Paweł Duch, Wojciech Kamiński, Jerzy Lewandowski, Jedrzej Świeżewski
In this addendum we clarify a point which strengthens one of the results from [the original paper]. Namely, we show that the algebra of the observables $F(r,θ)$ is yet simpler then it was described in [the original paper]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.
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In the article {\it Gen. Rel. Grav.} {\bf 32}, 1633 (2000), by J. G. Pereira and C. M. Zhang, the special relativity energy-momentum tensor was used to discuss the neutrino phase-splitting in a weak gravitational field. However, it would be more appropriate to use the general relativity energy-momentum tensor. When we do that, as we are going to see, some results change, but the basic conclusion remains the same.
In this addendum to [arXiv:1402.5674] two points are discussed. In the first additional evidence is provided for a dual connection between the geometric length of an Einstein-Rosen bridge and the computational complexity of the quantum state of the dual CFT's. The relation between growth of complexity and Page's ``Extreme Cosmic Censorship" principle is also remarked on. The second point involves a gedanken experiment in which Alice measures a complete set of commuting observables at her end of an Einstein-Rosen bridge is discussed. An apparent paradox is resolved by appealing to the propertie…
In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity observables, whose observables can now be interpreted as particular representative functions of observables of a conformal theory at fixed York time. An application of the observable equivalence of General Relativity and Shape Dynamics is to define the quantization of General Relativity through quantizing Shape Dynamics and using observab…
A proposal for the issue of time and observables in any parameterized theory such as general relativity is addressed. Introduction of a gauge potential 3-form A in the theory of relativity enables us to define a gauge-invariant quantity which can be used by observers as a clock to measure the passage of time. This dynamical variable increases monotonically and continuously along a world line. Then we define world line observables to be any covariantly defined quantity obtained from the field configurations on any such causal past with dynamical time T.
I present a complete set of gauge invariant observables, in the context of general relativity coupled with a minimal amount of realistic matter (four particles). These observables have a straightforward and realistic physical interpretation. In fact, the technology to measure them is realized by the Global Positioning System: they are defined by the physical reference system determined by GPS readings. The components of the metric tensor in this physical reference system are gauge invariant quantities and, remarkably, their evolution equations are local.
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-di…
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role played by a system of observers. Some features of the reduction of the gauge group are discussed, including the fact that in the process of a partial gauge fixing the reduction at the level of the gauge group and the reduction at the level of the variational principle do not commute. Distinctions between the mathematical and the physical concept of gauge symmetry…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The observables are invariant with respect to spatial diffeomorphisms which preserve the observer. The limited residual spatial gauge freedom is studied and fully understood. A full canonical analysis of the observables is presented: we analyze their variations, Poisson algebra and discuss their dynamics. Lastly, the observables are used to solve the vector constraint, wh…
The boundary conditions for canonical vacuum general relativity is investigated at the quasi-local level. It is shown that fixing the area element on the 2- surface S (rather than the induced 2-metric) is enough to have a well defined constraint algebra, and a well defined Poisson algebra of basic Hamiltonians parameterized by shifts that are tangent to and divergence-free on $. The evolution equations preserve these boundary conditions and the value of the basic Hamiltonian gives 2+2 covariant, gauge-invariant 2-surface observables. The meaning of these observables is also discussed.
Eigenvalues of the Weyl operator as observables of general relativity
我们考虑三维Weyl算子的特征值定义的（欧几里德）Ashtekar变量，我们研究它们的依赖于引力场。我们注意到，这些特征值可以被用作引力变量，并推导出明确的公式，其泊松括号和它们的时间演化。
In the canonical approach to general relativity it is customary to parametrize the phase space by initial data on spacelike hypersurfaces. However, if one seeks a theory dealing with observations that can be made by a single localized observer, it is natural to use a different description of the phase space. This results in a different set of Dirac observables from that appearing in the conventional formulation. It also suggests a possible solution to the problem of time, which has been one of the obstacles to the development of a satisfactory quantum theory of gravity.
Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic f…
A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of the coordinates given by matter. Local Dirac observables and coherent states are defined to explore physical content of the model. Expectation values of commutators between the observables for the coherent states recover the four-dimensional diffeomorphism algebra and the large-scale dynamics of the gravitational field relative to the matter coordinates. Both results conform with general relativity up to calculable corrections…
The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity since the 1950s. This paper considers the unrecognized variety of ideas about observables in the thought of Peter Bergmann, who invented observables. Whereas initially he required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity: observables were _invariant_ under transformations generated by _each individual_ first-class constraint. While moder…
Partial and Complete Observables for Canonical General Relativity
本研究提出仅处理一个约束即可计算广义相对论狄拉克可观测量的方法，引入空间微分同胚不变的哈密顿约束并将其构造为阿贝尔形式，建立了时空与正则图景可观测量的联系。
Gravitational lensing observables in stationary and axisymmetric solutions in general relativity
本文研究广义相对论中稳态轴对称旋转尘埃流体自引力系统的光传播特性，分析时空度规非对角分量对光线偏折角的影响，指出其等效于额外有效质量且可通过背景源图像的特征不对称性探测。
All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces $Σ_-$ and $Σ_+$. The whole configuration thus consists of three regions, the internal one containing a wormhole throat, and two flat external ones, considered in rotating reference frames. Using a special kind of anisotropic fluid respecting the Weak Energy Condition (WEC) as a source of gravity in t…
A review of the pseudo-complex General Relativity (pc-GR) is presented, with the emphasis on observational consequences. First it is argued why to use an algebraic extension and why the pseudo-complex is a viable one. Afterward, the pc-GR is formulated. Posterior, several observational consequences are discussed, as the perihelion shift of Mercury, Quasi Periodic Objects, the emission profile of accretion discs, the pc-Robertson-Walker model of the universe, neutron stars and gravitational ring-down modes of a black hole.
The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D diffeomorphism symmetries. Some properties of this group were first explored by Bergmann and Komar. More recently the group has been analyzed from the perspective of projectability under the Legendre map. Time translation is not a realizeable symmetry, and is therefore distinct from diffeomorphism-induced symmetries. This issue is explored further in this paper. I…
$κ$-General-Relativity II: An Astrophysical Observable from a 2-Body system
本研究以双黑洞引力波为对象，探究量子引力现象学中κ-闵可夫斯基时空的相对定域性效应，发现其会在旋近阶段旋转频率中引入1.25阶后牛顿偏差，为通过观测约束量子引力理论提供了新途径。
Hamiltonian Constraints and Dirac's Observables: from Relativistic Particles towards Field Theory and General Relativity.
本文综述了相对论物理系统的前辛方法及其狄拉克观测量的确定。在相对论力学和Nambu弦的基础上，给出了在无质量矢量玻色子（如QED）情况下，含费米子的Yang-Mills理论的Dirac可观量。通过对经典场论在Dirac-Tomonaga-Schwinger意义下协变化的研究，发现了一个Dirac-Yukawa型内禀紫外截止，并指出了它对解决四粒子引力约束的意义.
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincaré symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observables associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localisation may be applied to massive as well as massless fields. Localisation observables are defined as to obey Lorentz covariant commutations relations and in particular include a time observable conjugat…
We review recent studies that rigorously define several key observables of the large-scale structure of the Universe in a general relativistic context. Specifically, we consider i) redshift perturbation of cosmic clock events; ii) distortion of cosmic rulers, including weak lensing shear and magnification; iii) observed number density of tracers of the large-scale structure. We provide covariant and gauge-invariant expressions of these observables. Our expressions are given for a linearly perturbed flat Friedmann-Robertson-Walker metric including scalar, vector, and tensor metric perturbations…
Change and local spatial variation are missing in Hamiltonian General Relativity according to the most common definition of observables (0 Poisson bracket with all first-class constraints). But other definitions have been proposed. Seeking Hamiltonian-Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit n…
Canonical vacuum gravity is expressed in generally-covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance, the time mapping ${\T}: {\yman} \to {\rman}$ and the space mapping ${\X}: {\yman} \to {\xman}$ that define the Dirac-ADM foliation are incorporated into the framework of the Hilbert variational principle. The resulting canonical action encompasses all individual Dirac-ADM actions, corresponding to different choices of foliating vacuum spacetimes by spacelike hypersurfaces. In this fram…
Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable A_μ is equivalent …
In this manuscript, we present analytical external spherical solutions of entangled relativity, which we compare to numerical solutions obtained in a Tolman-Oppenheimer-Volkoff framework. Analytical and numerical solutions match perfectly well outside spherical compact objects, therefore validating both types of solutions at the same time. The analytical external (hairy) solutions -- which depend on two parameters only -- may be used in order to easily compute observables -- such as X-ray pusle profiles -- without having to rely on an unknown equation of state for matter inside the compact obj…
The main focus is on the Hamilton-Jacobi techniques in classical general relativity that were pursued by Peter Bergmann and Arthur Komar in the 1960's and 1970's. They placed special emphasis on the ability to construct the factor group of canonical transformations, where the four-dimensional diffeomorphism phase space transformations were factored out. Equivalence classes were identified by a set of phase space functions that were invariant under the action of the four-dimensional diffeomorphism group. This is contrasted and compared with approaches of Paul Weiss, Julian Schwinger, Richard Ar…
We address the problem of observables in generally invariant spacetime theories such as Einstein's general relativity. Using the refined notion of an event as a ``point-coincidence'' between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.
Large-Scale-Structure Observables in General Relativity Validated at Second Order
本文在宇宙学微扰论中计算宇宙尺与宇宙钟的二阶相对论大尺度结构可观测量，经三类度规验证后明确其尺度依赖特性，为二阶相对论星系数密度研究提供核心支撑。
Fuzzy spacetime from a null-surface version of GR
最近引入的广义相对论的零表面公式为描述引力场提供了新的工具，也为观察引力场提供了新的物理方法。新的公式提供了与构成时空流形的点的坐标相对应的“局部”观测量--在{ \em几何定义的图表\/}中，以及对应于光锥切割和光锥的非局部可观测量。在量子理论中，时空点观测量变成了算符，时空流形本身变成了“量子化的”或"模糊的“。这种新颖的观点可能会对引力的量子理论的某些解释问题有所启发。的确，正如我们简要讨论的那样，广义相对论的零面表述提供了（局部）几何量--时空点观测量--这是量子理论长期寻求的物理算符的候选者。
Relational Observables and Physical Perspectivalism in General Relativity: The View from Nowhere vs. The View from Everywhere
本文探讨了广义相对论中参考系与本体论问题，提出两种解释路径：从无处视角认为关系可观测是框架无关的描述，从 everywhere视角则主张每个关系描述代表最全面的物理情况。
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} Λ) and extremely small 10^{-120}. We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expressed as an expectation value of a certain topologically invariant observable. This sets up a framework in which quantum gravity can be studied perturbatively using the techniques of topological …
We provide explicit partial differential equations - in finite cases - and functional differential equations - in field-theoretic cases - which determine observables or beables in the senses of Kuchař and of Dirac. These cover a wide range of relational mechanics models as well as Electromagnetism, Yang--Mills Theory and General Relativity. We give an underlying reason why pure-configuration Kuchař observables are already well-known: various types of shape, E-fields, B-fields, loops and 3-geometries. The partial differential equations or functional differential equations for pure-momentum obse…
A model is proposed to demonstrate that classical general relativity can emerge from loop quantum gravity, in a relational description of gravitational field in terms of coordinates given by matter. Local Dirac observables and coherent states are defined to explore physical content of the model. Expectation values of commutators between the observables for the coherent states recover the four-dimensional diffeomorphism algebra and the large-scale dynamics of the gravitational field relative to the matter coordinates. Both results conform with general relativity up to calculable corrections nea…
The investigation of relativistic effects in the most general way requires a unified treatment of light propagation in cosmology. This goal can be achieved with the new interpretation of the geodesic deviation equation in terms of the bilocal geodesic operators (BGO). The BGO formalism extends the standard formulation, providing a unified framework to describe all possible optical phenomena due to the interaction between light and spacetime curvature. In my dissertation, I present {\tt BiGONLight}, a {\tt Mathematica} package that applies the BGO formalism to study light propagation in numeric…
Incompleteness Theorems for Observables in General Relativity
本文运用描述集合论方法证明在广义相对论中丰富的时空集合不存在Borel可定义的完备观测量，揭示该问题与规范自由度相关，并指出理论物理与描述集合论的新联系。
S-stars in the Galactic Center are excellent testbeds of various general relativistic effects. While previous works focus on modeling their orbital motion around Sgr A*--the supermassive black hole in the Galactic Center--here we explore the possibility of using the rotation of S-stars to test the de Sitter precession predicted by general relativity. We show that by reorienting the rotation axes of S-stars, de Sitter precession will change the apparent width of the absorption lines in the stellar spectra. Our numerical simulations suggest that the newly discovered S4714 and S62 are best suited…
GPS Observables in Newtonian Spacetime or Why We Do Not Need 'Physical' Coordinate Systems
本文反对广义相对论需要“物理坐标系”和“可观测量”的观点，通过牛顿时空类比论证Rovelli的GPS坐标提议无法提取新物理信息，认为该观点缺乏动机。
We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables which encode the dynamics of the system. We apply this scheme to perturbations around a homogeneous and isotropic sector (cosmology) of general relativity. The background variables of this homogeneous and isotropic sector are treated fully dynamically which allows us to approximate the observables to arbitrary high order in a self--consistent and fully gauge …
We study the action for the three-space formalism of General Relativity, better known as the BFÓ (Barbour--Foster--Ó Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discus…
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $Λ\to\infty$ limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. The zeroth order corresponds to highly degenerate space-times with vanishing volume. Perturbations give rise to space-times with non-vanishing volumes in a natural way. The spectrum of area- and volume-related observables cons…
We propose a generalization of the isometry transformations to the geometric context of the field theories with spin where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations that leave invariant the equations of the fields with spin have generators with specific spin terms which represent new physical observables. The examples we present are the generators of…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension?" are presented. The availability as well as clarity of the arguments depend on which framework is being used, for which currently special relativity, general relativity and some schemes of quantum gravity are available. Canonical gravity provides means to anal…
(abridged)The achievements of the present work include: a) A clarification of the multiple definition given by Bergmann of the concept of {\it (Bergmann) observable. This clarification leads to the proposal of a {\it main conjecture} asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict connection with the Hamiltonian treatment of the initial value …
(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the {\it weak} ADM energy. The main results of the investigation are the following: 1) A re-interpretation of {\it active} diffeomorphisms as {\it passive and metric-dependent} dynamical symmetries of Einstein's equations, a re-interpretation that discloses their (up to now …
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and velocities in a specific coordinate system or gauge. The method of choice for simulating large-scale structure is numerical N-body simulations which are performed in the Newtonian limit. Even though one might worry that the use of the Newtonian approximation would make it impossible to use these simulations to compute properties on very large-scales, we show tha…
We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a totally constrained theory with vanishing canonical Hamiltonian. This fact, often referred to as the problem of time, provides the main conceptual difficulty towards the construction of gauge-invariant local observables. Nevertheless, within the framework of complete observables, that encode relations between dynamical fields, progress has been made during t…
The individuation of point-events and the Hamiltonian way of distinguishing gravitational from inertial effects in general relativity are discussed.
Cosmic inflation, a period of accelerated expansion in the early universe, can give rise to large amplitude ultra-large scale inhomogeneities on distance scales comparable to or larger than the observable universe. The cosmic microwave background (CMB) anisotropy on the largest angular scales is sensitive to such inhomogeneities and can be used to constrain the presence of ultra-large scale structure (ULSS). We numerically evolve nonlinear inhomogeneities present at the beginning of inflation in full General Relativity to assess the CMB quadrupole constraint on the amplitude of the initial flu…
Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the FLRW coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays towards the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to ob…
Contrary to recent claims in the literature, Newtonian N-body simulations of collisionless Dark Matter in a LambdaCDM background are compatible with general relativity and are not invalidated by general relativistic effects at the linear level. This verdict is based on four facts. (1) The system of linearized Einstein equations and conservation laws is well-posed in the gauge invariant formulation and physically meaningful. (2) Comparing general relativity with its Newtonian approximation at a given order in perturbation theory is only meaningful at the level of observables. (3) The dynamics o…
It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes appear in General Relativity and how it leaves an observable footprint in space-time. In cosmology we show that such topological observable is the cosmic radiation produced by the acceleration of the universe. The cosmological constant is a very particular case which occurs when the expansion of the universe into the vacuum occurs only in the direction of the cos…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of …
Extra dimensions, which led to the foundation and inception of string theory, provide an elegant approach to force-unification. With bulk curvature as high as the Planck scale, higher curvature terms, namely f(R) gravity seems to be a natural addendum in the bulk action. These can not only pass the classic tests of general relativity but also serve as potential alternatives to dark matter and dark energy. With interesting implications in inflationary cosmology, gravitational waves and particle phenomenology it is worth exploring the impact of extra dimensions and f(R) gravity in black hole acc…
We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that 1.Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and Hamiltonian constraints of General Relativity, can be easily constructed. 2. The physical time evolution of those observables is generated by a natural physical Hamiltonian which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kuchař. In order that the physical Hamiltonian is clos…
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. We further demonstrate that subalgebras which commute before imposing the symmetry constraint ca…
In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically underpins miscellaneous investigations of phenomenological and quantum extensions of General Relativity. We discuss how it allows quantum field theory to be a theoretical laboratory for testing Einstein's theory of gravity and demonstrate the current state of the art of an efficient and practical scheme for evaluating the classical components of perturbative weak-…
The main science driver for the coming generation of cosmological surveys is understanding dark energy which relies on testing General Relativity on the largest scales. Once we move beyond the simplest explanation for dark energy of a cosmological constant, the space of possible theories becomes both vast and extremely hard to compute realistic observables. A key discriminator of a cosmological constant, however, is that the growth of structure is scale-invariant on large scales. By carefully weighting observables derived from distributions of galaxies and a dipole pattern in their apparent si…
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