Estimate for the size of the compactification radius of a one extra dimension universe

Pascoal, F.; Oliveira, L. F. A.; Rosa, F. S. S.; Farina, C.

doi:10.1590/s0103-97332008000500009

Cited by 24 publications

(34 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is some overlap with an article by Teo [48] that appeared on the archive in the meantime and gives special attention to the finite temperature theory. The recent cosmological papers [20,21,31,45] do not explicitly consider the outer chamber of a piston, but nevertheless they do not report a repulsive force; we investigate the reason for that apparent discrepancy.…”

Section: Introductionmentioning

confidence: 86%

See 1 more Smart Citation

Kaluza-Klein models as pistons

Kirsten

Fulling

2009

Phys. Rev. D

View full text Add to dashboard Cite

We consider the influence of extra dimensions on the force in Casimir pistons. Suitable analytical expressions are provided for the Casimir force in the range where the plate distance is small, and that where it is large, compared to the size of the extra dimensions. We show that the Casimir force tends to move the center plate toward the closer wall; this result is true independently of the cross-section of the piston and the geometry or topology of the additional Kaluza-Klein dimensions. The statement also remains true at finite temperature. In the limit where one wall of the piston is moved to infinity, the result for parallel plates is recovered. If only one chamber is considered, a criterion for the occurrence of Lukosz-type repulsion, as opposed to the occurrence of renormalization ambiguities, is given; we comment on why no repulsion has been noted in some previous cosmological calculations that consider only two plates.

show abstract

Section: Introductionmentioning

confidence: 86%

“…However, the papers [20,21,31,45] did not take the outer chamber of the Kaluza-Klein piston into account, but nevertheless they did not find a repulsive force. Closer examination (see, for example, eqs.…”

Section: Pistons With Finite Cross Sectionmentioning

confidence: 99%

Kaluza-Klein models as pistons

Kirsten

Fulling

2009

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…Extra-dimensional theories with low-energy compactification scale predict Yukawa-type corrections to Newton's gravitational law and the measurements of the Casimir forces between macroscopic bodies provide a sensitive test for constraining the parameters of the corresponding long-range interactions [28][29][30][31][32]. The influence of extra compactified dimensions on the Casimir effect in the classical configuration of two parallel plates has been recently discussed for scalar [33][34][35][36][37][38][39][40], electromagnetic [41][42][43][44][45] and fermionic [46][47][48] fields.…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for scalar current densities in topologically nontrivial spaces

2015

View full text Add to dashboard Cite

We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum state becomes unstable. The stability condition depends on the lengths of compact dimensions and is less restrictive than that for background with trivial topology. The vacuum current density is a periodic function of the magnetic flux, enclosed by compact dimensions, with the period equal to the flux quantum. It is explicitly decomposed into the boundary-free and boundary-induced contributions. In sharp contrast to the VEVs of the field squared and the energy-momentum tensor, the current density does not contain surface divergences. Moreover, for Dirichlet condition it vanishes on the boundaries. The normal derivative of the current density on the boundaries vanish for both Dirichlet and Neumann conditions and is nonzero for general Robin conditions. When the separation between the plates is smaller than other length scales, the behavior of the current density is essentially different for non-Neumann and Neumann boundary conditions. In the former case, the total current density in the region between the plates tends to zero. For Neumann boundary condition on both plates, the current density is dominated by the interference part and is inversely proportional to the separation. a

show abstract

“…Casimir effect for electromagnetic fields confined between a pair of parallel and perfectly conducting plates in R d+1 was considered in [60]. In the case the extra dimension is compactified to a circle S 1 , it was studied in [25,61,62,63]. For the Randall-Sundrum spacetime model, the Casimir force due to massless scalar fields subject to Dirichlet boundary conditions on two parallel plates were calculated in [64,65,66].…”

mentioning

confidence: 99%

Finite temperature Casimir effect in spacetime with extra compactified dimensions

Teo

2009

Physics Letters B

View full text Add to dashboard Cite

In this letter, we derive the explicit exact formulas for the finite temperature Casimir force acting on a pair of parallel plates in the presence of extra compactified dimensions within the framework of Kaluza-Klein theory. Using the piston analysis, we show that at any temperature, the Casimir force is always attractive and the effect of extra dimensions becomes stronger when the size or number of the extra dimensions increases. These properties are not affected by the explicit geometry and topology of the Kaluza-Klein space. Theories with extra space dimensions can be dated back to the work of Kaluza and Klein [1,2] in an attempt to unify gravity and classical electrodynamics. The advent of string theory has made the idea of extra dimensions indispensable [3]. Recently, the interest for physical models that contain extra warped dimensions come from the endeavor to explain the large gap between the Planck and electroweak scale (the hierarchy problem), and the dark energy and cosmological constant problem [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. In this letter, we are interested in studying the Casimir effect in the presence of extra compactified dimensions. The research on Casimir effect in the scenarios with extra dimensions have been studied in the context of string theory [26,27,28,29], dark energy and cosmological constant [16,17,18,19,21,22,25,30,31,32,33,34,35,36,37], as well as stabilization of extra dimensions [23,24,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. Casimir force for massless scalar field with Dirichlet boundary conditions on a pair of parallel plates inside space with extra dimensions compactified to a torus T n = (S 1 ) n have been calculated in [54,55,56,57,58,59]. The dependence of the Casimir energy on a cut-off scale was investigated in [25]. Casimir effect for electromagnetic fields confined between a pair of parallel and perfectly conducting plates in R d+1 was considered in [60]. In the case the extra dimension is compactified to a circle S 1 , it was studied in [25,61,62,63]. For the Randall-Sundrum spacetime model, the Casimir force due to massless scalar fields subject to Dirichlet boundary conditions on two parallel plates were calculated in [64,65,66].Despite the importance of the thermal corrections, most of the works mentioned above dealt with Casimir effect at zero temperature. In particular, we would like to mention the two papers by Cheng [56,58] where he calculated the Casimir force acting on a pair of parallel plates due to massless scalar field with Dirichlet boundary conditions in spacetime with n extra dimensions compactified to a torus. As pointed out in the comment [59], the earlier paper [56] concluded that the presence of extra dimensions will give rise to repulsive Casimir force under certain conditions. However, this result was invalidated by the author himself in the later paper [58], where he redid the calculations in a more physical setup known as piston [67] and concluded that the Casimir force shall always be attractive. The fini...

show abstract

Estimate for the size of the compactification radius of a one extra dimension universe

Cited by 24 publications

References 34 publications

Kaluza-Klein models as pistons

Kaluza-Klein models as pistons

Casimir effect for scalar current densities in topologically nontrivial spaces

Finite temperature Casimir effect in spacetime with extra compactified dimensions

Contact Info

Product

Resources

About