A note on quasi-local energy
A definition of quasi-local energy in a gravitational field based upon its embedding into flat space is discussed. The outcome is not satisfactory from many points of view.
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arXiv subjects
Enrique Alvarez
Publications and source records attributed to Enrique Alvarez.
Physical content of Quadratic Gravity
We have recently undergone an analysis of gravitational theories as defined in first order formalism, where the metric and the connection are treated as independent fields. The physical meaning of the connection field has historically been somewhat elusive. In this paper, a complete spin analysis of the torsionless connection field is performed, and its consequences are explored. The main properties of a hypothetical consistent truncation of the theory are discussed as well.
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Quasi-local energy and compactification
Based on the quasi-local energy definition of Brown and York, we compute the integral of the trace of the extrinsic curvature over a codimension-2 hypersurface. In particular, we study the difference between the uncompactified Minkowski spacetime and the toroidal Kaluza-Klein compactification. For the latter, we find that this quantity interpolates between zero and the value for the uncompactified spacetime, as the size of the compact dimension increases. Thus, the quasi-local energy is able to discriminate between the two spacetimes.
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Quadratic gravity in first order formalism
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than $\tfrac{1}{p^2}$. Calculations are somewhat involved when all monomials are considered, but we have intended to laid down the general case. The interaction between external sources is analyzed; this interaction is conveyed mainly by the three-index connection field. The theory as it stands, is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
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Ghost-free higher derivative unimodular gravity
The unimodular version of the ghost-free higher derivative gravity is obtained. It is the unimodular reduction of some particular lagrangians quadratic in curvature.
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A candidate for an UV completion: quadratic gravity in first order formalism
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than $\tfrac{1}{p^2}$. The UV regime is in a conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated.
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Weyl Gravity Revisited
The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent dynamical variables, there are no quartic propagators for any dynamical variable. This suggests that it is possible to get both renormalizability and unitarity along these lines. We have studied a particular instance of those theories, namely Weyl gravity. Although the ground state of this system is difficult to analyze, we have been able to study the physical effects of some external sources.
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Unimodular Trees versus Einstein Trees
The maximally helicity violating (MHV) tree level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in both theories.
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Weyl invariance with a nontrivial mass scale
A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed.
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Theoretical Framework and Simulation Results for Implementing Weighted Multiple Sampling in Scientific CCDs
The Digital Correlated Double Sampling (DCDS) is a technique based on multiple analog-to-digital conversions of every pixel when reading a CCD out. This technique allows to remove analog integrators, simplifying the readout electronics circuitry. In this work, a theoretical framework that computes the optimal weighted coefficients of the pixels samples, which minimize the readout noise measured at the CCD output is presented. By using a noise model for the CCD output amplifier where white and flicker noise are treated separately, the mathematical tool presented allows for the computation of the optimal samples coefficients in a deterministic fashion. By modifying the noise profile, our simulation results get in agreement and thus explain results that were in mutual disagreement up until now.
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Conformal and non Conformal Dilaton Gravity
The quantum dynamics of the gravitational field non-minimally coupled to an (also dynamical) scalar field is studied in the {\em broken phase}. For a particular value of the coupling the system is classically conformal, and can actually be understood as the group averaging of Einstein-Hilbert's action under conformal transformations. Conformal invariance implies a simple Ward identity asserting that the trace of the equation of motion for the graviton is the equation of motion of the scalar field. We perform an explicit one-loop computation to show that the DeWitt effective action is not UV divergent {\em on shell} and to find that the Weyl symmetry Ward identity is preserved {\em on shell} at that level. We also discuss the fate of this Ward identity at the two-loop level --under the assumption that the two-loop UV divergent part of the effective action can be retrieved from the Goroff-Sagnotti counterterm-- and show that its preservation in the renormalized theory requires the introduction of counterterms which exhibit a logarithmic dependence on the dilaton field.
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Some Comments on Dilaton Gravity
A Weyl invariant extension of Einstein gravity is studied. It simply consists in the group averaging of Einstein's action under Weyl transformations. Contradicting cherished beliefs, a conformal anomaly is found in the trace of the equations of motion if diffeomorphism invariance is to be a symmetry of the quantum theory. This anomaly however vanishes on shell, which signals the existence of another gauge in which the anomaly is absent. It can be made also to vanish off-shell at the price of losing diffeomorphism invariance
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Consistent Asymptotic Scalar Wavefunction in de Sitter Space
The approximate late conformal time wavefunction for self-interacting scalar quantum fields in de Sitter space is computed. It dominates for conformal times much larger than a certain critical value, $η=η_{\text{crit}}$ which depends on the dimension and on other characteristics of the matter fields. Its self-consistency (i.e., whether the back reaction is consistent with the de Sitter symmetry) is analyzed.
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Unimodular Cosmological Space-times
Some cosmological solutions of the unimodular theory of gravity are studied. These solutions can always be mapped to solutions of Einstein's general relativity in an appropiate frame. Constant scalar potentials however do not gravitate. Some physical consequences are pointed out.
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The weight of matter
Einstein's traceless 1919 gravitational theory is analyzed from a variational viewpoint. It is shown to be equivalent to a transverse (invariant only under diffeomorphisms that preserve the Lebesgue measure) theory, with an additional Weyl symmetry, in which the gauge is partially fixed so that the metric becomes unimodular. In spite of the fact that this symmetry forbids direct coupling of the potential energy with the gravitational sector, the equivalence principle is recovered in the unimodular gauge owing to Bianchi's identities.
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Bottom up approach to quantum gravity
A general introduction is given to what can be predicated about quantum gravity once the lessons from the standard model of particle physics are taken into account. In particular, the effective lagrangian point of view is briefly commented upon .
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Ultraviolet behavior of transverse gravity
The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the metric transforms as a true scalar instead of a density. Generically, the models include an additional scalar degree of freedom contained in the metric besides the usual spin two component. When the cosmological constant is fine tuned to zero, there are only two theories which are on shell finite, namely the one in which the symmetry is enhanced to the full group of diffeomorphisms, i.e. Einstein's gravity, and another one denoted by WTDiff which enjoys local Weyl invariance. Both of them are free from the additional scalar.
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A comment on the matter-graviton coupling
We point out a generic inconsistency of the coupling of ordinary gravity as described by general relativity with matter invariant under the subgroup of unimodular diffeomorphisms (TDiffs), and some previously studied exceptions are pointed out. The most general Lagrangian invariant under TDiff up to dimension five operators is determined, and restrictions on parameters coming from existing observations are studied in some cases.
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