Pub Date : 2024-08-27DOI: 10.1088/1361-6382/ad6e4d
Oliver Friedrich, ChunJun Cao, Sean M Carroll, Gong Cheng and Ashmeet Singh
The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension 2n, it is possible to define Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ‘overlapping degrees of freedom’. We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff . This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, i.e. using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory. The numerical tools used in this work are publicly available within the GPUniverse package, https://github.com/OliverFHD/GPUniverse.
{"title":"Holographic phenomenology via overlapping degrees of freedom","authors":"Oliver Friedrich, ChunJun Cao, Sean M Carroll, Gong Cheng and Ashmeet Singh","doi":"10.1088/1361-6382/ad6e4d","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6e4d","url":null,"abstract":"The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension 2n, it is possible to define Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ‘overlapping degrees of freedom’. We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff . This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, i.e. using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory. The numerical tools used in this work are publicly available within the GPUniverse package, https://github.com/OliverFHD/GPUniverse.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-27DOI: 10.1088/1361-6382/ad7185
Takeshi Chiba and Tsuyoshi Houri
A scalar field with an exponential potential has been proposed as a model of inflation (called power-law inflation). Although it admits an exact solution, the integrability of the system has not been shown. We uncover the hidden symmetries behind the system by utilizing the Eisenhart lift of field theories. We find that a conformal Killing vector field in the field space exists only for a particular combination of exponential functions that includes a single exponential potential. This implies the existence of additional conserved quantity and explains the integrability of the system.
{"title":"Hidden symmetries of power-law inflation","authors":"Takeshi Chiba and Tsuyoshi Houri","doi":"10.1088/1361-6382/ad7185","DOIUrl":"https://doi.org/10.1088/1361-6382/ad7185","url":null,"abstract":"A scalar field with an exponential potential has been proposed as a model of inflation (called power-law inflation). Although it admits an exact solution, the integrability of the system has not been shown. We uncover the hidden symmetries behind the system by utilizing the Eisenhart lift of field theories. We find that a conformal Killing vector field in the field space exists only for a particular combination of exponential functions that includes a single exponential potential. This implies the existence of additional conserved quantity and explains the integrability of the system.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-26DOI: 10.1088/1361-6382/ad6f68
J A Silva, F C Carvalho and A R G Garcia
In this paper we propose a reinterpretation of the Mansouri–Nozari signature-change approach to the early Universe, in which the metric signature only occurs for t < 0 within the Euclidean regime, posing a challenge in providing coherent physical interpretations in advance. We ensure that the sign change occurs for t > 0 in the Euclidean regime. Our findings show that the energy-momentum tensor does not vanish on the signature-changing surface, even when we adopt conditions commonly used in the literature. Furthermore, we formulate a modified cosmology within the framework of signature-changing and discuss the modifications that our approach introduces to the cosmological equations. We establish a constraint relating the equation of state parameter and its singular part and we determine an effective equation of state as function of the redshift. Finally, we show that the law of conservation of matter in the modified ΛCDM model remains valid.
在本文中，我们提出了对早期宇宙的曼苏里-诺扎里（Mansouri-Nozari）签名变化方法的重新解释，即在欧几里得体系中，度量签名只发生在 t 0 时。我们的研究结果表明，即使我们采用文献中常用的条件，能动张量在签名变化面上也不会消失。此外，我们在签名变化的框架内提出了一种修正的宇宙学，并讨论了我们的方法对宇宙学方程的修正。我们建立了状态方程参数及其奇异部分的约束条件，并确定了红移函数的有效状态方程。最后，我们证明在修正的ΛCDM模型中物质守恒定律仍然有效。
{"title":"New insights on the signature change via the Colombeau framework","authors":"J A Silva, F C Carvalho and A R G Garcia","doi":"10.1088/1361-6382/ad6f68","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6f68","url":null,"abstract":"In this paper we propose a reinterpretation of the Mansouri–Nozari signature-change approach to the early Universe, in which the metric signature only occurs for t < 0 within the Euclidean regime, posing a challenge in providing coherent physical interpretations in advance. We ensure that the sign change occurs for t > 0 in the Euclidean regime. Our findings show that the energy-momentum tensor does not vanish on the signature-changing surface, even when we adopt conditions commonly used in the literature. Furthermore, we formulate a modified cosmology within the framework of signature-changing and discuss the modifications that our approach introduces to the cosmological equations. We establish a constraint relating the equation of state parameter and its singular part and we determine an effective equation of state as function of the redshift. Finally, we show that the law of conservation of matter in the modified ΛCDM model remains valid.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-26DOI: 10.1088/1361-6382/ad6e4a
Jerónimo Cortez, Guillermo A Mena Marugán, Álvaro Torres-Caballeros and José Velhinho
We address the issue of inequivalent Fock representations in quantum field theory in a curved homogenous and anisotropic cosmological background, namely Kantowski–Sachs spacetime, which can also be used to describe the interior of a nonrotating black hole. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.
{"title":"Time-dependent scalings and Fock quantization of a massless scalar field in Kantowski–Sachs","authors":"Jerónimo Cortez, Guillermo A Mena Marugán, Álvaro Torres-Caballeros and José Velhinho","doi":"10.1088/1361-6382/ad6e4a","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6e4a","url":null,"abstract":"We address the issue of inequivalent Fock representations in quantum field theory in a curved homogenous and anisotropic cosmological background, namely Kantowski–Sachs spacetime, which can also be used to describe the interior of a nonrotating black hole. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-22DOI: 10.1088/1361-6382/ad6e4e
Pranav Prasanthan, Sarath Nelleri, Navaneeth Poonthottathil and Sreejith E K
Utilizing Kaniadakis entropy associated with the apparent horizon of the Friedmann–Robertson–Walker Universe and applying the emergence of cosmic space paradigm, we deduce the modified Friedmann equation for a non-flat (n+1)-dimensional Universe. Employing the first law of thermodynamics, we arrive at the same modified Friedmann equation, showing the connection between emergence of cosmic space and first law of thermodynamics. We also establish the condition to satisfy the generalized second law of thermodynamics within the Kaniadakis framework. Our study illuminates the intricate connection between the law of emergence and horizon thermodynamics, offering a deeper insight through the lens of Kaniadakis entropy.
{"title":"Emergence of cosmic space and horizon thermodynamics from Kaniadakis entropy","authors":"Pranav Prasanthan, Sarath Nelleri, Navaneeth Poonthottathil and Sreejith E K","doi":"10.1088/1361-6382/ad6e4e","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6e4e","url":null,"abstract":"Utilizing Kaniadakis entropy associated with the apparent horizon of the Friedmann–Robertson–Walker Universe and applying the emergence of cosmic space paradigm, we deduce the modified Friedmann equation for a non-flat (n+1)-dimensional Universe. Employing the first law of thermodynamics, we arrive at the same modified Friedmann equation, showing the connection between emergence of cosmic space and first law of thermodynamics. We also establish the condition to satisfy the generalized second law of thermodynamics within the Kaniadakis framework. Our study illuminates the intricate connection between the law of emergence and horizon thermodynamics, offering a deeper insight through the lens of Kaniadakis entropy.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142042464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-22DOI: 10.1088/1361-6382/ad6d26
Carlo Cepollaro and Flaminia Giacomini
The Einstein equivalence principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.
{"title":"Quantum generalisation of Einstein’s equivalence principle can be verified with entangled clocks as quantum reference frames","authors":"Carlo Cepollaro and Flaminia Giacomini","doi":"10.1088/1361-6382/ad6d26","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6d26","url":null,"abstract":"The Einstein equivalence principle (EEP) is of crucial importance to test the foundations of general relativity. When the particles involved in the test exhibit quantum properties, it is unknown whether this principle still holds. A violation of the EEP would have drastic consequences for physics. A more conservative possibility is that the EEP holds in a generalised form for delocalised quantum particles. Here we formulate such a generalised EEP by extending one of its paradigmatic tests with clocks to quantum clocks that are in a quantum superposition of positions and velocities. We show that the validity of such a generalised version of the EEP is equivalent to the possibility of transforming to the perspective of an arbitrary Quantum Reference Frame (QRF), namely a reference frame associated to the quantum state of the clock. We further show that this generalised EEP can be verified by measuring the proper time of entangled clocks in a quantum superposition of positions in the Earth gravitational field. The violation of the generalised EEP corresponds to the impossibility of defining dynamical evolution in the frame of each clock, and results in a modification to the probabilities of measurements calculated in the laboratory frame. Hence, it can be verified experimentally, for instance in an atom interferometer.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142042462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-22DOI: 10.1088/1361-6382/ad6e4b
Kaushlendra Kumar and Harold C Steinacker
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor Cµν capturing the classical Yang–Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat Friedmann–Lemaître–Robertson–Walker cosmological evolution governed by the classical action.
{"title":"Modified Einstein equations from the 1-loop effective action of the IKKT model","authors":"Kaushlendra Kumar and Harold C Steinacker","doi":"10.1088/1361-6382/ad6e4b","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6e4b","url":null,"abstract":"We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor Cµν capturing the classical Yang–Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat Friedmann–Lemaître–Robertson–Walker cosmological evolution governed by the classical action.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142042503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-21DOI: 10.1088/1361-6382/ad6dcc
Seth K Asante and Taylor Brysiewicz
Area variables are intrinsic to connection formulations of general relativity, in contrast to the fundamental length variables prevalent in metric formulations. Within 4D discrete gravity, particularly based on triangulations, the area-length system establishes a relationship between area variables associated with triangles and the edge length variables. This system is comprised of polynomial equations derived from Heron’s formula, which relates the area of a triangle to its edge lengths. Using tools from numerical algebraic geometry, we study the area-length systems. In particular, we show that given the ten triangular areas of a single 4-simplex, there could be up to 64 compatible sets of edge lengths. Moreover, we show that these 64 solutions do not, in general, admit formulae in terms of the areas by analyzing the Galois group, or monodromy group, of the problem. We show that by introducing additional symmetry constraints, it is possible to obtain such formulae for the edge lengths. We take the first steps toward applying our results within discrete quantum gravity, specifically for effective spin foam models.
{"title":"Solving the area-length systems in discrete gravity using homotopy continuation","authors":"Seth K Asante and Taylor Brysiewicz","doi":"10.1088/1361-6382/ad6dcc","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6dcc","url":null,"abstract":"Area variables are intrinsic to connection formulations of general relativity, in contrast to the fundamental length variables prevalent in metric formulations. Within 4D discrete gravity, particularly based on triangulations, the area-length system establishes a relationship between area variables associated with triangles and the edge length variables. This system is comprised of polynomial equations derived from Heron’s formula, which relates the area of a triangle to its edge lengths. Using tools from numerical algebraic geometry, we study the area-length systems. In particular, we show that given the ten triangular areas of a single 4-simplex, there could be up to 64 compatible sets of edge lengths. Moreover, we show that these 64 solutions do not, in general, admit formulae in terms of the areas by analyzing the Galois group, or monodromy group, of the problem. We show that by introducing additional symmetry constraints, it is possible to obtain such formulae for the edge lengths. We take the first steps toward applying our results within discrete quantum gravity, specifically for effective spin foam models.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142021932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-20DOI: 10.1088/1361-6382/ad6f67
Alexander F Jercher, Luca Marchetti and Andreas G A Pithis
A major challenge at the interface of quantum gravity (QG) and cosmology is to explain the emergence of the large-scale structure of the Universe from Planck scale physics. In this letter, we extract the dynamics of scalar isotropic cosmological perturbations from full QG, as described by the causally complete Barrett–Crane group field theory (GFT) model. From the perspective of the underlying QG theory, cosmological perturbations are represented as nearest-neighbor two-body entanglement of GFT quanta. Their effective dynamics is obtained via mean-field methods and described relationally with respect to a causally coupled physical Lorentz frame. We quantitatively study these effective dynamical equations and show that at low energies they are perfectly consistent with those of general relativity, while for trans-Planckian scales quantum effects become important. These results therefore not only provide crucial insights into the potentially purely quantum gravitational nature of cosmological perturbations, but also offer rich phenomenological implications for the physics of the early Universe.
{"title":"Scalar cosmological perturbations from quantum gravitational entanglement","authors":"Alexander F Jercher, Luca Marchetti and Andreas G A Pithis","doi":"10.1088/1361-6382/ad6f67","DOIUrl":"https://doi.org/10.1088/1361-6382/ad6f67","url":null,"abstract":"A major challenge at the interface of quantum gravity (QG) and cosmology is to explain the emergence of the large-scale structure of the Universe from Planck scale physics. In this letter, we extract the dynamics of scalar isotropic cosmological perturbations from full QG, as described by the causally complete Barrett–Crane group field theory (GFT) model. From the perspective of the underlying QG theory, cosmological perturbations are represented as nearest-neighbor two-body entanglement of GFT quanta. Their effective dynamics is obtained via mean-field methods and described relationally with respect to a causally coupled physical Lorentz frame. We quantitatively study these effective dynamical equations and show that at low energies they are perfectly consistent with those of general relativity, while for trans-Planckian scales quantum effects become important. These results therefore not only provide crucial insights into the potentially purely quantum gravitational nature of cosmological perturbations, but also offer rich phenomenological implications for the physics of the early Universe.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142013789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-19DOI: 10.1088/1361-6382/ad4130
Thorsten Lang and Susanne Schander
This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site carries a set of canonical variables given by the components of the spatial metric and the corresponding conjugate momenta. In order to quantize this theory, we describe a representation of the canonical commutation relations that enforces the positivity of the operators for all choices of s. Moreover, symmetry of and is ensured. This reflects the physical requirement that the spatial metric should be a positive definite, symmetric tensor. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We want to emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.
本文是一系列旨在重振量子几何动力学项目的论文中的第二篇。我们的方法引入了超曲面形变代数的晶格正则化，使每个晶格位点都携带一组由空间度量分量和相应共轭矩给出的典型变量。为了量子化这一理论，我们描述了一种典型换向关系的表示方法，该方法在所有 s 的选择下都能确保算子的正向性。这反映了空间度量应该是正定对称张量的物理要求。为了达到这一目的，我们将空间度量分解为对角线项为正的上三角矩阵。此外，我们的希尔伯特空间还携带了维尔贝因场的表示，并自然地将物理自由度和规规自由度分开。最后，我们为我们的表示引入了韦尔量子化的广义。我们想强调的是，我们提出的方法可应用于物理学的其他领域，尤其是在构型空间受自由度之间复杂关系限制的情况下。
{"title":"Quantum geometrodynamics revived: II. Hilbert space of positive definite metrics","authors":"Thorsten Lang and Susanne Schander","doi":"10.1088/1361-6382/ad4130","DOIUrl":"https://doi.org/10.1088/1361-6382/ad4130","url":null,"abstract":"This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site carries a set of canonical variables given by the components of the spatial metric and the corresponding conjugate momenta. In order to quantize this theory, we describe a representation of the canonical commutation relations that enforces the positivity of the operators for all choices of s. Moreover, symmetry of and is ensured. This reflects the physical requirement that the spatial metric should be a positive definite, symmetric tensor. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We want to emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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