Gravitational Casimir energy in non-Abelian Kaluza-Klein theories

Chodos, Alan; Myers, Eric

doi:10.1103/physrevd.31.3064

Cited by 38 publications

(18 citation statements)

References 12 publications

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“…But this is not here the case, and the fact that q < 0 does not allow for such a beautiful analysis. Henceforth, we shall apply in what follows what we have called the extended binomial expansion approach (see also [15]), namely, we will introduce an extra summation via 5) where the validity of the binomial expansion is defined for…”

Section: A Extended Binomial Expansionmentioning

confidence: 99%

Casimir effect in rugby-ball type flux compactifications

2007

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As a continuation of the work in [1], we discuss the Casimir effect for a massless bulk scalar field in a 4D toy model of a 6D warped flux compactification model, to stabilize the volume modulus. The one-loop effective potential for the volume modulus has a form similar to the Coleman-Weinberg potential. The stability of the volume modulus against quantum corrections is related to an appropriate heat kernel coefficient. However, to make any physical predictions after volume stabilization, knowledge of the derivative of the zeta function, ζ ′ (0) (in a conformally related spacetime) is also required. By adding up the exact mass spectrum using zeta function regularization, we present a revised analysis of the effective potential. Finally, we discuss some physical implications, especially concerning the degree of the hierarchy between the fundamental energy scales on the branes. For a larger degree of warping our new results are very similar to the ones given in Ref [1] and imply a larger hierarchy. In the non-warped (rugby-ball) limit the ratio tends to converge to the same value, independently of the bulk dilaton coupling.

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Section: A Extended Binomial Expansionmentioning

confidence: 99%

Casimir effect in rugby-ball type flux compactifications

2007

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“…ef given by (6) and ǫ given by (13). The evaluation of V (1) ef , using the zeta function method implicitly removes the divergences while for ǫ we must run over an explicit renormalization procedure in order to eliminate the divergences.…”

Section: Myers' Extra Term and Zpamentioning

confidence: 99%

On the equivalence between the effective potential and zero-point energy

Nogueira

Maia

1997

Physics Letters B

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We investigate a possible difference between the effective potential and zero-point energy. We define the zero-point ambiguity (ZPA) as the difference between these two definitions of vacuum energy. Using the zeta function technique in order to obtain renormalized quantities, we show that ZPA vanishes, implying that both of the above definitions of vacuum energy coincide for a large class of geometries and a very general potential. In addition, we show explicitly that an extra term, obtained by E. Myers some years ago for the ZPA, disappears when a scale parameter µ is consistently introduced in all zeta functions in order to keep them dimensionless.

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“…Generalizations to a spacetime structure M 4 ×S N have been done in Candelas & Weinberg (1984) and Chodos & Myers (1985) for odd N and later in Myers (1986) and Kantowski & Milton (1987) for even N. Such generalizations to extra dimension N can be written as…”

Section: Casimir Effect From a Higher Compact Dimensionmentioning

confidence: 99%

“…The second colum gives the relation between the gravitational Casimir energy ρ and the radius of the extra dimension in R 4 ×S N compactification for different values of N (the differences with Candelas & Weinberg (1984) and Chodos & Myers (1985) being the polarization factors p d+2 ). The third column gives the radius of the extradimension, such that this gravitational Casimir energy is equal to the observed dark energy density (the sign being the one of the normalization constant in Col. 2).…”

Section: Casimir Effect From a Higher Compact Dimensionmentioning

confidence: 99%

Can dark energy emerge from quantum effects in a compact extra dimension?

Dupays

Lamine

Blanchard

2013

A&A

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The origin of the accelerated expansion of the universe is a major problem in both modern cosmology and theoretical physics. In quantum field theory, simple estimations of the vacuum contribution to the density energy of the Universe are known to lead to catastrophically high values compared to observations. A gravitational Casimir effect from an additional compact dimension of space is known to lead to an effective cosmological constant. Nevertheless, such a contribution by itself is usually not regarded as a plausible source for accelerating the expansion, given the constraints on such scenarios. Here, we propose that the Casimir vacuum contribution of the gravitational field actually provides a low positive value to the density energy of the universe. The key new ingredient is to assume that only modes with shorter wavelengths than the Hubble radius contribute to the vacuum energy. Such a contribution gives a positive energy density, has a naturally Lorentz invariant equation of state in the usual 4D spacetime, and can thus be interpreted as a cosmological constant. Its value agrees with observations for a radius of a fifth extra dimension given by 35 µm. The implied modification of the gravitational inverse square law is close but below existing limits from experiments testing gravity at short range.

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Gravitational Casimir energy in non-Abelian Kaluza-Klein theories

Cited by 38 publications

References 12 publications

Casimir effect in rugby-ball type flux compactifications

Casimir effect in rugby-ball type flux compactifications

On the equivalence between the effective potential and zero-point energy

Can dark energy emerge from quantum effects in a compact extra dimension?

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