BRST analysis of physical fields and states for 4D quantum gravity on R × S 3

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We study the effective potential in renormalizable quantum gravity with a single dimensionless conformal coupling without a Landau pole. In order to describe a background-free dynamics at the Planck scale and beyond, the conformal-factor field is quantized exactly in a nonperturbative manner. Since this field does not receive renormalization, the field-independent constant in the effective potential becomes itself invariant under the renormalization group flow. That is to say, it gives the physical cosmological constant. We explicitly calculate the physical cosmological constant at the one-loop level in the Landau gauge. We find that it is given by a function of renormalized quantities of the cosmological constant, the Planck mass and the coupling constant, and it should be the observed value. It will give a new perspective on the cosmological constant problem free from an ultraviolet cutoff.

Section: Renormalizations Of Mass Parameterssupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Physical cosmological constant in asymptotically background-free quantum gravity

Hamada

Matsuda

2017

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“…is the charge for the cosmological constant operator defined by d 4 x : e γφ : [5,9,10,11]. In this way, we have seen that the renormalization manner proposed here can reproduce the exact anomalous dimension.…”

Section: Cosmological Constant Operatormentioning

confidence: 56%

“…It has been known that the Riegert action plays a significant role to realize it [4,5,6,7,8]. We then have shown that the Riegert theory including the kinetic term of the Weyl action has such a gauge symmetry as a part of diffeomorphism invariance, which is so strong that physical fields are restricted to "real composite scalars" (called primary scalars) only [9,10,11]. 2 The model we consider here is the renormalizable quantum theory of gravity expanded just from this background-free system by a single dimensionless coupling constant that brings the dynamics of traceless tensor fields.…”

Section: Introductionmentioning

confidence: 96%

Renormalization group analysis for quantum gravity with a single dimensionless coupling

Hamada¹

2014

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We study the quantum conformal gravity whose dynamics is governed by a single dimensionless gravitational coupling with negative beta function. Since the Euler term is not dynamical classically, the constant in front of it is not an independent coupling. Quantum mechanically, however, it induces the Riegert conformal-factor dynamics with Becchi-Rouet-Stora-Tyutin conformal symmetry representing background free nature. In this paper, we propose how to handle the Euler term systematically, incorporating such dynamics on the basis of renormalization group analysis using dimensional regularization. As a nontrivial test of renormalization, we explicitly calculate the three-loop anomalous dimension of the cosmological constant operator and show that it agrees with the exact expression derived using the Becchi-Rouet-Stora-Tyutin conformal symmetry. The physical significance to inflation and the cosmic microwave background is also discussed.Due to the presence of this symmetry, the ghost modes in fourth-order gravitational fields, which are necessary for the conformal algebra to close, are not gauge invariant. So we will be able to begin an argument toward the resolution of the nonperturbative issue of unitarity. PHYSICAL REVIEW D 90, 084038 (2014) 1550-7998=2014=90(8)=084038 (8) 084038-1

“…In this way, we can realize the background-free nature of quantum gravity. The BRST conformal algebra has been constructed, and by solving the BRST invariance condition, it has been shown that physical states are given by real primary scalar fields only [17,18], 1 which is consistent with scalar-dominated spectra of the early universe. 1 Due to the presence of this symmetry, ghost modes are no longer gauge invariant.…”

Section: Introductionmentioning

confidence: 99%

Two-loop quantum gravity corrections to the cosmological constant in Landau gauge

Hamada

Matsuda

2016

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The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.