Regularization, renormalization, and covariant geodesic point separation

Christensen, Steven M.

doi:10.1103/physrevd.17.946

Cited by 364 publications

(447 citation statements)

References 19 publications

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“…However, since we have a finite Planck scale cutoff, no terms in the effective action diverge. Following along the calculation of [185], we find that the energy density is suppressed by powers of H=M P compared to (B4), so the black brane does not actually match the dual gauge theory during inflation. In other words, not only does the black brane fail to match the correct equation of state, but it also has the wrong magnitude of energy density.…”

Section: Black-brane Horizonmentioning

confidence: 74%

Stringy effects during inflation and reheating

2006

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We consider inflationary cosmology in the context of string compactifications with multiple throats. In scenarios where the warping differs significantly between throats, string and Kaluza-Klein physics can generate potentially observable corrections to the cosmology of inflation and reheating. First we demonstrate that a very low string scale in the ground state compactification is incompatible with a high Hubble scale during inflation, and we propose that the compactification geometry is altered during inflation. In this configuration, the lowest scale is just above the Hubble scale, which is compatible with the effective field theory but still leads to potentially observable cosmic microwave background corrections. Also in the appropriate region of parameter space, we find that reheating leads to a phase of long open strings in the standard model sector (before the usual radiation-dominated phase). We sketch the cosmology of the long string phase and we discuss possible observational consequences.

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Section: Black-brane Horizonmentioning

confidence: 74%

Stringy effects during inflation and reheating

2006

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“…The above expression is still (ultraviolet) divergent in the coincidence limit due to the summation over n. In a general spherically symmetric space-time, the expression that needs to be subtracted from the Green function, before taking the ǫ → 0 limit, is known to be given by [13,39] …”

Section: Coincidence Limitmentioning

confidence: 99%

Vacuum polarization in asymptotically anti-de Sitter black hole geometries

Flachi

Tanaka

2008

Phys. Rev. D

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We study the polarization of the vacuum for a scalar field, φ 2 , on a asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and pointsplitting regularization, similarly to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counter-terms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result expressed in terms of some generalized zeta-functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes φ 2 as a series in such zeta-functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the 'remainder' of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The general results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semi-classical Einstein's equations taking into account the back-reaction from quantum fields on asymptotically anti-de Sitter black holes.

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“…For spin-1/2 fields, however, the adiabatic expansion takes a different form [10,11] (see also [12]). The adiabatic method has been proven to be equivalent to the DeWitt-Schwinger point-splitting scheme [13,14] for both scalar fields [9,15], and spin-1/2 fields [16]. The method is specially suitable for numerical calculations, [17,18] and also for analytic approximations [19,20].…”

Section: Introductionmentioning

confidence: 99%

Adiabatic regularization with a Yukawa interaction

et al. 2017

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We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stressenergy tensor T µν and the bilinear ψ ψ in a spatially flat Friedmann-Lemaitre-RobertsonWalker (FLRW) spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat-kernel method using the effective action.

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Regularization, renormalization, and covariant geodesic point separation

Cited by 364 publications

References 19 publications

Stringy effects during inflation and reheating

Stringy effects during inflation and reheating

Vacuum polarization in asymptotically anti-de Sitter black hole geometries

Adiabatic regularization with a Yukawa interaction

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