Closed form effective conformal anomaly actions in D≥4

Deser, S.

doi:10.1016/s0370-2693(00)00315-4

Cited by 50 publications

(49 citation statements)

References 10 publications

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“…This 4th order differential operator appears in conformal anomalies [61]. The relation between it and the volume of the past light-cone is that 8π/D P acting on one agrees with V for arbitrary homogeneous and isotropic spacetimes [62],…”

Section: B a Timelike 4-vector Fieldmentioning

confidence: 95%

Nonlocal metric formulations of modified Newtonian dynamics with sufficient lensing

2011

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We demonstrate how to construct purely metric modifications of gravity which agree with general relativity in the weak field regime appropriate to the solar system, but which possess an ultra-weak field regime when the gravitational acceleration becomes comparable to a0 ∼ 10 −10 m/s 2 . In this ultra-weak field regime, the models reproduce the MOND force without dark matter and also give enough gravitational lensing to be consistent with existing data. Our models are nonlocal and might conceivably derive from quantum corrections to the effective field equations.

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Section: B a Timelike 4-vector Fieldmentioning

confidence: 95%

Nonlocal metric formulations of modified Newtonian dynamics with sufficient lensing

2011

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“…The outcome of this calculation is well-known [19][20][21][22][23][24][25][26][27] and the calculation for the spin 0, …”

Section: Divergences Due To Mattermentioning

confidence: 99%

A Class of Elementary Particle Models Without Any Adjustable Real Parameters

2011

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Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor and scalar fields. There seems to be no physical principle to determine these parameters as long as they stay within certain domains dictated by the renormalization group. Here however, reasons are given to demand that, when gravity is coupled to the system, local conformal invariance should be a spontaneously broken exact symmetry. The argument has to do with the requirement that black holes obey a complementarity principle relating ingoing observers to outside observers, or equivalently, initial states to final states. This condition fixes all parameters, including masses and the cosmological constant. We suspect that only examples can be found where these are all of order one in Planck units, but the values depend on the algebra chosen. This paper combines findings reported in two previous preprints (G. 't Hooft in arXiv:1009.0669 [gr-qc], 2010; arXiv:1011.0061 [gr-qc], 2010) and puts these in a clearer perspective by shifting the emphasis towards the implications for particle models.

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“…The reason why the non-local contribution −1 is taken is that it is a simplest choice for the the inverse of some differential operator to provide the required time lag between the transition from radiation dominance to matter dominance at the radiation-matter equality time t eq ∼ 10 5 years. Much larger values can be obtained through other operators, for example, the Paneitz operator arising in the context of conformal anomalies [22], which is given by (1/ √ −g) △ P . One gets about 10 6 from the dimensionless combination of the inverse of this operator acting on R 2 .…”

Section: A De Sitter Solutionmentioning

confidence: 99%

“…(2.19). We here describe the Lagrangian for the part of the Lagrange multiplier field as 22) where Υ denotes the Lagrange multiplier field λ and the scalar field ψ. Through the conformal transformation in (3.21), the action in the Einstein frame is expressed as…”

Section: Non-local Gravity With Lagrange Constraint Multipliermentioning

confidence: 99%

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Screening of cosmological constant for de Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

et al. 2012

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We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an R 2 term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an R 2 term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.

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Closed form effective conformal anomaly actions in D≥4

Cited by 50 publications

References 10 publications

Nonlocal metric formulations of modified Newtonian dynamics with sufficient lensing

Nonlocal metric formulations of modified Newtonian dynamics with sufficient lensing

A Class of Elementary Particle Models Without Any Adjustable Real Parameters

Screening of cosmological constant for de Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

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