Is inflation theory really dead? I know the title is little bit challenging but maybe most of you heard about the last BICEP2 paper on February. As I have read about it here and here. My understanding is, BICEP2 results released on March, revealed B-mode polarization and physicists support this observation with inflation theory. But the last paper published that these B modes represent of a cosmic high-dust. 
I am not expert in cosmology but the inflation theory makes sense for many physicists. Now is it all dead or new findings twisted a little bit? 
 A: While a B-mode signal in the CMB would be a smoking gun for inflation, inflation is not even under pressure, even if BICEP2 only measured dust.
Inflation explains a number of early universe puzzles neatly. Most importantly it explains why we find an extremely homogeneous CMB. Furthermore, without inflation it is hard to explain that the perturbations on the CMB are correlated between points that seem to never have been in causal contact.
There are many models of inflation out there and most of them (the ones most popular before BICEP2 actually) predict an ubobservably low amplitude for tensor perturbations - which in turn lead to the B-mode signal BICEP2 looked for.
So, while some of the models people cooked up just to encompass BICEP2's unexpectedly large signal might be dead, inflation as a cosmologically well-motivated framework is perfectly fine. 
Direct observational evidence beyond B-modes are tough to find. Gravitational waves with a nearly scale-invariant power spectrum are a generic prediction, but we have not even observed these at a single scale yet. However, there are a number of experiments planned within the next decade that aim to put an upper bound on the so-called tensor-to-scalar-ratio $r \lesssim 10^{-3}$, which is the order of magnitude predicted by  generic models of inflation.
Very very long edit:
The only kind of signal we can recieve from inflation are of gravitational nature. If one takes the CMB as a given and looks only at cosmic evolution afterwards, the $\Lambda$CDM can explain basically all observations with only a few parameters. No photon signal can come from before recombination, making the CMB the oldest thing we can literally "look" at.
The sucess of inflation is to actually give a mechanism to create the CMB. It is non-trivial to get the CMB to be so homogenous and at the same time to create anisotropies with correlations over space-like intervals. 
But note that in inflation, the CMB fluctuations are actually also variations in the metric tensor - they just are in its scalar component ($\sum_i g_{ii}$). So besides these scalar fluctuations there could be vector-like or tensor perturbations in the metric. Direct computations shows that no vector-like perturbations are created in de-Sitter like inflation, leaving tensor perturbations as the only other possible signal.
Now depending on your model of inflation, more or less of these tensor perturbations are created. So you can try to get as much information from two spectra (that are predicted to be nearly scale-invariant):


*

*The amplitude of one of the signals must be fixed by observation. This is done as the so-called "COBE Normalization" of scalar perturbations.

*The ratio of the amplitude of the two spectra at a fiducial scale. This is what we call $r$, the "tensor-to-scalar ratio". All models of inflation predict $r > 0$, but well-motivated values range from $10^{-4}$ to $0.2$ (where the latter are models more or less tailor-made for BICEP's $r = 0.2$ claim).

*The spectral tilt of each spectrum. Perfectly de-Sitter inflation with a constant Hubble parameter predicts a perfectly scale-invariant spectrum. Actual models are close to this, with only tiny variations of the Hubble parameter during inflation, leaving a nearly-scale invariant spectrum. This observable is called the spectral index, $n_s$ for scalars and $n_t$ for tensors, but measuring $n_t$ is nigh impossible.

*The running of the spectral index, i.e. its value at different scales can also give you information about the inflaton potential. For this you need to measure $n_s$ at different scales; while the CMB allows for measurements of $n_s$, measuring it at other scales than the CMB scale is challeging.

*One can even dream about measuring the running of $n_t$, but this will stay a dream for a long time...


I hope that I could elucidate why we are looking for grav. waves so hard and not for anything else - because there just isn't any other signal that is directly tied to inflation.
