New form for the coincidence limit of the Feynman propagator, or heat kernel, in curved spacetime

Parker, Leonard; Toms, David J.

doi:10.1103/physrevd.31.953

Cited by 101 publications

(107 citation statements)

References 12 publications

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“…Consider a free, massive quantized scalar field of inverse Compton wavelength m, and curvature coupling ξ. The effective action for gravity coupled to such a field is obtained by integrating out the vacuum fluctuations of the field [16][17][18][19][20] and renormalized as in Ref. [16].…”

Section: Nonperturbative Vacuum Energy Effectsmentioning

confidence: 99%

New quantum aspects of a vacuum-dominated universe

Parker

Raval

2000

Phys. Rev. D

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In a new model that we proposed, nonperturbative vacuum contributions to the effective action of a free quantized massive scalar field lead to a cosmological solution in which the scalar curvature becomes constant after a time tj (when the redshift z ∼ 1) that depends on the mass of the scalar field and its curvature coupling. This spatially-flat solution implies an accelerating universe at the present time and gives a good one-parameter fit to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and energy density of the universe. Here we show that the imaginary part of the nonperturbative curvature term that causes the cosmological acceleration, implies a particle production rate that agrees with predictions of other methods and extends them to non-zero mass fields. The particle production rate is very small after the transition and is not expected to alter the nature of the cosmological solution. We also show that the equation of state of our model undergoes a transition at tj from an equation of state dominated by non-relativistic pressureless matter (without a cosmological constant) to an effective equation of state of mixed radiation and cosmological constant, and we derive the equation of state of the vacuum. Finally, we explain why nonperturbative vacuum effects of this ultralow-mass particle do not significantly change standard early universe cosmology.

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Section: Nonperturbative Vacuum Energy Effectsmentioning

confidence: 99%

New quantum aspects of a vacuum-dominated universe

Parker

Raval

2000

Phys. Rev. D

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“…The above form for the heat-kernel in curved spacetime was conjectured in Ref. [28] and demonstrated in Ref. [29].…”

Section: Computation Of the Effective Actionmentioning

confidence: 99%

“…This effectively sums, in the sense described in Refs. [28,29], all powers of R and E(x) (with any functional form of coefficients) in the proper-time series. When using the above resummed form for the heat-trace, the heat-kernel coefficients become slightly simpler and can be easily written down to relatively high order.…”

Section: Computation Of the Effective Actionmentioning

confidence: 99%

Chiral modulations in curved space I: formalism

Flachi

Tanaka

2011

J. High Energ. Phys.

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The goal of this paper is to present a formalism that allows to handle fourfermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization and supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.

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“…[4], we consider a free, massive quantized scalar field of inverse Compton wavelength (or mass) m, and curvature coupling ξ. The effective action for gravity coupled to such a field is obtained by integrating out the vacuum fluctuations of the field [4,7]. This effective action is the simplest one that gives the standard trace anomaly in the massless-conformally-coupled limit, and contains the explicit sum (in arbitrary dimensions) of all terms in the propagator having at least one factor of the scalar curvature, R.…”

Section: Our Modelmentioning

confidence: 99%

“…We considered a free quantized scalar field (with possible coupling to the scalar curvature, R). The propagator of the field included an infinite sum of all terms having at least one factor of R [7,8]. The effective action was given in [4], which can be referred to by the reader for a more complete exposition of the theory.…”

Section: Introductionmentioning

confidence: 99%

Erratum: Vacuum effects of an ultralow mass particle account for the recent acceleration of the universe [Phys. Rev. D60, 123502 (1999)]

Parker¹,

Raval²

2003

Phys. Rev. D

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In recent work, we showed that non-perturbative vacuum effects of a very low mass particle could induce, at a redshift of order 1, a transition from a matter-dominated to an accelerating universe. In that work, we used the simplification of a sudden transition out of the matter-dominated stage and were able to fit the Type Ia supernovae (SNe-Ia) data points with a spatially-open universe. In the present work, we find a more accurate, smooth spatially-flat analytic solution to the quantumcorrected Einstein equations. This solution gives a good fit to the SNe-Ia data with a particle mass parameter m h in the range 6.40 × 10 −33 eV to 7.25 × 10 −33 eV. It follows that the ratio of total matter density (including dark matter) to critical density, Ω0, is in the range 0.58 to 0.15, and the age t0 of the universe is in the range 8.10 h −1 Gyr to 12.2 h −1 Gyr, where h is the present value of the Hubble constant, measured as a fraction of the value 100 km/(s Mpc). This spatially-flat model agrees with estimates of the position of the first acoustic peak in the small angular scale fluctuations of the cosmic background radiation, and with light-element abundances of standard big-bang nucleosynthesis. Our model has only a single free parameter, m h , and does not require that we live at a special time in the evolution of the universe. PACS numbers: 98.80. Cq, 04.62.+v, 98.80.Es

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New form for the coincidence limit of the Feynman propagator, or heat kernel, in curved spacetime

Cited by 101 publications

References 12 publications

New quantum aspects of a vacuum-dominated universe

New quantum aspects of a vacuum-dominated universe

Chiral modulations in curved space I: formalism

Erratum: Vacuum effects of an ultralow mass particle account for the recent acceleration of the universe [Phys. Rev. D60, 123502 (1999)]

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