What was the major discovery on gravitational waves made March 17th, 2014, in the BICEP2 experiment? The Harvard-Smithsonian Centre for Astrophysics held a press conference today to announce a major discovery relating to gravitational waves. What was their announcement, and what are the implications?
Would this discovery be confirmation of gravitational waves as predicted by general relativity (even though Sean Carroll links to the Nobel website implying that G-waves was detected decades ago, while my book on GR (B. Schutz) says they're still looking...I'm confused) 
Also, regarding inflation theory, would this discovery confirm inflation or refute it? Or something else, a la string theory?
 A: Dr. Matt Strassler has some great info on his site, see here:
http://profmattstrassler.com/2014/03/17/a-primer-on-todays-events/
http://profmattstrassler.com/2014/03/17/bicep2-new-evidence-of-cosmic-inflation/
http://profmattstrassler.com/2014/03/18/if-its-holds-up-what-might-bicep2s-discovery-mean/
Here's a summary of some key points in my own words (any mistakes are my own):
It's believed that in the first tiny fraction of a second after the Big Bang, the universe underwent an extremely fast expansion known as inflation.  We can see leftover radiation, not from that far back, but from 380,000 years after the Big Bang, which was the point at which the universe was finally cool enough for electrons to bind to protons.  This radiation has been studied and been found to be very uniform.  It has slight temperature variations, which have also been studied.  These observations support the idea of inflation.  The temperature variations are understood as being due to quantum fluctuations in the early universe, and these fluctuations got blown up (expanded) by inflation along with everything else.
In addition to the temperature variations, there are also small variations in the polarization of the radiation.  These come in two types, E-mode and B-mode.  E-mode polarization has a similar cause to the temperature variations.  (Prof. Strassler has a nice picture illustrating the difference.)  The E-mode polarization was studied a while ago, and nothing surprising was found there.  The B-mode polarization on small scales (that is, observed across small patches of sky) can arise from the E-mode polarization, or from gravitational lensing that happened as the radiation was on its way to us.  But large-scale B-mode polarization is evidence of something else: gravitational waves produced by inflation.  This is what's been claimed by the new result: large scale B-mode polarization.
Some important things to remember:
(1) While the experimenters detected B-mode polarization at the more than 5 sigma level, you can't say it's a 5 sigma detection of inflationary gravitational waves.  To quote Prof. Strassler: "For that, they need enough data to show their observed data agrees in detail with the predictions of inflation.  The 5.2 sigmas refers to the level of the detection of B-mode polarization that is not merely due to lensing."
(2) This is not a direct observation of gravitational waves.  Rather, it's believed that they're observing how gravitational waves produced in the first fraction-of-a-second of the universe affected radiation produced 380,000 years later.
(3) This is not the first indirect observation of gravitational waves.  That was the  Hulse–Taylor binary pulsar, which resulted in a Nobel prize.  Basically two neutron stars were found to be orbiting each other and losing energy in a way which is consistent with what you'd expect if they're radiating gravitational waves.
(4) It is the first indirect observation of gravitational waves produced by inflation.
(5) It's a very important result (if correct) because it's evidence for inflation, and can help to determine which theory of inflation is correct.
(6) It's also a very important result (if correct) because it tells us the energy density during inflation.  This is suggestive of new beyond-the-Standard-Model physics at this energy scale.  And as it turns out, the energy scale, $10^{16}$ GeV, is right around where the coupling constants for the electromagnetic, weak, and strong forces unify.
(7) Like all new experimental results, it should be taken with a grain of salt until another experiment reproduces it.
Again, that's just my summary, I highly recommend reading through all the links I posted above.
A: The actual paper (pdf) is very heavy in error quantification - and rightly so.  They presented an experiment result that is statistically extremely difficult to obtain.  But for the rest of us, conclusion is the most important part.  The abstract says:

The observed B-mode power spectrum is well fit by a lensed-$\lambda$CDM + tensor theoretical model with tensor/scalar ratio r = 0.20

As far as I can tell, this is their conclusion.  To start to understand, we have to get a grasp on the component theories.


*

*Lambda-CDM_model is a cosmology model, basically

*The Cosmic Microwave Background (CMB) is the light from the last scatter from when the early universe was still opaque

*The scalar density perturbations (fluctuations) of the CMB are from quantum fluctuations in the energy universe, and these were the "seeds" that allowed galaxies to form, giving rise to the structure we live among.

*The tensor/scalar ratio (variable r) in the paper is a measure of the magnitude of tensor fluctuations of the CMB relative to the already-measured scalar fluctuations.  I satisfy myself by saying the tensor fluctuations are "vector" fluctuations.

*B-mode is the type of polarization signal.  Apparently another type of this signal was discovered earlier, but this is beyond my understanding.


The paper is also very clear that the r value is not 0.  Their experiment proves this fact to $5.9 \sigma$.  By my standards, that makes the proposition true.
The physicist who predicted this was visited by someone who worked on it, and there's a video of it online.  First words said was that "it's 5 sigma at .2".  The 5 sigma just means it's right.  The .2 is referring to the r value above.  That was the shock that the media is referencing.  The fact r=.2 is new information to science here.
The blog post by another user's blog is also very informative.  It's also much more heavy on the implications of the discovery.  For instance, the discovery gives us much better information on the energy at which the inflation epoch took place.  However, the impacts of the discovery are extraordinarily far reaching.  So, I would say that the specific discovery at hand here is that r does not equal zero, and is close to 0.2.

Here are some quotes from the first part of the paper which hint at the motivations for the experiment in the first place.  Emphasis mine:

Inflation predicts that the quantization of the gravitational field coupled to exponential expansion produces a primordial background of stochastic gravitational waves with a characteristic spectral shape (Grishchuk 1975; Starobinsky 1979; Rubakov et al. 1982; Fabbri & Pollock 1983; Abbott & Wise 1984; also see Krauss
  & Wilczek 2013). 

The wording here is crucial, note "quantization of the gravitational field".  This is quantum gravity, and a theory-based prediction that led to a measured result.  To me, this fact is even more incredible than getting direct evidence for gravitational waves.  In fact, from my reading, this seems to be from treating the graviton's properties within the context of quantum fields.
For more detail:

Though unlikely to be directly detectable in modern instruments, these gravitational waves would have imprinted a unique signature upon the CMB. Gravitational waves induce local quadrupole anisotropies in the radiation field within the last-scattering surface, inducing polarization in the scattered light (Polnarev 1985). This polarization pattern will include a “curl” or B-mode component at degree angular scales that cannot be generated primordially by density perturbations.

This is going over how to get from gravitational waves to the polarization.  I'm still a little iffy on exactly what property of gravitational waves leads to this.  However, their visuals page gives a helpful hint for me.  See their depiction of polarization.  The "density wave" is what I had typically associated with a gravity wave.  However, I recognize that a more complicated alternative is also possible.  This is trivially true because general relativity uses tensors.  It's the difference between pushing a slinky forward-and-back versus side-to-side.  If we're talking about those side-to-side modes, then I would expect that to polarize things passing through... as opposed to just redshifting them and blueshifting them back.
For more on that:

Gravitational lensing of the CMB’s light by large scale structure at relatively late times produces small deflections of the primordial pattern, converting a small portion of E-mode power into B-modes.

This looks like it covers some of the more fine detail, but also explains why this work is set apart from previous experiments that are said to have results regarding both the E-mode and B-modes.  The polarization effect, as long as it's sufficiently ancient, would seem to necessarily have come from quantum gravity effects.

I have 3 even more detailed points that I have found from various writeups of this event.  These relate to what was measured, what makes BICEP2 different from other experiments, and why the experiment is so important.  These specific details are:


*

*The pattern sought was a 45$^{\circ}$ polarization relative to the temperature (?) gradient

*Setting a lower bound on the value of r was the novel contribution of BICEP2

*A relationship called the Lyth bound calculates the time/energy of inflation from this r value


The first bullet comes from a youtube video by minute physics.  They state that the density, motion, and temperature of matter at the genesis of the CMB impacts its polarization.  Making no reference to gravity waves, we expect polarization at 0$^{\circ}$ and 90$^{\circ}$ relative to the temperature gradient (note: there is some confusion in the video whether this is density of temperature graident, they say one thing, but write another).  They go on to say that the BICEP2 result is that about 15% of the polarization comes from the 45$^{\circ}$ "jiggles", which are tale-tale signs of gravity waves.  It's much more difficult to explain why this should be true.
Next bullet - let's clarify why this matters when the same thing has been measured by previous experiments.  Other experiments have estimated the r value, but those estimates are inherently clustered around r=0.  This still constrains the value, but it is not effective to determine if it is non-zero, which has value for theorists.  Without a doubt, this is related to my first bullet - that the critical measurement involves measuring polarization angle relative to the density gradient of a scalar field.

Third bullet, something called the Lyth bound/relationship is oft-quoted in discussions of this subject.  For more reading, there is discussion on Quora.  The equation is:
$$ \Delta \phi = m_p N_e \sqrt{ \frac{ r}{8} }  $$
The variable $N_e$ has been measured by previous experiments.  It is being cited in various places, including follow-up academic articles, that the BICEP2 result narrows down the above equation to $\Delta \phi \approx 9.6 M_{pl}$.  The remaining variable is just the Planck mass.  I believe that this number is interpreted to be the energy that inflation "traversed".  In more practical terms, this gives us the energy/time at which inflation happened.  This is where people are coming from when they mention how this result allows us to look further into the past.
A: I guess, for completeness, someone needs to explain that this "discovery" was not a discovery but a mistake. This is not to deny that it was careful and serious scientific endeavour, but the data analysis underestimated the effect of interstellar dust, and furthermore it did not take long for experts in this area to suspect this (I mean they suspected that the conclusion was seriously questionable right away, after just a few hours' scrutiny). In short, the 2014 BICEP2 experimental data did not in fact indicate one way or the other whether there is a gravity-wave signature in the cosmic background radiation.
Interesting lessons. One newspaper headline was "Primordial gravitational wave discovery heralds 'whole new era' in physics". An answer on this site mentions "The paper is also very clear that the r value is not 0. Their experiment proves this fact to 5.9σ." If this $\sigma$ is the standard deviation on a normal distribution, then the probability of such an outcome arising by chance when $r$ is really zero is about 1 in 6 million. But of course this is not what is happening here. In fact the signal analysis was faulty owing to a failure to model dust correctly.
As I understand it, the scientists involved subsequently both did a further study and also, on reflection, felt that the way the publicity was handled the first time around was not as good as they would wish. I would like to underline that the effort here was of high quality and this approach may yet reveal a gravity wave signature. Explanations of what such a signature would tell us, given in some of the other answers here, remain mostly valid.
A: Astrophysicists of the BICEP2 collaboration announced the detection of inflationary gravitational waves in the B-mode power spectrum, providing strong evidence for Guth's theory of inflation and the Big Bang.
Here's one of my favorite videos of assistant Professor Chao-Lin Kuo surprising Professor Andrei Linde with evidence that supports cosmic inflation theory.

The discovery, made by Kuo and his colleagues at the BICEP2 experiment, represents the first images of gravitational waves, or ripples in space-time. These waves have been described as the "first tremors of the Big Bang."

A: They announced that through observation of the Cosmic Microwave Background, via the BICEP2 experiment in Antarctica, particularly the polarization on a 2-4 degree angular scale, gravitational waves from inflation during the early universe are being indirectly observed.
Link to FAQs about the release:
http://bicepkeck.org/faq.html
Link to pre-print:
http://bicepkeck.org/b2_respap_arxiv_v1.pdf
Link to press release images and captions:
http://bicepkeck.org/visuals.html
Based upon measurements of the B-mode of polarization of CMB photons, BICEP2 reports, regarding the lamba-CMB + tensor model, that the tensor to scalar ratio (r) is 
$r = 0.20_{-0.05}^{+0.07}$ at a 68% confidence level, without considering the effects of dust.
$r = 0.16_{-0.05}^{+0.06}$ is reported, when corrected for a model than considers dust.
Other results from the South Pole Telescope and Planck Satellite, base upon large scale tempeature measurements of the CMB have constained the tensor/scalar ratio to $r<0.11$ at the 95% confidence level.
Update 6/2014:
In the published version of the results, the BICEP2 group states "polarized dust
emission may be stronger than any of the models" considered in the paper and that they cannot "exclude the possibility of dust emission bright enough to explain the entire excess signal".
A: We have only looked back to the CMB time thus far - i.e. about 300,000 years after BB. Now having viewed this gravitational imprint on the CMB, we have pushed back our earliest observation to about 10^-35 seconds. That's a huge leap in the scope of our comprehension (a factor of about 10^47), and it's that which is probably the most impressive aspect of this result to the layman.
Also, we now have the very first indication that gravity is quantised.
And it seems that spacetime truly can expand faster than light. Perhaps one day our engineers will be able to exploit this amazing property of our universe.
