Weyl-transverse gravity with boundaries

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

Transverse Diffeomorphism (TDiff) theories are well-motivated theories of gravity from the quantum perspective, which are based upon a gauge symmetry principle. The main contribution of this work is to firmly establish a correspondence between TransverseDiff and the better-known scalar-tensor gravity — in its more general form —, a relation which is completely analogous to that between unimodular gravity and General Relativity. We then comment on observational aspects of TDiff. In connection with this proof, we derive a very general rule that determines under what conditions the procedure of fixing a gauge symmetry can be equivalently applied before the variational principle leading to the equations of motion, as opposed to the standard procedure, which takes place afterwards; this rule applies to gauge-fixing terms without derivatives.

Analysis of cosmic data is the only way to determine whether General Relativity is the law of gravity also on the largest scales in our Universe. The current standard model of cosmology, ΛCDM, is based on General Relativity, and fits all currently available data flawlessly. However, theoretical dissatisfaction with ΛCDM exists: cosmological data probe gravitational interactions, and ΛCDM fits the data only because it introduces two components of startling gravitional behaviour, the cosmological constant, Λ, and cold dark matter (CDM). The cosmological constant has a suspiciously small value when regarded from the perspective of quantum field theories, and cold dark matter has so far not been detected in any experiment of particle physics. This thesis examines the cosmological standard model from the vantage point of statistics. A non-Gaussian likelihood approximation is presented and the need of an unbiased mechanism for dealing with estimated covariance matrices is addressed. Concerning neutrinos, a previously existent parameterization bias in the analysis of the cosmic microwave background is resolved. Using weak lensing and type Ia supernova data of the next generation, it is estimated how much can be learned about dark energy from these future data sets.

The Toverline{T} deformed 2D CFTs correspond to AdS3 gravity with Dirichlet boundary condition at finite cutoff or equivalently a mixed boundary condition at spatial infinity. In this work, we use the latter perspective and Chern-Simons formalism of AdS3 gravity to construct the surface charges and associated algebra in Toverline{T} deformed theories. Starting from the Bañados geometry, we obtain the Chern-Simons gauge fields for the Toverline{T} deformed geometry, which are parametrized by two independent charges. With help of the mixed boundary condition, the residual gauge symmetries of the deformed gauge fields and the associated surface charges were obtained respectively. The charge algebra turns out to be a non-linear deformed Virasoro algebra, which was obtained in different way by applying the cutoff perspective. Finally, we propose a way to construct the time-independent charges from these surface charges and they satisfy the field-dependent Virasoro algebra.

Volume 6 of The Collected Papers of Albert Einstein includes Einstein's writings during 1914 - 1917, his first three years in Berlin. Einstein moved to Berlin in April 1914 from Zurich where he had been a Professor at his old undergraduate school, The Federal Institute of Technology, since February 1912. In the spring of 1913, Max Planck and Walther Nernst journeyed from Berlin to visit Einstein in Zurich in order to make him an offer that, in the end, he could not refuse: a professorship with no teaching obligations and the directorship of the fledgling Kaiser Wilhelm Institute for Physics. Soon after their arrival in Berlin, the Einsteins separated. Mileva departed for Zurich with their sons Hans Albert and Eduard. At this point Einstein's relationship with his cousin Elsa Löwenthal deepened further. Thus, as the editors put so well, in the period covered in this volume, `Einstein's life and career entered a new phase'. Amongst the key documents in Volume 6 are publications from 1914 in which Einstein concluded that gravitational field equations `cannot possibly be generally covariant'. After having realized his errors, Einstein returned to the theme of general covariance and, in 1915, published three papers in succession in which he developed the generalized theory of relativity. The third paper, published on 25 November 1915 and entitled `The Field Equations of Gravitation', is the capstone of the trio, correcting as it does errors in the previous two. A week prior to its publication Einstein published a result of his new theory: the calculation from the new generally covariant field equations of Mercury's perihelion motion of 43 seconds of arc per century, in agreement with observation. Some time later, Einstein told his former collaborator Adriaan Fokker that upon seeing the result emerge he had heart palpitations. On 8 February 1917 Einstein essentially started the field of modern cosmology with the publication of `Cosmological Considerations in the General Theory of Relativity'. One of the many points of interest in this pioneering paper is Einstein's modification of his field equations with the so-called `cosmological constant' in order to incorporate, as best he could, Machian ideas on effects of distant rotating masses. Besides tidying up general relativity theory with his review paper of 1916, Einstein made new and far reaching contributions to the quantum theory of radiation. In two papers of 1916 he published his A and B coefficients and went on to conclude that atoms need not emit radiation in spherical waves, but in light quanta with a specific direction and definite momentum. The presence of probability in this theory was to Einstein a `weakness'. The eclectic set of publications in Volume 6 include ones on molecular currents in magnets, book reviews, contributions to Bohr's atomic theory and statements on the war, as well as documents relating to Einstein's participation as an expert witness in a patent dispute between the German firm Anschütz & Co. and the American Sperry Gyroscope Company. In the end the court chose to follow the former patent clerk's report and decided to prohibit Sperry Gyroscope from manufacturing gyrocompasses that incorporated methods patented by Anschütz. In summary there is something for everyone in this fascinating collection of papers published by Einstein during 1914 - 1917 and assembled in what we have come to expect as a meticulous scholarly presentation replete with an up to date listing of secondary studies and informative footnotes. We eagerly await further volumes of this truly historic project.

Numerous papers deal with asymptotic methods for boundary value problems in domains depending on a small parameter in a complicated way (perforated domains, partially perforated domains, framework structures, thin domains); e.g., see [1–9]. Boundary value problems in thick singularly degenerating junctions (the number of components of such junctions grows infinitely as the perturbation parameter tends to zero) have specific difficulties and require a separate consideration. It was shown in [10] that boundary value problems in thick junctions lose their coercivity under the passage to the limit, which substantially complicates asymptotic studies. The papers [11, 12] were the first in this direction. In [13–19], a classification of thick junctions was given and rigorous mathematical methods were developed for analyzing the main boundary value problems of mathematical physics in thick singularly degenerating junctions of various types. The study of boundary value problems in thick junctions is focused on the asymptotic behavior of their solutions as e → 0, i.e., as the number of thin attached domains grows infinitely and their thickness tends to zero. In the present paper, we consider a thick junction whose thin attached cylinders are divided into two levels depending on the boundary conditions posed on the lateral surface of these cylinders (inhomogeneous Neumann boundary conditions and homogeneous Dirichlet conditions). In addition, thin cylinders of each level e-periodically alternate along the junction zone. Such thick junctions will be called thick two-level junctions. A problem on a thick plane two-level junction was considered for the first time in [20], where the asymptotic behavior of eigenvalues and eigenfunctions of a spectral boundary value problem was analyzed. Other boundary value problems in plane two-level junctions were considered in [21–23]. Asymptotic analysis of boundary value problems with a periodic change of boundary conditions (Neumann and Dirichlet conditions) on the boundary of smooth unperturbed domains was carried out in [24–26], where it was shown that the first term of the asymptotics is mainly the solution of the corresponding boundary value problem with the Dirichlet conditions. The qualitatively new result of the present paper implies that the first term of the asymptotics is a vector function whose components are solutions of two independent boundary value problems (one in the junction body and another in a domain filled with thin cylinders in the limit) with homogeneous Dirichlet conditions in the junction zone. Note also that the second problem is a problem for a second-order ordinary differential equation with a new right-hand side that “remembers” the inhomogeneity in the Neumann boundary conditions of the original problem and the specific “packing density” of thin cylinders.

It is known that the cosmological constant can be dynamically tuned to an arbitrary small value in classes of scalar tensor theories. The trouble with such schemes is that effective gravity itself vanishes. We explore the possibility of avoiding this “no-go” with a spatially varying effective gravity. We demonstrate this in principle with the non-minimally coupled scalar field having an additional coupling to a fermionic field. The expectation value of the scalar field gets anchored to a non-trivial value inside compact domains. But for the non-minimal coupling to the scalar curvature, these configurations are analogous to the non-topological solutions suggested by Lee and Wick. With non-minimal coupling, this leads to a peculiar spatial variation of effective gravity. As before, one can dynamically have the long distance (global) gravitational constant G and Λ, the cosmological constant, tending to zero. However, inside compact domains, G can be held to a universal (non-vanishing) value. Long distance gravitational effects turn out to be indistinguishable from those expected of general theory of relativity (GTR). There are two ways in which the ensuing theory may lead to a viable effective gravity theory: a) the compact domains could be of microscopic (sub-nuclear) size, or b) the domains could be large enough to accommodate structures as large as a typical galaxy. Aspects of effective gravity and cosmology that follow are described. A toy Freidman-Robertson-Walker (FRW) model free from several standard model pathologies and characteristic features emerges. Although this proposed model remained less studied but became an important aspect in initiating a viable approach in addressing the cosmological constant problem. Comparison with some additional observational constraints like quantitative constraints on gravitational constant. G, from some high precision tests will be included our forthcoming paper which will address the limitations of the present paper.

I give a brief review of the search for a proper definition of energy in General Relativity (GR), a far from trivial quest, which was only completed after four and a half decades. The equally (or perhaps more) difficult task of establishing its positivity—it was to take another 15 plus years—will then be summarized. Extension to cosmological GR is included. Mention is made of some recent offshoots. An invitation to submit a review to the Proceedings of the Royal Society prompts revisiting a subject of central importance both to GR and to my own past research—its energy definition and positivity. While there are no loose ends left, a summary may be of some use to students and non-experts. Exposure to introductory GR is useful. We will divide this survey into two unequal parts: first, the original GR without a cosmological constant, then extend it to the rather different two cases of Λ ≠ 0 .

We describe and study a certain class of modified gravity theories. Our starting point is the Plebański formulation of gravity in terms of a triple Bi of two-forms, a connection Ai and a ‘Lagrange multiplier’ field Ψij. The generalization we consider stems from the presence in the action of an extra term proportional to a scalar function of Ψij. As in the usual Plebański general relativity (GR) case, a certain metric can be constructed from Bi. However, unlike in GR, the connection Ai no longer coincides with the self-dual part of the metric compatible spin connection. Field equations of the theory are shown to be relations between derivatives of the metric and components of field Ψij, as well as its derivatives, the later being in contrast to the GR case. The equations are of second order in derivatives. An analog of the Bianchi identity is still present in the theory, as well as its contracted version tantamount to the energy conservation equation.

Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor perturbations in a closed universe with space-like boundaries. We also give a general method to reconstruct the covariant boundary action starting from a given set of boundary conditions for the cosmological background. These results may be of special relevance in the context of the path-integral formulation of quantum cosmology, where boundary terms contain essential physical information of the system.

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.

Spin foam models are an attempt at a covariant or path integral formulation of canonical loop quantum gravity. The construction of such models usually relies on the Plebanski formulation of general relativity as a constrained BF theory and is based on the discretization of the action on a simplicial triangulation, which may be viewed as an ultraviolet regulator. The triangulation dependence can be removed by means of group field theory techniques, which allows one to sum over all triangulations. The main tasks for these models are the correct quantum implementation of the Plebanski constraints, the existence of a semiclassical sector implementing additional ‘Regge-like’ constraints arising from simplicial triangulations and the definition of the physical inner product of loop quantum gravity via group field theory. Here we propose a new approach to tackle these issues stemming directly from the Holst action for general relativity, which is also a proper starting point for canonical loop quantum gravity. The discretization is performed by means of a ‘cubulation’ of the manifold rather than a triangulation. We give a direct interpretation of the resulting spin foam model as a generating functional for the n-point functions on the physical Hilbert space at finite regulator. This paper focuses on ideas and tasks to be performed before the model can be taken seriously. However, our analysis reveals some interesting features of this model: firstly, the structure of its amplitudes differs from the standard spin foam models. Secondly, the tetrad n-point functions admit a ‘Wick-like’ structure. Thirdly, the restriction to simple representations does not automatically occur—unless one makes use of the time gauge, just as in the classical theory.

Conserved vectors are divergencies of superpotentials. In field theory on curved backgrounds, they are useful in calculating global ‘charges’ in arbitrary coordinates and local conserved quantities for small perturbations with specific gauge conditions. Superpotentials are, however, ill–defined. A new criterion of Julia and Silva selects uniquely for Dirichlet boundary conditions the ‘KBL superpotential’ as proposed by Katz, Bičák and Lynden–Bell, which has remarkable properties.Here, we show that a Belinfante–type addition to the KBL superpotential in general relativity gives an expression that is independent of boundary conditions defined by a variational principle. The modified superpotential has the same global properties as the KBL one, except for angular momentum at null infinity, and it does not differ from the KBL superpotential in the linearized theory of gravitation.As an illustration in linearized theory on curved backgrounds, we calculate conserved quantities for small perturbations on a Friedmann–Robertson–Walker spacetime associated with conformal Killing vectors. Our unifying view relates a number of applications in cosmology found in the literature. Globally conserved quantities have simple physical interpretations in the ‘uniform Hubble expansion’ gauge.

We investigate a family of axial symmetry solution constructed in general relativity (GR) within the framework of Ricci-inverse (RI) gravity theory. In GR, these solutions admitted closed time-like curves at an instant of time from an initial spacelike hypersurface in a causally well-behaved manner, thus, violates the causality condition. Our aim is to examine these axial symmetry solutions within the context of Ricci-inverse gravity theory to determine whether closed time-like curves still appear in this new gravity theory. We consider two Classes of RI-gravity models: (i) Class-II models defined by a function f=f(R,AμνAμν)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f=f({\\mathcal {R}}, A^{\\mu \ u }\\,A_{\\mu \ u })$$\\end{document} gravity and (ii) Class-III models defined by f=f(R,A,AμνAμν)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f=f({\\mathcal {R}},{\\mathcal {A}}, A^{\\mu \ u }\\,A_{\\mu \ u })$$\\end{document}, where Aμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A^{\\mu \ u }$$\\end{document} is the anti-curvature tensor, A=gμνAμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}=g_{\\mu \ u }\\,A^{\\mu \ u }$$\\end{document} as its scalar, and Rμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{\\mu \ u }$$\\end{document} is the Ricci tensor. We are able solved the modified field equations considering these axial symmetry solutions as background in RI-gravity with null radiation as the matter content and the cosmological constant. This confirms that the chosen family of axial symmetry solutions are valid solutions in RI-gravity theory and, consequently, closed time-like curves is still form, analogous to their formation in GR.

Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of neutron stars can exist. Lau et al. [ApJ, 714, 1234 (2010)] found that the frequency of the $f$-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes [Science, 341, 365 (2013)] discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Thanks to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff [Phys. Rev. Lett., 109, 021101 (2012)], we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.