Gravitational waves in the extended theory of gravity

Extended theories of gravity are considered as a new approach for solving the infrared and ultraviolet scale problems; the standard theory of gravity (general relativity) and observational evidence of gravitational waves and subsequent identification of the number of existing polarizations are an effective tool for testing general relativity and extended theories of gravity. The Newman–Penrose method is used to characterize the polarization modes for specific forms of [Formula: see text] in the present study. Both the forms of the [Formula: see text] theory belong to far more general variational class of gravitational waves, capable of presenting up to six separate polarizations states. We have introduced a new [Formula: see text] gravity model as an attempt to have a theory with more parametric regulations so that the model can be used to describe existing issues and discover different directions in gravity physics. The primary goal of this research is to look into the properties of gravitational waves with new cases. The model shows the existence of scalar degrees of freedom in [Formula: see text] gravity metric notation.

Photon frequency shift in curvature-based Extended Theories of Gravity

We study the frequency shift of photons generated by rotating gravitational sources in the framework of curvature-based Extended Theories of Gravity. The discussion is developed considering the weak-field approximation. Following a perturbative approach, we analyze the process of exchanging photons between Earth and a given satellite, and we find a general relation to constrain the free parameters of gravitational theories. Finally, we suggest the Moon as a possible laboratory to test theories of gravity by future experiments which can be, in principle, based also on other Solar System bodies.

To Conserve, or Not to Conserve: A Review of Nonconservative Theories of Gravity

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

Reconstructing wormhole solutions in curvature based Extended Theories of Gravity

Static and spherically symmetric wormhole solutions can be reconstructed in the framework of curvature based Extended Theories of Gravity. In particular, extensions of the General Relativity, in metric and curvature formalism give rise to modified gravitational potentials, constituted by the classical Newtonian potential and Yukawa-like corrections, whose parameters can be, in turn, gauged by the observations. Such an approach allows to reconstruct the spacetime out of the wormhole throat considering the asymptotic flatness as a physical property for the related gravitational field. Such an argument can be applied for a large class of curvature theories characterising the wormholes through the parameters of the potentials. According to this procedure, possible wormhole solutions could be observationally constrained. On the other hand, stable and traversable wormholes could be a direct probe for this class of Extended Theories of Gravity.

The Solution to Graviton as Goldstone Boson

The study of Graviton as Goldstone bosons appeared in the 1960s, after Bjorken interacting idea of Electrodynamics. However, no recent advancement has been done in the field, because of very constraints as well as low-attractiveness of the theory. We do the non-metric tensor (covariant derivative of the metric tensor) case of Gravitation and eventually get SO(1,3) broken in the vacuum state of quantized field theory, then find the Graviton as Goldstone Boson. We, in final, see that Gravitons can have appearances in many modified (and extended) theories of Gravitation.

Extended Hořava Gravity with Physical Ground-State Wavefunction

We propose a new extended theory of Hořava gravity based on the following three conditions: (i) power-counting renormalizable, (ii) healthy IR behavior and (iii) a stable vacuum state in a quantized version of the theory. Compared with other extended theories, we stress that any realistic theory of gravity must have physical ground states when quantization is performed. To fulfill the three conditions, we softly break the detailed balance but keep its basic structure unchanged. It turns out that the new model constructed in this way can avoid the strong coupling problem and remains power-counting renormalizable, moreover, it has a stable vacuum state by an appropriate choice of parameters.

The generally covariant meaning of space distances

We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test bodies with horizons and singularities so that the definition extends through the horizons and it matches the protocol used to measure them. The definition we propose can be used in standard general relativity although it extends directly to Weyl geometries to encompass a number of modified theories, extended theories in particular.

The Non-Metric Solution to Graviton as Goldstone Boson

The study of Graviton as Goldstone bosons appeared in the 1960s, after Bjorken interacting idea of Electrodynamics. However, no recent advancement has been done in the field, because of very constraints as well as low-attractiveness of the theory. We do the non-metric tensor (covariant derivative of the metric tensor) case of Gravitation and eventually get SO(1,3) broken in the vacuum state of quantized field theory, then find the Graviton as Goldstone Boson. We, in final, see that Gravitons can have appearances in many modified (and extended) theories of Gravitation.