We discuss the relational strategy to solve the problem of time in quantum gravity and different ways in which it could be implemented, pointing out in particular the fundamentally new dimension that the problem takes in a quantum gravity context in which spacetime and geometry are understood as emergent. We realize concretely the relational strategy we have advocated in the context of the tensorial group field theory formalism for quantum gravity, leading to the extraction of an effective relational cosmological dynamics from quantum geometric models. We analyze in detail the emergent cosmological dynamics, highlighting the improvements over previous work, the contribution of the quantum properties of the relational clock to it, and the interplay between the conditions ensuring a bona fide relational dynamics throughout the cosmological evolution and the existence of a quantum bounce resolving the classical big bang singularity.
We introduce an approach to compute the renormalisation group flow of relational observables in quantum gravity which evolve from their microscopic expressions towards the full quantum expectation value. This is achieved by using the composite operator formalism of the functional renormalisation group. These methods can be applied to a large class of relational observables within a derivative expansion for different physical coordinate systems. As a first application we consider four scalar fields coupled to gravity to represent the physical coordinate frame from which relational observables c…
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of the matter clock observables, to test the validity of the relational evolution picture itself. Next, we compute quantum fluctuations of the universe volume and of other operators characterizing its evolution (number operator for the fundamental GFT quanta, effective Hamiltonian and scalar field momentum). In particular, we focus on the late (clock) time regim…
We study the impact of effective interactions onto relationally evolving GFT condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to mode…
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the application of Lieb-Robinson bounds to on-shell monotonic gauge-flow when there is a continuous external "time" parameter. An explicit Lieb-Robinson bound is derived for the differential on-shell evolution of the operator norm of the commutator of discretized Dirac observables, demonstrating how a local light cone-like causal structure emerges. Ultra-local const…
Relational path integral, effective actions and quantum frame covariance in gravity
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo（东京大学宇宙线研究所（WPI） Kavli宇宙物理数学研究所）
We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use of a 'universal dressing space', which contains as a subset every possible dynamical frame. We describe examples of such frames, including matter frames, a popular construction based on boundary-anchored geodesics and one using minimal surfaces -- but our formalism does not depend on the existence of a boundary. The class of observables we construct general…
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an arbitrary order. All the solutions are represented as a set of conditions on Hubble parameters.
In this paper we present an alternative cosmological extension of the three-dimensional extended Newtonian Chern-Simons gravity by switching on the torsion. The theory is obtained as a non-relativistic limit of an enhancement and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as the teleparallel analogue of the Newtonian gravity theory. The infinite-dimensional extension of our result is also explored through the Lie algebra expansion method. An infinite-dimensional torsional Galilean gravity model is presented which in the vanishing cosmological constant limit reprod…
Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $κ$-de Sitter and, in the vanishing cosmological limit, of $κ$-Poincaré kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.
In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent evolution of the linearised field equations of quasi-Newtonian universes are presented. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.
We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization group flow of gravity and gravity-matter systems to construct models of NGFP-driven inflation via a renormalization group improvement scheme. The cosmological predictions of these models depend sensitively on the characteristic properties of the NGFPs, including their position and stability coefficients, which in turn are determined by the field content of the underlying matter sector. We demonstrate that the NGFPs appearing in gravity-matter systems where the matter content is close to the one of the standard model …
In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.
In this paper, we consider $2+1$ dimensional gravitational theory including a Dirac field that is minimally coupled to New Massive Gravity. We investigate cosmological solutions of the field equations by using the self-interaction potential form obtained by the existence of Noether symmetry. In this context, we obtain cosmological solutions that corresponds to inflationary as well as the oscillationary epochs of the universe. Moreover, we have seen that the Dirac field behaves like a dark energy in these epochs of the universe.
In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the van…
In this paper we address the issue of exploring some cosmological scenarios in modified Einstein gravity through non-dynamical (auxiliary) fields. We found that all scenarios are controlled by a specific parameter associated with an auxiliary field. We explore the emergence of inflationary, radiation, matter and dark energy dominated regimes. Furthermore, an interesting possibility such as the emergence of a self-tuning mechanism to the cosmological constant problem in the radiation dominated era is also discussed.
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical spacetime is modified or disordered. It is then possible that the right quantum theory of gravity will also be a completion of quantum mechanics in which the foundational puzzles in both are addressed together. I review here the results of a program, developed with Roberto Mangabeira Unger, Marina Cortes and other collaborators, which aims to do just that. T…
We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions of the quantum constraint equation in a generalization of the Page-Wootters formalism. In this regard, we show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We also comment on how the dynamics of these observables can be related to a notion of quantum refere…
This brief contribution is devoted to phenomenological consequences of deviations from Lorentz invariance in gravity and dark matter. We will discuss main effects on cosmological observables and current constraints derived from astrophysical and cosmological data.
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
Quantum Reference Fields Transformations in Linearized Quantum Gravity
University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology（维也纳大学物理学院维也纳量子科学与技术中心）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Dipartimento di Fisica, Università di Roma Tor Vergata and Sezione INFN Roma2（罗马第二大学物理系及INFN罗马2分部）
New Cosmological Solutions in Nonlocal Modified Gravity
考虑了具有$Λ$项的非定域修正引力的宇宙学性质，其中非定域性是$R \mathcal{F}(\Box) R$型的。利用形式为$\Box R = r R +s,$的解析式，我们找到了几个a（t）非奇异的反弹宇宙学解，它们对应于空间曲率参数k的所有三个值。我们还从F（R）理论的角度讨论了这种改进的引力模型。
We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the gravity sector propagate on generic self-accelerating FLRW backgrounds. We study the stability of the cosmological solutions and put constraints on the parameters of the theory by demanding the correct sign for the kinetic terms for scalar, vector and tensor perturbations.
