Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNecessity of spacetime shear for cosmological gravitational waves
203
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that a general but shear-free perturbation of homogeneous and isotropic universes are necessarily silent, without any gravitational waves. We prove this in two steps. First we establish that a shear free perturbation of these universes are acceleration-free and the fluid flow geodesics of the background universe maps onto themselves in the perturbed universe. This effect then decouples the evolution equations of the electric and magnetic parts of the Weyl tensor in the perturbed spacetimes and the magnetic part no longer contains any tensor modes. Although the electric part, that drives the tidal forces, do have tensor modes sourced by the anisotropic stress, these modes have homogeneous oscillations at every point on a time slice without any wave propagation. We also show the presence of vorticity vector waves that are sourced by the curl of heat flux. This analysis shows the critical role of the shear tensor in generating cosmological gravitational waves in an expanding universe.
rate research
Read More
We show that solitonic cosmological gravitational waves propagated through the Friedmann universe and generated by the inhomogeneities of the gravitational field near the Big Bang can be responsible for increase of cosmological distances.
The issue of the gauge invariance of gravitational waves arises if they are produced in the early universe at second-order in perturbation theory. We address it by dividing the discussion about the gauge invariance in three parts: the production of gravitational waves, their propagation in the real universe, and their measurement.
We give a rigorous and mathematically clear presentation of the Covariant and Gauge Invariant theory of gravitational waves in a perturbed Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. As an example of a consistent analysis of tensor perturbations in Fourth Order Gravity, we apply the formalism to a simple background solution of R^n gravity. We obtain the exact solutions of the perturbation equations for scales much bigger than and smaller than the Hubble radius. It is shown that the evolution of tensor modes is highly sensitive to the choice of n and an interesting new feature arises. During the radiation dominated era, their exist a growing tensor perturbation for nearly all choices of n. This occurs even when the background model is undergoing accelerated expansion as opposed to the case of General Relativity. Consequently, cosmological gravitational wave modes can in principle provide a strong constraint on the theory of gravity independent of other cosmological data sets.
Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the de Donder gauge is imposed, its preservation under infinitesimal spacetime diffeomorphisms is guaranteed if and only if the associated covector is ruled by a second-order hyperbolic operator which is the classical counterpart of the ghost operator in quantum gravity. In such a wave equation, the Ricci term has opposite sign with respect to the wave equation for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate the solutions of the two problems, and the algorithm is applied to the case when the curved background geometry is the de Sitter spacetime. Such vector wave equations are studied in two different ways: i) an integral representation, ii) through a solution by factorization of the hyperbolic equation. The latter method is extended to the wave equation of metric perturbations in the de Sitter spacetime. This approach is a step towards a general discussion of gravitational waves in the de Sitter spacetime and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.
Cosmological Gravitational Waves (GWs) are usually associated with the transverse-traceless part of the metric perturbations in the context of the theory of cosmological perturbations. These modes are just the usual polarizations `+ and `x which appear in the general relativity theory. However, in the majority of the alternative theories of gravity, GWs can present more than these two polarization states. In this context, the Newman-Penrose formalism is particularly suitable for evaluating the number of non-null GW modes. In the present work we intend to take into account these extra polarization states for cosmological GWs in alternative theories of gravity. As an application, we derive the dynamical equations for cosmological GWs for two specific theories, namely, a general scalar-tensor theory which presents four polarization states and a massive bimetric theory which is in the most general case with six polarization states for GWs. The mathematical tool presented here is quite general, so it can be used to study cosmological perturbations in all metric theories of gravity.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
