If a spherically symmetric, pulsating object could generate gravitational radiation, this would be scalar radiation. However, a mass cannot generate such radiation because of the shell theorem/Birkhoff's theorem, which states that outside a spherically symmetric object, the object's field will be identical to the field of a similar point mass located at the center.

Next, dipole radiation is produced by charge separation: for instance, an antenna can radiate electromagnetic waves if positive and negative electric charges in it are separated by a voltage. This cannot happen for gravity though, because there is no negative gravitational charge (i.e., no negative mass).

So the "simplest" gravitational mode that there is is quadrupole radiation. This radiation leaves its imprint on the cosmic microwave background in the form of tensor perturbations.

Scalar perturbations, in contrast, are not due to gravitational waves, they arise as a result of the varying distribution of mass density across the Universe.

So to sum up, the mechanisms behind the two perturbations are very different: Scalar perturbations are caused by the presence of matter with variable mass density and hence, variable gravity (but no waves/radiation!) whereas tensor perturbations are caused by freely traveling gravitational radiation (i.e., waves).

If a spherically symmetric, pulsating object could generate gravitational radiation, this would be scalar radiation. However, a mass cannot generate such radiation because of the shell theorem/Birkhoff's theorem, which states that outside a spherically symmetric object, the object's field will be identical to the field of a similar point mass located at the center.

Next, dipole radiation is produced by charge separation: for instance, an antenna can radiate electromagnetic waves if positive and negative electric charges in it are separated by a voltage. This cannot happen for gravity though, because there is no negative gravitational charge (i.e., no negative mass).

So the "simplest" gravitational mode that there is is quadrupole radiation. This radiation leaves its imprint on the cosmic microwave background in the form of tensor perturbations.

Scalar perturbations, in contrast, are not due to gravitational waves, they arise as a result of the varying distribution of mass density across the Universe.

So to sum up, the mechanisms behind the two perturbations are very different: Scalar perturbations are caused by the presence of matter with variable mass density and hence, variable gravity (but no waves/radiation!) whereas tensor perturbations are caused by freely traveling gravitational radiation (i.e., waves).

"If a spherically symmetric, pulsating object could generate gravitational radiation, this would be scalar radiation."

cannot understand this sentense.

about E-model& B-model, really beautiful!!!

Nie: Imagine, for instance, a variable star that grows and shrinks periodically, but retains spherical symmetry in the process. Because of Birkhoff's theorem, the gravitational field outside such a star will remain constant. It is possible to construct theories of gravity in which Birkhoff's theorem is not valid, and the same star would cause propagating changes in the gravitational field as it expands and contracts. These propagating changes would be monopole gravitational radiation. However, such radiation is not possible in standard general relativity.

Just to be completely clear, the term 'gravity wave' unfortunately refers specifically to a phenomenon described in fluid dynamics (http://en.wikipedia.org/wiki/Gravity_wave)...

More to the point, see http://en.wikipedia.org/wiki/Gravitational_wave#Sources_of_gravitational_waves and http://en.wikipedia.org/wiki/Quadrupole#Gravitational_quadrupole - also, FYI - see http://physicsworld.com/cws/article/news/2014/apr/10/have-galactic-radio-loops-been-mistaken-for-b-mode-polarization..

In my simplistic understanding, according to Einstein's theory

of gravity, gravitational force can be traded with distortions of

space-time. Space time is homogeneous and isotropic at large

scales, but there are structures formed by matter; those are

first order effects. Therefore FRW metric, which does describe

a perfectly homogeneous and isotropic universe, works well

at the zero'th order. It cannot, however, take into account observed

cosmic structures such as galaxies and clusters of galaxies.

Metric is a 4x4 matrix, which is a tensor. Small fluctuations in the

metric will also thus be parametrized by a matrix having sixteen

small components. All these components are functions of

coordinates, because distortions in space-time foam is

changing from point to point. Small fluctuations in space-time

metric is therefore a 4x4 matrix whose components not

fixed but are functions. This point is important.

We know a scalar which is dependent on coordinates is

a scalar field (see Spiegel's vector analysis). Similarly

a 4x4 matrix whose components are functions can be called

a tensor field. These type of tensor perturbations over FRW

metric can be called gravity waves.

The metric is a 4x4 matrix. At the zero'th order the universe is

homogeneous and isotropic which is described by FRW metric.

Now distortions are first order or higher order effects. In general

a distortion will be encoded by a 4x4 matrix, which is a rank two

tensor, not a scalar. Then how does one perturb a matrix by a

scalar ? I can think of two scalar quantities associated with a

matrix. The trace and the determinant. Both are just numbers

associated with a given matrix. So by the terms "scalar perturbation

on the metric" do you imply that trace or determinant of the FRW

metric is perturbed ?

Biswajoy: The metric is not a matrix. It is a tensor. Matrices are representations of tensors in a specific coordinate system. This may sound like nitpicking but it is an important distinction. As for the trace of the metric tensor, it is equal to the dimensionality of spacetime, and not a dynamical quantity that can be perturbed. (The determinant, or rather its square root, is used to form the invariant volume element \sqrt{-g}dx^4.)

The perturbations in question are not perturbations of the metric, but perturbations of the density of matter. Scalar perturbations are density fluctuations; tensor perturbations arise as a result of primordial gravitational waves. In both cases, the stuff that is being perturbed is the matter density.

See the attachment that i uploaded. Perturbation is explained. Source---

http://www.damtp.cam.ac.uk/user/db275/Cosmology/Chapter4.pdf. Page no. 79-80.

Abhijit, Thank you for the link. I see that SVT decomposition

is explained very clearly in this note.

Any rank two tensor can be decomposed into scalars vectors

and tensors. The counting of the degrees of freedom is

complicated. It is 4+4+2. Do you know how to count them.

Another point is that perturbations in the metric around the

FRW metric, that I said in my previous post, will be linked

to the matter distribution via Einstein equations. I hope

that helps.

Not all symmetrical stress energy waves are of gravitational type.