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Register a new userGravitational Waves and Perspectives for Quantum Gravity
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Added by
Ilya Lvovich Shapiro
Publication date
2014
fields
Physics
and research's language is
English
Authors
Ilya L. Shapiro
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Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.
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We consider the gravitational radiation in conformal gravity theory. We perturb the metric from flat Mikowski space and obtain the wave equation after introducing the appropriate transformation for perturbation. We derive the effective energy-momentum tensor for the gravitational radiation, which can be used to determine the energy carried by gravitational waves.
124 -
Luz Marina Reyes
, Claudia Moreno
, Jose Edgar Madriz Aguilarn (Departamento de Matematicas
2012
We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during an early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild-de-Sitter metric, which is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza-Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that is possible to derive dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity- antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.
In this work we shall develop a quantitative approach for extracting predictions on the primordial gravitational waves energy spectrum for $f(R)$ gravity. We shall consider two distinct models which yield different phenomenology, one pure $f(R)$ gravity model and one Chern-Simons corrected potential-less $k$-essence $f(R)$ gravity model in the presence of radiation and non-relativistic perfect matter fluids. The two $f(R)$ gravity models were carefully chosen in order for them to describe in a unified way inflation and the dark energy era, in both cases viable and compatible with the latest Planck data. Also both models mimic the $Lambda$-Cold-Dark-Matter model and specifically the pure $f(R)$ model only at late times, but the Chern-Simons $k$-essence model during the whole evolution of the model up to the radiation domination era. In addition they guarantee a smooth transition from the inflationary era to the radiation, matter domination and subsequently to the dark energy era. Using a WKB approach introduced in the relevant literature by Nishizawa, we derive formulas depending on the redshift that yield the modified gravity effect, quantified by a multiplicative factor, a ``damping in front of the General Relativistic waveform. In order to calculate the effect of the modified gravity, which is the ``damping factor, we solve numerically the Friedmann equations using appropriate initial conditions and by introducing specific statefinder quantities. As we show, the pure $f(R)$ gravity gravitational wave energy spectrum is slightly enhanced, but it remains well below the sensitivity curves of future gravitational waves experiments. In contrast, the Chern-Simons $k$-essence $f(R)$ gravity model gravitational wave energy spectrum is significantly enhanced and two signals are predicted which can be verified by future gravitational wave experiments.
We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations.
We point out that there are only three polarizations for gravitational waves in $f(R)$ gravity, and the polarization due to the massive scalar mode is a mix of the pure longitudinal and transverse breathing polarization. The classification of the six polarizations by the Newman-Penrose quantities is based on weak, plane and null gravitational waves, so it is not applicable to the massive mode.
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