Curvature effects in the spectral dimension of spin foams

Jercher, Alexander F.; Steinhaus, Sebastian; Thürigen, Johannes

doi:10.1103/physrevd.108.066011

Cited by 3 publications

(3 citation statements)

References 92 publications

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“…Such a possibility relies on the existence of a non-monotonic behaviour of the spectral dimension at intermediate scales, a feature present only in very few models. Hints that such a feature could happen in certain kinematical states in loop quantum gravity, spin foams and group field theory [79] have been confirmed only recently [80].…”

Section: Dsi In Quantum Gravitymentioning

confidence: 99%

“…So far, evidence is scant but building up. For example, in ongoing investigations in spin foams, there are not yet any signs for a complex dimension but this is mostly because one is still limiting explicit calculations and simulations to the semi-classical (large-spin) approximation of spin foams [84] or due to other approximations and assumptions [80]. Complexity is mostly avoided in this regime but it is indeed expected to arise from the measure in the spin foam [85].…”

Section: Dsi In Quantum Gravitymentioning

confidence: 99%

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Log-periodic gravitational-wave background beyond Einstein gravity

Calcagni,

Kuroyanagi

2023

Class. Quantum Grav.

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Periodic patterns of logarithmic oscillations can arise in primordial curvature perturbation spectra and in the associated gravitational-wave background via different mechanisms. We show that, in the presence of log oscillations, the spectral shape of the stochastic background has a unique parametrization independent of its physical origin. We also show that this log-periodic modulation can be generated in any scenario beyond Einstein gravity endowed with an approximate discrete scale invariance, a symmetry typical of deterministic fractal spacetimes that could emerge in quantum gravity under certain conditions. We discuss how a log-oscillatory spectral shape arises from concrete inflationary models beyond Einstein gravity and the prospects for detection in Einstein Telescope and other next-generation gravitational-wave observatories. We find that these instruments will be sensitive to log-periodic features if the detection is made with a high signal-to-noise ratio (SNR) and that the error scales as 1 / SNR .

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Section: Dsi In Quantum Gravitymentioning

confidence: 99%

Section: Dsi In Quantum Gravitymentioning

confidence: 99%

Log-periodic gravitational-wave background beyond Einstein gravity

Calcagni,

Kuroyanagi

2023

Class. Quantum Grav.

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“…Recently, investigations were conducted to define a Hartle-Hawking no boundary wavefunction by computing the transition from nothing to an equilateral spatial triangulation in the EPRL model [22][23][24]. Other examples of symmetry reduced spin foam models, not necessarily tailored to cosmology, are given by the cuboid [25][26][27], frusta [11,[28][29][30] and parallelepiped models [31]. Due to the numerical challenges accompanying the evaluation of symmetry reduced quantum amplitudes for large spins [32], resorting to semi-classical amplitudes appeared fruitful in advancing explicit computations.…”

Section: Introductionmentioning

confidence: 99%

Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics

Jercher,

Steinhaus

2024

Class. Quantum Grav.

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We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing 4-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by gluing such 4-frusta in spatial and temporal direction, we find causality violations if the sub-cells connecting spatial slices are spacelike. A Wick rotation to the Euclidean theory can be defined globally by a complexification of the variables and an analytic continuation of the action. Introducing a discrete free massless scalar field, we study its equations of motion and show that it evolves monotonically. Furthermore, in a continuum limit, we obtain the equations of a homogeneous scalar field on a spatially flat Friedmann background. Vacuum solutions to the causally regular Regge equations are static and flat and show a restoration of time reparametrisation invariance. In the presence of a scalar field, the height of a frustum is a dynamical variable that has a solution if causality violations are absent and if an inequality relating geometric and matter boundary data is satisfied. Edge lengths of cubes evolve monotonically, yielding a contracting or an expanding branch of the universe. In a small deficit angle expansion, the system can be deparametrised via the scalar field and a continuum limit of the discrete theory can be defined which we show to yield the relational Friedmann equation. These properties are obstructed if higher orders of the deficit angle are taken into account. Our results suggest that the inclusion of timelike sub-cells is necessary for a causally regular classical evolution in this symmetry restricted setting. Ultimately, this works serves as a basis for forthcoming investigations on the cosmological path integral within the framework of effective spin foams.

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Monte Carlo algorithm for spin foam intertwiners

Steinhaus

2024

Phys. Rev. D

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Curvature effects in the spectral dimension of spin foams

Cited by 3 publications

References 92 publications

Log-periodic gravitational-wave background beyond Einstein gravity

Log-periodic gravitational-wave background beyond Einstein gravity

Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics

Monte Carlo algorithm for spin foam intertwiners

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