Spherically symmetric solutions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>λ</mml:mi><mml:mtext>−</mml:mtext><mml:mi>R</mml:mi></mml:mrow></mml:math>model

Loll, R.; Pires, Lucas

doi:10.1103/physrevd.96.044030

Cited by 9 publications

(19 citation statements)

References 42 publications

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“…Moreover, the universality classes of the system exhibit universal scaling behaviors which are in qualitative agreement with other approaches to quantum gravity. These findings support the idea [86] that a causal structure may play an important role for obtaining a well-defined longdistance completion of gravity from the quantum theory.…”

Section: Introductionsupporting

confidence: 78%

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed points characteristic for Asymptotic Safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the -expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

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Section: Introductionsupporting

confidence: 78%

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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“…Also, equations (38) and (39) with the inclusion of the terms proportional to P arising from the Hamiltonian and using µ = 0 are the same field equations as in Einstein-Maxwell theory,…”

Section: Equivalence To the Einstein-maxwell Theorymentioning

confidence: 99%

“…Moreover the conjugate momentum is also restricted by a first class constraint, which implies that it is transvers in the sense of York [38].The two constraints imply that the conjugate momentum is transvers-traceless. Besides, it follows that this component is independent of the parameter λ [38,39]. Furthermore a perturbation of the parameter λ can only appear through the conjugate momentum.…”

Section: Introductionmentioning

confidence: 99%

Pure electromagnetic-gravitational interaction in Hořava–Lifshitz theory at the kinetic conformal point

Restuccia

Tello‐Ortiz

2020

Eur. Phys. J. C

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We introduce the electromagnetic-gravitational coupling in the Hořava-Lifshitz framework, in 3 + 1 dimensions, by considering the Hořava-Lifshitz gravity theory in 4 + 1 dimensions at the kinetic conformal point and then performing a Kaluza-Klein reduction to 3 + 1 dimensions. The action of the theory is second order in time derivatives and the potential contains only higher order spacelike derivatives up to z = 4, z being the critical exponent. These terms include also higher order derivative terms of the electromagnetic field. The propagating degrees of freedom of the theory are exactly the same as in the Einstein-Maxwell theory. We obtain the Hamiltonian, the field equations and show consistency of the constraint system. The kinetic conformal point is protected from quantum corrections by a second class constraint. At low energies the theory depends on two coupling constants, β and α. We show that the anisotropic field equations for the gauge vector is a deviation of the covariant Maxwell equations by a term depending on β − 1.Consequently, for β = 1, Maxwell equations arise from the anisotropic theory at low energies. We also prove that the anisotropic electromagnetic-gravitational theory at the IR point β = 1, α = 0, is exactly the Einstein-Maxwell theory in a gravitational gauge used in the ADM formulation of General Relativity. * Electronic address: alvaro.restuccia@uantof.cl † Electronic address: francisco.tello@ua.cl

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“…Under this consideration, the kinetic term of the theory acquires a conformal invariance not present in the whole theory [1]. In a broader context, this theory has motivated research in various fields, for example in the framework of the so-called λ-R model [22], spherically symmetric solutions and the initial value problem have been explored [23][24][25]. Furthermore, studies on the cosmological setting and its properties have been analyzed in the following recent works [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Quantum aspects of the gravitational-gauge vector coupling in the Hořava-Lifshitz theory at the kinetic conformal point

Restuccia¹,

Tello‐Ortiz²

2020

Preprint

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This work presents the main aspects of the anisotropic gravity-vector gauge coupling at all energy scales ı.e., from the IR to the UV point. This study is carry out starting from the 4+1 dimensional Hořava-Lifshitz theory, at the kinetic conformal point.The Kaluza-Klein technology is employed as a unifying mechanism to couple both interactions. Furthermore, by assuming the so-called cylindrical condition, the dimensional reduction to 3+1 dimensions leads to a theory whose underlying group of symmetries corresponds to the diffeomorphisms preserving the foliation of the manifold and a U(1) gauge symmetry. The counting of the degrees of freedom shows that the theory propagates the same spectrum of Einstein-Maxwell theory. The speed of propagation of tensorial and gauge modes is the same, in agreement with recent observations. This point is thoroughly studied taking into account all the z = 1, 2, 3, 4 terms that contribute to the action. In contrast with the 3+1 dimensional formulation, here the Weyl tensor contributes in a non-trivial way to the potential of the theory. Its complete contribution to the 3+1 theory is explicitly obtained. Additionally, it is shown that the constraints and equations determining the full set of Lagrange multipliers are elliptic partial differential equations of eighth-order. To check and assure the consistency and positivity of the reduced Hamiltonian some restrictions are imposed on the coupling constants. The propagator of the gravitational and gauge sectors are obtained showing that there are not ghost fields, what is more they exhibit the z = 4 scaling for all physical modes at the high energy level. By evaluating the superficial degree of divergence and considering the structure of the second class constraints, it is shown that the theory is power-counting renormalizable.

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Spherically symmetric solutions of theλ−Rmodel

Cited by 9 publications

References 42 publications

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

Pure electromagnetic-gravitational interaction in Hořava–Lifshitz theory at the kinetic conformal point

Quantum aspects of the gravitational-gauge vector coupling in the Hořava-Lifshitz theory at the kinetic conformal point

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