Quadratic Gravity

Salvio, Alberto

doi:10.3389/fphy.2018.00077

Cited by 144 publications

(140 citation statements)

References 211 publications

(324 reference statements)

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“…Quadratic gravity [10][11][12] is an approach that keeps the curvature squared terms in the fundamental action at all energies. It is a renormalizable [10] and unitary [6] quantum field theory.…”

Section: Pacs Numbersmentioning

confidence: 99%

Arrow of Causality and Quantum Gravity

Donoghue

Menezes

2019

Phys. Rev. Lett.

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Causality in quantum field theory is defined by the vanishing of field commutators for space-like separations. However, this does not imply a direction for causal effects. Hidden in our conventions for quantization is a connection to the definition of an arrow of causality, i.e. what is the past and what is the future. If we mix quantization conventions within the same theory, we get a violation of microcausality. In such a theory with mixed conventions the dominant definition of the arrow of causality is determined by the stable states. In some quantum gravity theories, such as quadratic gravity and possibly asymptotic safety, such a mixed causality condition occurs. We discuss some of the implications. PACS numbers:When caught making a sign mistake in a phase, a colleague would say: "Physics does not depend on whether we use +i or −i", and happily change the sign. At first sight, this phrase seems true. Classical fields are real. The probabilities of quantum mechanics are absolute values squared. Measurements in physics do not seem to care if we defined √ −1 as +i or −i. On second thought, the sign in front of i often does make a major difference. We define time development byThis results in "positive energy" being defined via e −iEt/ . Canonical quantization is defined viaThe path integral treatment of quantum physics is defined using e iS , not e −iS (in units of = c = 1), with S being the action. The Feynman propagator has very important sign conventions in both the numerator and the denominator, withwith infinitesimal and positive. We see that the specific signs in front of i are important in the formalism of quantum mechanics. On third thought, we can see that these signs are a convention, although they do tie in with another feature of our physical description -in particular the time direction (arrow) of causality.In somewhat colloquial language, we would describe causality as "there is no effect before the cause". In relativistic quantum theories of course, one must be careful about what one means by "before". As a simple example, consider the Feynman diagram shown in Figure 1. The Feynman propagator in coordinate space includes both forward and backward propagation in timeFIG. 1: The simple Feynman diagram on the left is decomposed into two time ordered diagrams. In one of the time orderings the final particles emerge before the initial particles have annihilated.withwith E q = q 2 + m 2 and D back F (x) = (D for F (x)) * . What we commonly refer to as positive frequency, or e −iEt , is propagated forward in time and negative frequency backwards in time. However, we see that in one time ordering the final state particles (the effect) emerge before the initial particles have interacted (the cause). So our colloquial notion of causality is inadequate.We note in passing that the time advance of the final state vertex is not observable -due to the uncertainty principle. The time difference of the vertices is of order ∆t ∼ 1/E, where E is the center of mass energy. The time localization of the initial state ...

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Section: Pacs Numbersmentioning

confidence: 99%

Arrow of Causality and Quantum Gravity

Donoghue

Menezes

2019

Phys. Rev. Lett.

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“…[3] it was shown how a relativistic field theory of all interactions (gravity included) can reach infinite energy. In order to achieve this goal, terms quadratic in the curvature are added to the Einstein-Hilbert action, so this theory is also known as quadratic gravity (QG) (see [4] for a review). The UV completion is obtained by demanding that the Weyl symmetry breaking terms vanish in the infinite energy limit and all couplings enjoy a UV fixed point.…”

Section: Introductionmentioning

confidence: 99%

“…It reminds us that the Einstein-Hilbert term and other Weyl-breaking parameters can be present in the Lagrangian, generated, for example, through dimensional transmutation and various quantum effects [3,6,[15][16][17][18][19][20][21][22][23]. Note that an exactly Weyl invariant model would not be physically different from a Weyl-breaking one; indeed, any exactly conformal model can be written as a non-conformal one by fixing a gauge for Weyl symmetry and, conversely, any model of gravity coupled to an arbitrary matter sector can always be made exactly Weyl invariant 4 . What is proposed here is quasi-conformality, in which Weyl symmetry is approximate at high energy, but not exact apart from the strict UV limit.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-conformal models and the early universe

Salvio

2019

Eur. Phys. J. C

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Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all fundamental dimension-4 operators can (at least approximately) respect Weyl invariance at finite energy. An example is the Weyl-squared term, whose consistency and observational consequences are studied. This quasi-conformal scenario emerges from the UV complete quadratic gravity and is a possible framework for inflation. We find two realizations. In the first one the inflaton is a fundamental scalar with a quasiconformal non-minimal coupling to the Ricci scalar. In this case the field excursion must not exceed the Planck mass by far. An example discussed in detail is hilltop inflation. In the second realization the inflaton is a pseudo-Goldstone boson (natural inflation). In this case we show how to obtain an elegant UV completion within an asymptotically free QCD-like theory, in which the inflaton is a composite scalar due to new strong dynamics. We also show how efficient reheating can occur. Unlike the natural inflation based on Einstein gravity, the tensor-to-scalar ratio is well below the current bound set by Planck. In both realizations mentioned above, the basic inflationary formulae are computed analytically and, therefore, these possibilities can be used as simple benchmark models.---

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“…For this reason, gravitation theories including quadratic curvature terms may be renormalizable [1][2][3]. (See [4] for a recent review on quadratic gravity. )…”

Section: Introductionmentioning

confidence: 99%

Decreasing entropy of dynamical black holes in critical gravity

Maeda

Švarc

Podolský

2018

J. High Energ. Phys.

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Critical gravity is a quadratic curvature gravity in four dimensions which is ghost-free around the AdS background. Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition. In addition, the solution shows that the Wald-Kodama dynamical entropy of a black hole is negative and can decrease. These properties expose the pathological aspects of critical gravity at the non-perturbative level.

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Quadratic Gravity

Cited by 144 publications

References 211 publications

Arrow of Causality and Quantum Gravity

Arrow of Causality and Quantum Gravity

Quasi-conformal models and the early universe

Decreasing entropy of dynamical black holes in critical gravity

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