Sub-millimeter Spatial Oscillations of Newton's Constant: Theoretical Models and Laboratory Tests

Abstract

We investigate the viability of sub-millimeter wavelength oscillating deviations from the Newtonian potential at both the theoretical and the experimental/observational level. At the theoretical level such deviations are generic predictions in a wide range of extensions of General Relativity (GR) including $f(R)$ theories, massive Brans-Dicke theories, compactified extra dimension models and nonlocal extensions of GR. However, the range of parameters associated with such oscillating deviations is usually connected with instabilities. An exception emerges in nonlocal gravity theories where oscillating deviations from Newtonian potential occur naturally on sub-millimeter scales without instabilities. As an example of a model with unstable Newtonian oscillations we review an $f(R)$ expansion around General Relativity of the form $f(R)=R+\frac{1}{6m^2}{R}^2$ with $m^2<0$ pointing out possible stabilization mechanisms. As an example of a model with stable Newtonian oscillations we discuss nonlocal gravity theories. If such oscillations are realized in Nature on sub-millimeter scales, a signature is expected in torsion balance experiments testing Newton's law. We search for such a signature in the torsion balance data of the Washington experiment (combined torque residuals) testing Newton's law at sub-millimeter scales. We show that an oscillating residual ansatz with spatial wavelength $\lambda \simeq 0.1mm$ provides a better fit to the data compared to the residual Newtonian constant ansatz by $\Delta {\chi }^2=-15$. Similar improved fits, also occur in about $10\%$ of Monte Carlo realizations of Newtonian data. Thus, the significance level of this improved fit is at a level of not more than $2\sigma$. The energy scale corresponding to this best fit wavelength is identical to the dark energy length scale ${\lambda }_{de}\equiv \sqrt[4]{\hslash c/{\rho }_{de}}\approx 0.1mm$.

21 pages, 15 Figures. Published version (Phys. Rev. D 95, 084050, 2017). Typos corrected in eqs. (3.23), (3.34), (3.35). The Mathematica file producing the Figures of the paper along with the data analysis is unchanged and is publicly available at http://leandros.physics.uoi.gr/newt-oscil/

References in corpus (29)

• Dynamics of dark energy
• Cosmology and Fundamental Physics with the Euclid Satellite
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• Solar System constraints to general f(R) gravity
• Limit to General Relativity in f(R) theories of gravity
• The Newtonian Limit of F(R) gravity
• Matter instability in modified gravity
• Solar System tests DO rule out 1/R gravity
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Improved constraints on non-Newtonian forces at 10 microns
• A Singularity Problem with f(R) Dark Energy
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• Review of short-range gravity experiments in the LHC era
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Search for Screened Interactions Associated with Dark Energy Below the 100 $\mu \mathrm{m}$ Length Scale
• Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity
• Invariant quantities in the scalar-tensor theories of gravitation
• Dark energy, inflation and dark matter from modified F(R) gravity
• Nonlocal gravity and the diffusion equation
• A general solution in the Newtonian limit of f(R)- gravity
• Stringy gravity at short distances
• Brane world corrections to Newton's law
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Comments on "Solar System constraints to general f(R) gravity"
• Instabilities in tensorial nonlocal gravity
• Micro-orbits in a many-branes model and deviations from $1/r^2$ Newton's law

Cited by in corpus (31)

• Challenges for $\Lambda$CDM: An update
• Low-energy effects in a higher-derivative gravity model with real and complex massive poles
• On the gravitational seesaw in higher-derivative gravity
• Generalised uncertainty relations from superpositions of geometries
• Hints of Modified Gravity in Cosmos and in the Lab?
• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Model Comparison tests of modified gravity from the Eöt-Wash experiment
• Constraints on Spatially Oscillating Sub-mm Forces from the Stanford Levitated Microsphere Experiment Data
• Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?
• Novel constraints on fifth forces and ultralight dark sector with asteroidal data
• Generalized Uncertainty Principle and Black Holes in Higher Dimensional Self-Complete Gravity
• A Unified Spectral Approach for Quasinormal Modes of Lee-Wick Black Holes
• Is there a connection between "dark" and "light" physics?
• Solar chameleons: Novel channels
• Quantum spreading of a self-gravitating wave-packet in singularity free gravity
• Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles
• Revealing Infinite Derivative Gravity's true potential: The weak-field limit around de Sitter backgrounds
• Does space-time torsion determine the minimum mass of gravitating particles?
• Regular multi-horizon Lee-Wick black holes
• The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity
• Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate
• A New Approach to Generalised Uncertainty Relations
• $R^2$ Dark Energy in the Laboratory
• Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds
• Proposed experimental test of Randall-Sundrum Models
• Proposal for a Quantum Mechanical Test of Gravity at Millimeter Scale
• Fractal properties of particle paths due to generalised uncertainty relations
• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method
• Is a covariant virtual tachyon viable?
• Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints
• Dynamical measurements of deviations from Newton's $1/r^2$ law