Quantum Gravity Models Research Articles

Non-trivial quantum fluctuations in asymptotically non-flat black-hole space–times

Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one of the critical tests for a model of quantum gravity. However, Hawking’s original derivation used quantum field theory on a fixed background. Efforts have been made to include the space–time fluctuations arising from the quantization of the dynamical degrees of freedom of gravity itself and study the effects on the Hawking particles. Using semi-classical analysis, we study the effects of quantum fluctuations of scalar field stress-tensors in asymptotic non-flat spherically symmetric black-hole space–times. Using two different approaches, we obtain a critical length-scale from the horizon at which gravitational interactions become large, i.e., when the back reaction to the metric due to the scalar field becomes significant. For 4-D Schwarzschild AdS (SAdS) and Schwarzschild de Sitter (SdS), the number of relevant modes for the back-reaction is finite only for a specific range of values of M/L (where M is the mass of the black-hole, and L is related to the modulus of the cosmological constant). For SAdS (SdS), the number of relevant modes is infinite for M/L∼1 (0.2<M/L<1/(33). We discuss the implications of these results for the late stages of black-hole evaporation.

Searches for Violation of CPT Symmetry and Lorentz Invariance with Astrophysical Neutrinos

Neutrinos are a powerful tool for searching physics beyond the standard model of elementary particles. In this review, we present the status of the research on charge-parity-time (CPT) symmetry and Lorentz invariance violations using neutrinos emitted from the collapse of stars such as supernovae and other astrophysical environments, such as gamma-ray bursts. Particularly, supernova neutrino fluxes may provide precious information because all neutrino and antineutrino flavors are emitted during a burst of tens of seconds. Models of quantum gravity may allow the violation of Lorentz invariance and possibly of CPT symmetry. Violation of Lorentz invariance may cause a modification of the dispersion relation and, therefore, in the neutrino group velocity as well in the neutrino wave packet. These changes can affect the arrival time signal registered in astrophysical neutrino detectors. Direction or time-dependent oscillation probabilities and anisotropy of the neutrino velocity are manifestations of the same kind of new physics. CPT violation, on the other hand, may be responsible for different oscillation patterns for neutrino and antineutrino and unconventional energy dependency of the oscillation phase or of the mixing angles. Future perspectives for possible CPT and Lorentz violating systems are also presented.

Comment on Coleman-DeLuccia instantons

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

How to Decipher the Seegers-Tisserand-Gerber-Einstein Formula and the Soldner-Einstein Formula?

The famous Seegers-Tisserand-Gerber-Einstein Formula describing correctly the Mercury perihelion advance passed through hands of many scholars who tried to decipher the physical meaning of the perturbation factor Ω introduced by Carl Seegers in 1864. Based on the Gauss´s law for gravity we have newly interpreted this perturbation factor Ω as the active solid angle of the Solar gravitational field Ω = 3 steradians. We have inserted this model of the active solid angle of the Solar gravitational field the famous Soldner-Einstein Formula describing the light deflection in the vicinity of the Sun with 1 ≤ Ω ≤ 8. The enormous scatter of experimental data of the light deflections measured during the Solar eclipses was interpreted as the quantum jumps of the deflection angle with the quantum jump 0”.44. All known existing data on the light deflection taken during the last hundred years were depicted into the graphs. In some cases we have discovered these quantum jumps of the deflection angle during the individual runs of the Solar eclipse experiment. We propose to reanalyze all historical data taken for individual stars and to search for a hidden structure in these data. Moreover, we want to initiate new experimental activities for the coming Solar eclipses in order to collect more precise data that might guide us towards the model of quantum gravity.

Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.

Replica wormholes from Liouville theory

The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the bulk entanglement entropy can be reproduced from the twist operator correlators. We propose the precise dictionary and show how this correspondence works in detail.

Analysis methods used and planned for VIP-2

VIP-2 (VIolation of Pauli exclusion principle - 2) is an underground experiment sited in the underground “Laboratori Nazionali del Gran Sasso.” It aims to investigate possible violations of the Pauli Exclusion Principle (PEP) and, in this context, Quantum Gravity models implying violations of PEP. While an upper limit of PEP violation probability is recently published, the data requires further developments of accurate analysis techniques and methods. In this contribution, we present an overview of the methodologies proposed for current and planned analysis.

Quantum flatness in two-dimensional quantum gravity

Flatness -- the absence of spacetime curvature -- is a well-understood property of macroscopic, classical spacetimes in general relativity. The same cannot be said about the concepts of curvature and flatness in nonperturbative quantum gravity, where the microscopic structure of spacetime is not describable in terms of small fluctuations around a fixed background geometry. An interesting case are two-dimensional models of quantum gravity, which lack a classical limit and therefore are maximally "quantum". We investigate the recently introduced quantum Ricci curvature in CDT quantum gravity on a two-dimensional torus, whose quantum geometry could be expected to behave like a flat space on suitably coarse-grained scales. On the basis of Monte Carlo simulations we have performed, with system sizes of up to 600.000 building blocks, this does not seem to be the case. Instead, we find a scale-independent "quantum flatness", without an obvious classical analogue. As part of our study, we develop a criterion that allows us to distinguish between local and global, topological properties of the toroidal quantum system.

Infrared signatures of a quantum bounce in a minisuperspace analysis of Lemaître-Tolman-Bondi dust collapse

In the quantum treatment of collapsing matter, a viable mode analysis is supposed to give information regarding emission during the collapse. Nevertheless, partly owing to operator ordering ambiguities involved in a typical quantum gravity analysis, the availability of such well-defined modes is not guaranteed. We study the mode decomposition of the unitarily evolving wave packet constructed for the quantum model of spherically symmetric dust collapsing in a marginally bound Lema\^{\i}tre-Tolman-Bondi (LTB) model. We identify the observable depicting mode decomposition, and using the freedom of operator ordering ambiguity, we obtain the Hermitian extension of this operator alongside the Hermitian Hamiltonian. After identifying incoming and outgoing modes with this operator's eigenstates, we estimate their contributions to the radiation profile. The infrared sector of this process demonstrates some characteristic features which turn out to be highly sensitive to the near-bounce dynamics of the dust cloud. Near the epoch of classical singularity, there is a significant contribution from incoming/outgoing modes of small wavenumber in the expanding/collapsing phase of the dust cloud, which keeps on decreasing as one moves away from the singularity. The information of the bounce is carried over to the infrared modes through a flip from largely incoming to largely outgoing radiation as the evolution progresses from collapsing to expanding phase, much before the information of bounce comes about to any observer. In the infrared sector, the saturation value of the amplitude marks the bounce radius. Thus, we argue that the information of the short scale physics is essentially carried over to the longest wavelength in this quantum gravity model, which we argue is rather more prominent for low energy processes.

Covariant origin of the U(1)3 model for Euclidean quantum gravity

If one replaces the constraints of the Ashtekar–Barbero SU(2) gauge theory formulation of Euclidean gravity by their U(1)3 version, one arrives at a consistent model which captures significant structures of its SU(2) version. In particular, it displays a non-trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. The simplification from SU(2) to U(1)3 can be performed simply by hand within the Hamiltonian formulation by dropping all non-abelian terms from the Gauss, spatial diffeomorphism, and Hamiltonian constraints respectively. However, one may ask from which Lagrangian formulation this theory descends. For the SU(2) theory it is known that one can choose the Palatini action, Holst action, or (anti-)selfdual action (Euclidean signature) as starting point all leading to equivalent Hamiltonian formulations. In this paper, we systematically analyse this question directly for the U(1)3 theory. Surprisingly, it turns out that the abelian analog of the Palatini or Holst formulation is a consistent but topological theory without propagating degrees of freedom. On the other hand, a twisted abelian analog of the (anti-)selfdual formulation does lead to the desired Hamiltonian formulation. A new aspect of our derivation is that we work with (1) half-density valued tetrads which simplifies the analysis, (2) without the simplicity constraint (which admits one undesired solution that is usually neglected by hand) and (3) without imposing the time gauge from the beginning. As a byproduct, we show that also the non-abelian theory admits a twisted (anti-)selfdual formulation. Finally, we also derive a pure connection formulation of Euclidean GR including a cosmological constant by extending previous work due to Capovilla, Dell, Jacobson, and Peldan which may be an interesting starting point for path integral investigations and displays (Euclidean) GR as a Yang–Mills theory with non-polynomial Lagrangian.

Wick rotation for spin foam quantum gravity

Models of spin foam quantum gravity come in different spacetime signatures, either Euclidean or Lorentzian. The choice is reflected in the use of $Spin(4)$ or $SL(2,\mathbb{C})$ as gauge groups for the holonomies of the connection. In this work we show that a rotation of the Immirzi parameter to purely imaginary values maps the Euclidean Engle-Pereira-Rovelli-Livine spin foam model to its Lorentzian version and vice versa. Our methods provide a general recipe for relating spin foam models of different signature through analytic continuation of the gauge groups and their unitary irreducible representations.

Primordial big bang nucleosynthesis and generalized uncertainty principle

The Generalized Uncertainty Principle (GUP) naturally emerges in several quantum gravity models, predicting the existence of a minimal length at Planck scale. Here, we consider the quadratic GUP as a semiclassical approach to thermodynamic gravity and constrain the deformation parameter by using observational bounds from Big Bang Nucleosynthesis and primordial abundances of the light elements {}^4 He, D, {}^7 Li. We show that our result fits with most of existing bounds on beta derived from other cosmological studies.

Emergent unitarity in de Sitter from matrix integrals

We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and an infinite-time evolution operator between the far past and far future. This evolution is not unitary, although we find that it acts unitarily on a subspace up to non-perturbative corrections. These corrections come from processes which involve changes in the spatial topology, including the nucleation of baby universes. There is significant evidence that this 1+1 dimensional model is dual to a 0+0 dimensional matrix integral in the double-scaled limit. So the bulk quantum mechanics, including the Hilbert space and approximately unitary evolution, emerge from a classical integral. We find that this emergence is a robust consequence of the level repulsion of eigenvalues along with the double scaling limit, and so is rather universal in random matrix theory.

Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom

In the tensorial group field theory approach to quantum gravity, the theory is based on discrete building blocks and continuum spacetime is expected to emerge from their collective dynamics, possibly at criticality, via a phase transition. On a compact group of fixed volume this can be expected to be only possible in a large-volume or thermodynamic limit. Here we show how phase transitions are possible in TGFTs in two cases: a) considering the non-local group degrees of freedom on a non-compact Lie group instead of a compact one (or taking a large-volume limit of a compact group); b) in models including ℝ-valued local degrees of freedom (that can be interpreted as discrete scalar fields, often used in this context to provide a matter reference frame). After adapting the Landau-Ginzburg approach to this setting of mixed local/non-local degrees of freedom, we determine the critical dimension beyond which there is a Gaussian fixed point and a continuous phase transition which can be described by mean-field theory. This is an important step towards the realization of a phase transition to continuum spacetime in realistic TGFT models for quantum gravity.

Momentum-space entanglement in scalar field theory on fuzzy spheres

Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.

Detecting deformed commutators with exceptional points in optomechanical sensors

Models of quantum gravity imply a modification of the canonical position-momentum commutation relations. In this paper, working with a binary mechanical system, we examine the effect of quantum gravity on the exceptional points of the system. On the one side, we find that the exceedingly weak effect of quantum gravity can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibits non-analytic and even discontinuous behavior. On the other side, the gravity perturbation will affect the sensitivity of the system to deposition mass. In order to further enhance the sensitivity of the system to quantum gravity, we extend the system to the other one which has a third-order exceptional point. Our work provides a feasible way to use exceptional points as a new tool to explore the effect of quantum gravity.

Constraints on quantum gravity and the photon mass from gamma ray bursts

Lorentz invariance violation in quantum gravity (QG) models or a nonzero photon mass, $m_\gamma$, would lead to an energy-dependent propagation speed for photons, such that photons of different energies from a distant source would arrive at different times, even if they were emitted simultaneously. By developing source-by-source, Monte Carlo-based forward models for such time delays from gamma ray bursts, and marginalising over empirical noise models describing other contributions to the time delay, we derive constraints on $m_\gamma$ and the QG length scale, $\ell_{\rm QG}$, using spectral lag data from the BATSE satellite. We find $m_\gamma < 4.0 \times 10^{-5} \, h \, {\rm eV}/c^2$ and $\ell_{\rm QG} < 5.3 \times 10^{-18} \, h \, {\rm \, GeV^{-1}}$ at 95% confidence, and demonstrate that these constraints are robust to the choice of noise model. The QG constraint is among the tightest from studies which consider multiple gamma ray bursts and the constraint on $m_\gamma$, although weaker than from using radio data, provides an independent constraint which is less sensitive to the effects of dispersion by electrons.

Renormalizable and Unitary Lorentz Invariant Model of Quantum Gravity

We analyze the R+R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

Extending the Tutte and Bollobás–Riordan polynomials to rank 3 weakly coloured stranded graphs

AbstractThe Bollobás–Riordan (BR) polynomial [(2002), Math. Ann.323 81] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects, called rank 3 weakly coloured stranded graphs. Stranded graphs arise in the study of tensor models for quantum gravity in physics, and generalize graphs and ribbon graphs. We present a seven-variable polynomial invariant of these graphs, which obeys a contraction/deletion recursion relation similar to that of the Tutte and BR polynamials. However, it is defined on a much broader class of objects, and furthermore captures properties that are not encoded by the Tutte or BR polynomials.