System tests [8]. On the other hand, laboratory tests constrain new fields to be heavier than about 10eV, if they couple to matter gravitationally [9]. So to make dark energy detectable in laboratory searches and consistent with long range gravity, we need models where its mass changes by at least thirty orders of magnitude between the Earth and the extragalactic space. Indeed, if the masses of dark fields are fixed by the current laboratory bounds, we could integrate them out at scales below their masses and end up with dark energy practically indistinguishable from the pure cosmological constant, without a direct link to laboratory phenomena. In this note we will outline a model of quintessence which may be within reach of future terrestrial searches for sub-millimeter corrections to Newton’s law of gravity. It controls cosmology at largest scales with a very weak potential, logarithmic in the field value. Yet at shorter scales, due to large environmental masses as in [10, 11, 12], this field could decouple at the scales probed by current laboratory tests, but perhaps just barely, so that it could be revealed by future probes. Its signatures, in addition to possible sub-millimeter gravitational effects, would include an equation of state w 6= −1, distinguishing it from the cosmological constant, stronger gravity in less dense mediums, which can influence BBN, and induce a weak spatio-temporal variation of Newton’s constant, affecting structure formation and possibly simulating an excess of dark matter abundance over its actual density. This model could therefore be a useful benchmark for future observational explorations of the signatures of dark energy. We start our discussion with a review of the mechanisms that make the masses of fields dependent on the medium in which they propagate [10]-[14]. They may provide a way around the usual decoupling argument, and are most simply formulated for models where the scalar couples to matter universally, by interaction Lagrangians Lmatter(ge4 ,Ψ) like a Brans-Dicke field. In these cases, the effective potential controlling the propagation of Wider classes of models where the coupling changes from species to species were studied in [11].