Class Of Metric Theories Research Articles

Spatially covariant gravity with 2 degrees of freedom: Perturbative analysis

We revisit the problem of building the Lagrangian of a large class of metric theories that respect spatial covariance, which propagate at most two degrees of freedom and in particular no scalar mode. The Lagrangians are polynomials built of the spatially covariant geometric quantities. By expanding the Lagrangian around a cosmological background and focusing on the scalar modes only, we find the conditions for the coefficients of the monomials in order to eliminate the scalar mode at the linear order in perturbations. We find the conditions up to $d=4$ with $d$ the total number of derivatives in the monomials and determine the explicit Lagrangians for the cases of $d=2$, $d=3$ as well as the combination of $d=2$ and $d=3$. We also expand the Lagrangian of $d=2$ to the cubic order in perturbations, and find additional conditions for the coefficients such that the scalar mode is eliminated up to the cubic order. This perturbative analysis can be performed order by order, and one expects to determine the final Lagrangian at some finite order such that the scalar mode is fully eliminated. Our analysis provides an alternative and complimentary approach to building spatially covariant gravity with only tensorial degrees of freedom. The resulting theories can be used as alternatives to the general relativity to describe the tensorial gravitational waves in a cosmological setting.

Spatially covariant gravity: Perturbative analysis and field transformations

We make a perturbative analysis of the number of degrees of freedom in a large class of metric theories respecting spatial symmetries, of which the Lagrangian includes kinetic terms of both the spatial metric and the lapse function. We show that, as long as the kinetic terms are degenerate, the theory propagates a single scalar mode at the linear order in perturbations around a Friedmann-Robertson-Walker background. Nevertheless, an unwanted mode will reappear pathologically, either at nonlinear orders around the Friedmann-Robertson-Walker background, or at linear order around an inhomogeneous background. In both cases, it turns out that a consistency condition has to be imposed in order to remove the unwanted mode. This perturbative approach provides an alternative and also complementary point of view of the conditions derived in a Hamiltonian analysis. We also discuss the relation under field redefinitions, between theories with and without the time derivative of the lapse function.

Parameterized post-Newtonian cosmology

Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).

Extension of Loop Quantum Gravity to Metric Theories beyond General Relativity

The successful background-independent quantization of Loop Quantum Gravity relies on the key observation that classical General Relativity can be cast into the connection-dynamical formalism with the structure group of SU(2). Due to this particular formalism, Loop Quantum Gravity was generally considered as a quantization scheme that applies only to General Relativity. However, we will show that the nonperturbative quantization procedure of Loop Quantum Gravity can be extended to a rather general class of metric theories of gravity, which have received increased attention recently due to motivations coming form cosmology and astrophysics. In particular, we will first introduce how to reformulate the 4-dimensional metric f(R) theories of gravity, as well as Brans-Dicke theory, into connection-dynamical formalism with real SU(2) connections as configuration variables. Through these formalisms, we then outline the nonpertubative canonical quantization of the f(R) theories and Brans-Dicke theory by extending the loop quantization scheme of General Relativity.

Could the Pioneer anomaly have a gravitational origin?

If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity over long distances or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Following the general assumption that the Pioneer spacecraft move geodesically in a spherically symmetric space-time metric, we derive the metric disturbance that is needed in order to account for the Pioneer anomaly. We then analyze the residual effects on the astronomical observables of the three outer planets that would arise from this metric disturbance, given an arbitrary metric theory of gravity. Providing a method for comparing the computed residuals with actual residuals, our results imply that the presence of a perturbation to the gravitational field necessary to induce the Pioneer anomaly is in conflict with available data for the planets Uranus and Pluto, but not for Neptune. Wemore » therefore conclude that the motion of the Pioneer spacecraft must be nongeodesic. Since our results are model-independent within the class of metric theories of gravity, they can be applied to rule out any model of the Pioneer anomaly that implies that the Pioneer spacecraft move geodesically in a perturbed space-time metric, regardless of the origin of this metric disturbance.« less

Errata: A class of metric theories of gravitation of Minkowski spacetime

A mistake which occurred in the derivation of the field equations from the Lagrangian is corrected. Unfortunately many of the expressions given in the article have to be changed, although the results do not change qualitatively, but only quantitatively.

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.

NEW CLASS OF METRIC THEORIES OF GRAVITY NOT DESCRIBED BY THE PARAMETRIZED POST-NEWTONIAN (PPN) FORMALISM

After an introduction to theories of gravity alternative to general relativity, metric theories (Sec. 1) and the parametrized post-Newtonian (PPN) formalism (Sec. 2), we define a new class of metric theories of gravity (Sec. 3). It turns out that the post-Newtonian approximation of these new theories is not described by the PPN formalism (Sec. 4); in fact, in the limit of weak field and slow motions, the post-Newtonian expression of the metric tensor contains an, a priori, infinite set of new terms and correspondingly an, a priori, infinite set of new PPN parameters. As a consequence, the parametrized post-Newtonian formulas describing the classical relativistic tests should include these new parameters, and therefore the experimental values of the classical relativistic effects should not be used to put limits only on the standard ten PPN parameters. Finally, we note that a subset of this new class of theories has the same post-Newtonian limit and value of the PPN parameters as general relativity, and therefore is automatically in agreement with the classical general-relativistic tests (Sec. 4, theory III).

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer. Theoretical principles.

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of ${10}^{\mathrm{\ensuremath{-}}10}$ of the Newtonian tidal terms arising from the mass of the Earth. These components could be detected in principle by sensitive superconducting gravity gradiometers currently under development. We lay out the theoretical principles of such an experiment by using the parametrized post-Newtonian formalism to derive the locally measured Riemann tensor in an orbiting proper reference frame, in a class of metric theories of gravity that includes general relativity. A gradiometer assembly consisting of three gradiometers with axes at mutually right angles measures three diagonal components of a 3\ifmmode\times\else\texttimes\fi{}3 ``tidal tensor,'' related to the Riemann tensor. We find that, by choosing a particular assembly orientation relative to the orbit and taking a sum and difference of two of the three gradiometer outputs, one can isolate the gravitomagnetic relativistic effect from the large Newtonian background.

Gravitational Stokes Parameters

view Abstract Citations (26) References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gravitational Stokes Parameters Anile, A. Marcello ; Breuer, Reinhard A. Abstract The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters, for both high-frequency electromagnetic and gravitational waves. We conclude by generalizing the concept of Stokes parameters for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present. Sabject headings: polarization - radiative transfer - relativity Publication: The Astrophysical Journal Pub Date: April 1974 DOI: 10.1086/152766 Bibcode: 1974ApJ...189...39A full text sources ADS |