gravitational waves and inflation theory I am not a technical guy and I have no scientific knowloedge in physics but I have been reading books, watching videos in order to understand our cosmology and existance. Forgive me if I ask nonsense questions, if I do I'd do it because of my lack of knowledge.
As we all know gravitational waves have been found. I have also been reading Hidden Reality of Brian Greene which I think a little bit confusing (it is funny that his videos are much more understandable than his books). I understand that GW occur on very high levels of energy (although I don't why it requires such energy levels). Based on this, what I want to ask are:


*

*Why GW requires such energy levels?

*Why attractive gravity doesn't create GW?

*removed
I hope I explained me and my questions clear. 
Regards
 A: Gravitational waves have never been directly detected.  
Gravitational waves are predicted by general relativity and have been inferred from other observations.  
Strong evidence of gravitational waves is the change in period of the Hulse-Talyor binary star system.  Energy is being lost from the system at a rate consistent with radiation of gravitational waves.
The March 17th 2014 report of evidence of primordial gravitational waves is not a direct observation of the waves.  Instead photons were being observed and gravitation waves inferred from the photons.  Now that the research group (BICEP2) has published their work in a peer reviewed journal, they state that dust may in fact be responsible for the effect attributed to gravitational waves.  Quoting their published paper "models are not sufficiently constrained ... to exclude the possibility of dust emission bright enough to explain the entire excess signal". So it is not yet confirmed that primordial gravitation waves have been detected. 

•Why GW requires such energy levels?

There is no threshold energy for producing gravitation waves.  For example a rotating rod, rotating perpendicualr to the axis of the rod, would produce gravitation waves.  However gravitation is relatively weak force and it is very difficult, so far impossible, to detect gravitational waves. 

•Why attractive gravity doesn't create GW?

At the risk of oversimplifying, time varying gravitational fields produce gravitational waves. Or more technically, the nth time derivative of the n-multipole moment (such as the 3rd derivative of the quadrople moment) of the stress-energy tensor must be non-zero for gravitation waves to be produced.  Attractive gravity (such a two objects attracting each other and orbiting their common center of mass) can cause graviational waves if there is time dependence such as orbitting.   
A: From the title I'd guess you're thinking about the reports that gravitational waves had been detected by the BICEP2 team. They measured the polarisation of the cosmic microwave background and found patterns that they concluded must have been caused by primordial gravitational waves during inflation. However it now seems likely that they misjudged the background noise in their data, and it's no longer clear whether they did detect GW or not. If anyone's interested their paper is here, or Google BICEP2 for many, many blog articles on the subject.
So at the moment the only secure GW detection is the indirect detection from measurements of the Hulse-Taylor binary, as Dave mentioned in his answer. However this doesn't invalidate your question and we can still address the points you raised.

Why GW requires such energy levels?

Cosmic inflation happened early in the evolution of the universe when energies were enormously high, and (assuming our theories are correct) it would have generated copious amounts of gravitational radiation. But gravitational waves don't require a high energy. As an analogy consider creating sound waves: if you clap your hands it makes a sound people can hear from a few yards away, while if you let off a hydrogen bomb it makes a sound people can hear from miles away! It doesn't take high energies to make a sound, but high energies make a very loud sound.
In principle you and I generate gravity waves just by moving around, but the intensity of these waves is absurdly small. The Hulse-Taylor binary is vastly more energetic than you and I, but even that generates such small amounts of gravitational waves that it requires exceedingly careful measurements to detect them. It isn't that the very high energies involved at the time of inflation were needed to generate gravitational waves, but rather that such high energies were needed to generate gravitational waves that we can still detect 13.7 billion years later.

Why attractive gravity doesn't create GW?

It isn't the attractiveness or otherwise of gravity that matters. Gravity waves are created by any distribution of matter or energy that has an oscillating quadropole moment. This would apply to exotic matter and negative matter (if they existed, which they probably don't) in the same way it applies to normal matter.
And finally:

If GW supports Inflation Theory, why the exponential growth of the universe stopped (or did it ever stop?)

No-one knows the answer to this because we don't have a fundamental theory of inflation. The various theories of inflation postulate a scalar field that causes it, but without giving any concrete description of the physics that creates the field. Generally the field will be selected so inflation ends after the required number of e-foldings.
There are attempts to provide fundamental descriptions of the scalar field, e.g. linking it to the Higgs particle, but as yet no widely accepted theory has been found. 
