Linear stability of noncommutative spectral geometry

Sakellariadou, Mairi; Watcharangkool, Apimook

doi:10.1103/physrevd.93.064034

Cited by 5 publications

(6 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(15), we can rewrite the total action given by the sum of the S g , S s , S H and S v contributions from Eqs. (20), (18), (21) and (19), respectively, and including the potential Eq. (22) as…”

Section: Coupling the Higgs Field To Gravitymentioning

confidence: 99%

See 1 more Smart Citation

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

2017

View full text Add to dashboard Cite

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal.

show abstract

Section: Coupling the Higgs Field To Gravitymentioning

confidence: 99%

“…In that case, conformal symmetry is implemented by taking the square of the Weyl tensor as the Lagrangian. The Weyl tensor squared also appears in the bosonic spectral action in the context of noncommutative geometry [17,18] and in the computation of the (formal) functional integral for quantum gravity [19].…”

Section: Introductionmentioning

confidence: 99%

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

2017

View full text Add to dashboard Cite

show abstract

“…Considering the spectral action of an almost commutative torsion geometry, it has been shown[20] that the obtained Hamiltonian is bounded from below, hence non-commutative spectral geometry, a theory that offers a purely geometric explanation for the Standard Model of particle physics[21], does not suffer from linear instability.…”

mentioning

confidence: 99%

Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces

et al. 2018

View full text Add to dashboard Cite

Observations of gravitational radiation from compact binary systems provide an unprecedented opportunity to test General Relativity in the strong field dynamical regime. In this paper, we investigate how future observations of gravitational radiation from binary neutron star mergers might provide constraints on finite-range forces from a universally coupled massive scalar field. Such scalar degrees of freedom are a characteristic feature of many extensions of General Relativity. For concreteness, we work in the context of metric f (R) gravity, which is equivalent to General Relativity and a universally coupled scalar field with a non-linear potential whose form is fixed by the choice of f (R). In theories where neutron stars (or other compact objects) obtain a significant scalar charge, the resulting attractive finite-range scalar force has implications for both the inspiral and merger phases of binary systems. We first present an analysis of the inspiral dynamics in Newtonian limit, and forecast the constraints on the mass of the scalar and charge of the compact objects for the Advanced LIGO gravitational wave observatory. We then perform a comparative study of binary neutron star mergers in General Relativity with those of a one-parameter model of f (R) gravity using fully relativistic hydrodynamical simulations. These simulations elucidate the effects of the scalar on the merger and post-merger dynamics. We comment on the utility of the full waveform (inspiral, merger, post-merger) to probe different regions of parameter space for both the particular model of f (R) gravity studied here and for finite-range scalar forces more generally.

show abstract

“…Spectral geometric ideas have also entered in other models related to quantum aspects of Euclidean spacetime, such as non-commutative geometry, see e.g. [19][20][21]. In this work, however, we consider Lorentzian spectral geometry.…”

Section: Overviewmentioning

confidence: 99%

Towards spectral geometry for causal sets

Yazdi

Kempf

2017

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. We show that the Feynman propagator (or the d'Alembertian) of a causal set contains the complete information about the causal set. Intuitively, this is because the Feynman propagator, being a correlator that decays with distance, provides a measure for the invariant distance between pairs of events. Further, we show that even the spectra alone (of the self-adjoint and anti-self-adjoint parts) of the propagator(s) and d'Alembertian already carry large amounts of geometric information about their causal set. This geometric information is basis independent and also gauge invariant in the sense that it is relabeling invariant (which is analogue to diffeomorphism invariance). We provide numerical evidence that the associated spectral distance between causal sets can serve as a measure for the geometric similarity between causal sets.

show abstract

Linear stability of noncommutative spectral geometry

Cited by 5 publications

References 21 publications

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces

Towards spectral geometry for causal sets

Contact Info

Product

Resources

About