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

Leandros Perivolaropoulos

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

Leandros Perivolaropoulos

Astrophysics · Submitted 12 Feb 2008

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID0802.1531 (version 1)

Pith ID3EVGLPGW, Pith's permanent record of this paper and its review

CitationLeandros Perivolaropoulos. "Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments." arXiv:0802.1531 (2008). https://pith.science/paper/3EVGLPGW

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.66 · human participants 0.02 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.78 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.49	0.31	0.02	asserted 0.59
s1	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.	method 0.54	0.95	0.02	asserted 0.99
s2	We find that there are critical values of these scales where the Casimir force between the plates changes sign.	result 1.00	0.95	0.03	asserted 1.00
s3	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).	result 1.00	0.94	0.05	asserted 1.00
s4	This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of $100nm$.	interpretation 0.57	0.14	0.04	asserted 0.77
s5	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.	result 0.96	0.88	0.04	asserted 1.00
s6	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.	interpretation 0.83	0.76	0.98	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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full text
figures and tables
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P abstract

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C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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.

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7 arXiv papers cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe.

Can Dark Energy emerge from quantum effects in compact extra dimension ? · 0.99

Papers citing it · 4 sentences without a confident label

Compares with it 1 paper

Our final result PEM naturally differs from previous results [ref] because the correction to Casimir's result is not derived using three discrete modes but two discrete and one continuum mode.

Compact dimensions and the Casimir effect: the Proca connection · Proca continuum mode · 0.89

Cites it as background 4 papers

The UV cut-off dependence of the Casimir energy for perfect conductors with an extra compact dimension was also studied recently in [ref] (the compactification scheme is not explicitly stated).

Compact dimensions and the Casimir effect: the Proca connection · Introduction · 0.95
There are several works where extra dimensions have been invoked [ref] to explain the cosmological constant.

The cosmological constant from the zero point energy of compact dimensions · The energy density in the regular THREE dimensional space · 0.95
Then the Casimir energy is calculated as [equation] where the result can be expressed formally in terms of Epstein $ζ$-function.[The Casimir energy in relation to extra dimensions has been studied by many authors [ref] .

Casimir force for cosmological domain walls · Casimir energy for the domain walls with a small mass-gap · 0.98

What it cites · 13 sentences without a confident label

Uses data or values from 1 paper

Even though the current experimental experimental bounds on $R$ are quite stringent ($R(300GeV)^-1≃10^-9nm$ [ref] ) it is still instructive to consider this possibility in the context of the Casimir effect with a cutoff in the vacuum energy.

Bounds on Universal Extra Dimensions · Introduction · 0.91

Compares with 1 paper

Finally, we point out that our approach connecting the Casimir effect in the presence of a cutoff with the cosmological constant is distinct from previous global approaches [ref] which view the universe as a system of large (cosmological size) and small compact dimensions (finite system) where the vacuum energy gets modified due to the finiteness of the system.

Matching the observational value of the cosmological constant · Introduction · 0.93

Cites as background 10 papers

According to the Casimir effect [ref] , the presence of macroscopic bodies (like a pair of conducting plates) leads to a modification of the zero point vacuum fluctuations due to the introduction of non-trivial boundary conditions.

Dimensional and Dynamical Aspects of the Casimir Effect: Understanding the Reality and Significance of Vacuum Energy · Introduction · 1.00
According to the Casimir effect [ref] , the presence of macroscopic bodies (like a pair of conducting plates) leads to a modification of the zero point vacuum fluctuations due to the introduction of non-trivial boundary conditions.

The Casimir effect: Recent controversies and progress · Introduction · 1.00
Such experiments include measurements of the Casimir force [ref] and measurements of the current noise in Josephson junctions [ref] .

Josephson junctions and dark energy · Introduction · 0.81

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