The influence of the chameleon field potential on transition frequencies of gravitationally bound quantum states of ultra-cold neutrons

Abstract

We calculate the chameleon field potential for ultracold neutrons, bouncing on top of one or between two neutron mirrors in the gravitational field of the Earth. For the resulting non--linear equations of motion we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit. The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultra-cold neutrons bound in the gravitational field of the Earth.

11 pages, 4 figures

References in corpus (7)

• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• Evading Equivalence Principle Violations, Cosmological and other Experimental Constraints in Scalar Field Theories with a Strong Coupling to Matter
• Strongly Coupled Chameleon Fields: New Horizons in Scalar Field Theory
• Detecting Chameleons through Casimir Force Measurements
• A quantum mechanical description of the experiment on the observation of gravitationally bound states
• Unveiling Chameleons in Tests of Gravitational Inverse-Square Law
• Chameleon Gravity, Electrostatics, and Kinematics in the Outer Galaxy

Cited by in corpus (32)

• Tests of Chameleon Gravity
• Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios
• Probing Dark Energy with Atom Interferometry
• A Compendium of Chameleon Constraints
• Chameleon Dark Energy and Atom Interferometry
• Neutron Interferometry constrains dark energy chameleon fields
• Probing Strongly Coupled Chameleons with Slow Neutrons
• Constraining symmetron fields with atom interferometry
• Probing Dark Energy models with neutrons
• Constraining screened fifth forces with the electron magnetic moment
• Exact Solution for Chameleon Field, Self-Coupled Through the Ratra-Peebles Potential with n = 1 and Confined Between Two Parallel Plates
• Ellipticity Weakens Chameleon Screening
• The shape dependence of chameleon screening
• Probing of violation of Lorentz invariance by ultracold neutrons in the Standard Model Extension
• A general study of chameleon fifth force in gravity space experiments
• Probing Modified Gravity with Atom-Interferometry: a Numerical Approach
• A Proposed Experimental Search for Chameleons using Asymmetric Parallel Plates
• Fifth force induced by a chameleon field on nested cylinders
• Non-Relativistic Approximation of the Dirac Equation for Slow Fermions in Static Metric Spacetimes
• Non-Relativistic Approximation of Dirac Equation for Slow Fermions Coupled to the Chameleon and Torsion Fields in the Gravitational Field of the Earth
• Spin Precession of Slow Neutrons in Einstein-Cartan Gravity with Torsion, Chameleon and Magnetic Field
• Effects of a scalar fifth force on the dynamics of a charged particle as a new experimental design to test chameleon theories
• Solving nonlinear Klein-Gordon equations on unbounded domains via the Finite Element Method
• Casimir Tests of Scalar-Tensor Theories
• Standard Electroweak Interactions in Gravitational Theory with Chameleon Field and Torsion
• Internal Consistency of Neutron Coherent Scattering Length Measurements from Neutron Interferometry and from Neutron Gravity Reflectometry for Exotic Yukawa Analyses
• Effective Low-Energy Potential for Slow Dirac Fermions in Einstein-Cartan Gravity with Torsion and Chameleon
• A quantized frequency reference in the short-ranged gravity potential and its application for dark matter and dark energy searches
• What laboratory experiments can teach us about cosmology: A chameleon example
• Can Chameleon Field be identified with Quintessence ?
• Fundamental Neutron Physics: a White Paper on Progress and Prospects in the US
• Spatial distribution of ultracold neutron probability density in the gravitational field of the earth above a mirror