Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale

We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and 55 micrometers, probing distances less than the dark-energy length scale $\lambda_{\rm d}=\sqrt[4]{\hbar c/\rho_{\rm d}}\approx 85 \mu$m. We find with 95% confidence that the inverse-square law holds ($|\alpha| \leq 1$) down to a length scale $\lambda = 56 \mu$m and that an extra dimension must have a size $R \leq 44 \mu$m.Comment: 4 pages, 6 figure

f(R) actions, cosmic acceleration and local tests of gravity

We study spherically symmetric solutions in f(R) theories and its compatibility with local tests of gravity. We start by clarifying the range of validity of the weak field expansion and show that for many models proposed to address the Dark Energy problem this expansion breaks down in realistic situations. This invalidates the conclusions of several papers that make inappropriate use of this expansion. For the stable models that modify gravity only at small curvatures we find that when the asymptotic background curvature is large we approximately recover the solutions of Einstein gravity through the so-called Chameleon mechanism, as a result of the non-linear dynamics of the extra scalar degree of freedom contained in the metric. In these models one would observe a transition from Einstein to scalar-tensor gravity as the Universe expands and the background curvature diminishes. Assuming an adiabatic evolution we estimate the redshift at which this transition would take place for a source with given mass and radius. We also show that models of dynamical Dark Energy claimed to be compatible with tests of gravity because the mass of the scalar is large in vacuum (e.g. those that also include R^2 corrections in the action), are not viable.Comment: 26 page

Acceleressence: Dark Energy from a Phase Transition at the Seesaw Scale

Simple models are constructed for "acceleressence" dark energy: the latent heat of a phase transition occurring in a hidden sector governed by the seesaw mass scale v^2/M_Pl, where v is the electroweak scale and M_Pl the gravitational mass scale. In our models, the seesaw scale is stabilized by supersymmetry, implying that the LHC must discover superpartners with a spectrum that reflects a low scale of fundamental supersymmetry breaking. Newtonian gravity may be modified by effects arising from the exchange of fields in the acceleressence sector whose Compton wavelengths are typically of order the millimeter scale. There are two classes of models. In the first class the universe is presently in a metastable vacuum and will continue to inflate until tunneling processes eventually induce a first order transition. In the simplest such model, the range of the new force is bounded to be larger than 25 microns in the absence of fine-tuning of parameters, and for couplings of order unity it is expected to be \approx 100 microns. In the second class of models thermal effects maintain the present vacuum energy of the universe, but on further cooling, the universe will "soon" smoothly relax to a matter dominated era. In this case, the range of the new force is also expected to be of order the millimeter scale or larger, although its strength is uncertain. A firm prediction of this class of models is the existence of additional energy density in radiation at the eV era, which can potentially be probed in precision measurements of the cosmic microwave background. An interesting possibility is that the transition towards a matter dominated era has occurred in the very recent past, with the consequence that the universe is currently decelerating.Comment: 10 pages, references adde

Possible black universes in a brane world

A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. Such spherically symmetric configurations have been recently found as solutions to the Einstein equations with phantom scalar fields (with negative kinetic energy) as sources of gravity. They have a Schwarzschild-like causal structure but a de Sitter infinity instead of a singularity. It is attempted to obtain similar configurations without phantoms, in the framework of an RS2 type brane world scenario, considering the modified Einstein equations that describe gravity on the brane. By building an explicit example, it is shown that black-universe solutions can be obtained there in the presence of a scalar field with positive kinetic energy and a nonzero potential.Comment: 8 pages, 5 figures, gc styl

Renormalization group improved black hole space-time in large extra dimensions

By taking into account a running of the gravitational coupling constant with an ultra violet fixed point, an improvement of classical black hole space-times in extra dimensions is studied. It is found that the thermodynamic properties in this framework allow for an effective description of the black hole evaporation process. Phenomenological consequences of this approach are discussed and the LHC discovery potential is estimated.Comment: 13 pages, 6 figure

Dark Energy and Extending the Geodesic Equations of Motion: Its Construction and Experimental Constraints

With the discovery of Dark Energy, $\Lambda_{DE}$, there is now a universal length scale, $\ell_{DE}=c/(\Lambda_{DE} G)^{1/2}$, associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we will study a specific class of such extensions, and show that contrary to expectations, they are not automatically ruled out by either theoretical considerations or experimental constraints. In particular, we show that while these extensions affect the motion of massive particles, the motion of massless particles are not changed; such phenomena as gravitational lensing remain unchanged. We also show that these extensions do not violate the equivalence principal, and that because $\ell_{DE}=14010^{800}_{820}$ Mpc, a specific choice of this extension can be made so that effects of this extension are not be measurable either from terrestrial experiments, or through observations of the motion of solar system bodies. A lower bound for the only parameter used in this extension is set.Comment: 19 pages. This is the published version of the first half of arXiv:0711.3124v2 with corrections include

Sub-millimeter Tests of the Gravitational Inverse-square Law

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R <= 160 microns, and on two equal-sized large extra dimensions of R <= 130 microns. Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of pseudoscalars with m <= 10 meV/c^2.Comment: 34 pages, 38 figure

Probing the dark matter issue in f(R)-gravity via gravitational lensing

For a general class of analytic f(R)-gravity theories, we discuss the weak field limit in view of gravitational lensing. Though an additional Yukawa term in the gravitational potential modifies dynamics with respect to the standard Newtonian limit of General Relativity, the motion of massless particles results unaffected thanks to suitable cancellations in the post-Newtonian limit. Thus, all the lensing observables are equal to the ones known from General Relativity. Since f(R)-gravity is claimed, among other things, to be a possible solution to overcome for the need of dark matter in virialized systems, we discuss the impact of our results on the dynamical and gravitational lensing analyses. In this framework, dynamics could, in principle, be able to reproduce the astrophysical observations without recurring to dark matter, but in the case of gravitational lensing we find that dark matter is an unavoidable ingredient. Another important implication is that gravitational lensing, in the post-Newtonian limit, is not able to constrain these extended theories, since their predictions do not differ from General Relativity.Comment: 7 pages, accepted for publication in EPJ