Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments

Abstract

We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero point energy of the vacuum. We derive the Casimir force between parallel conducting plates as a function of the following scales: plate separation, radius of the extra dimension and cutoff energy scale. We find that there are critical values of these scales where the Casimir force between the plates changes sign. For the cutoff energy scale required to reproduce the observed value of the cosmological constant, we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation $d_0=0.6mm$, assuming a zero radius of the extra dimension (no extra dimension). This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of $100nm$. For a non-zero extra dimension radius, the critical separation $d_0$ gets even larger than $0.6mm$ and remains inconsistent with Casimir force experiments. We conclude that with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff can not play the role of the cosmological constant.

5 pages, 5 figures

References in corpus (39)

• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• Cosmological Imprint of an Energy Component with General Equation of State
• Cosmological Constant - the Weight of the Vacuum
• The Case for a Positive Cosmological Lambda-term
• Cosmology and the Fate of Dilatation Symmetry
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• The Cosmological Constant
• An alternative to quintessence
• Quantum gravity and minimum length
• Bounds on Universal Extra Dimensions
• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Measurement of the Casimir force between parallel metallic surfaces
• Can the Chaplygin gas be a plausible model for dark energy?
• The Casimir effect: Recent controversies and progress
• Hawking Spectrum and High Frequency Dispersion
• Trans-Planckian dispersion and scale-invariance of inflationary perturbations
• Duality and zero-point length of spacetime
• Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant
• The Casimir Effect in the Presence of a Minimal Length
• Casimir Effect in the Presence of Minimal Lengths
• Anthropic prediction for Lambda and the Q catastrophe
• (De)Stabilization of an extra dimension due to a Casimir force
• The Casimir Effect in the Presence of Compactified Universal Extra Dimensions
• Testing Dispersion Relations of Quantum $\kappa$-Poincaré Algebra on Cosmological Ground
• Brane Worlds and the Cosmic Coincidence Problem
• Dynamical Instability of Brane Solutions with a Self-Tuning Cosmological Constant
• Could dark energy be measured in the lab?
• Casimir Effect confronts Cosmological Constant
• Matching the observational value of the cosmological constant
• Bayesian Evidence for a Cosmological Constant using new High-Redshift Supernovae Data
• A cosmological constant from degenerate vacua
• Constraints on extra dimensions from cosmological and terrestrial measurements
• Has Dark Energy really been discovered in the Lab?
• On the Casimir effect for parallel plates in the spacetime with one extra compactified dimension
• Josephson junctions and dark energy
• Multi-(super)graviton theory on topologically non-trivial backgrounds
• What measurable zero point fluctuations can(not) tell us about dark energy

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• Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
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• The Shape of Compact Toroidal Dimensions $T_{\theta }^d$ and the Casimir Effect on $M^D\times T_{\theta }^d$ spacetime
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• Testing axion physics in a Josephson junction environment
• Zeldovich Lambda and Weinberg Relation: An Explanation for the Cosmological Coincidences
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• Revisiting Vacuum Energy in Compact Spacetimes
• Thermal Casimir effect in Kerr spacetime with quintessence and massive gravitons
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• Casimir free energy for massive fermions: a comparative study of various approaches
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• Casimir force for cosmological domain walls
• Singularities of the Casimir Energy for Quantum Field Theories with Lifshitz Dimensions
• Fermionic Casimir effect in the presence of compact dimension in field theory with Lorentz invariance violation
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