The standard cosmological model involves assumptions. Some of those are made somewhat ad hoc and most of the credence they enjoy comes from the very fact that the model fits the existing data so well. And that alternatives, at least the ones we have thought of, typically seem to fare far worse.

Some of these assumptions involve unknown components, most notably: dark energy and dark matter discussed elsewhere, some consider other aspects such as geometrical properties of the Universe like the geometrical flatness. Still others consider the properties of the primordial fluctuations.

These primordial fluctuations play a key role in the cosmological evolution giving raise to the structures we see in the present-day Universe. However the standard cosmological model takes their presence in the very early Universe for granted and merely derives its consequences on our observables. To match the data the standard model has to assume that the primordial fluctuations are present on all scales including the extreme scales comparable to the present-day horizon, i.e., the region of the Universe, which could have been traversed by photons during the existence of the Universe and therefore could have been in a causal contact. As the Universe expands these scales must have been larger than the horizon in the past, say at the time when the Universe became transparent and the photons, known today under a collective name of cosmic microwave background, started traveling essentially unhindered, with some of them eventually detected by our instruments. Moreover these initial perturbations need to have amplitudes which are random Gaussian variables with zero mean and the rms decaying as an inverse of some power of their typical size. All components need moreover to be perturbed in the some way so called adiabatic fluctuations.

Some of these assumptions can be relaxed or yet some additional features can be introduced. However, a key lesson drawn from the analysis of the current measurements is that relaxing them seems to harm rather than help and that any extensions are not really needed. At least not yet.
Particularly, the existence of the primordial fluctuations on scales larger then the size of the causally connected regions seems unavoidable. Such fluctuations could not be however generated via a local, causal process, therefore calling for some exotic mechanism to do so.

For years a leading candidate for such a mechanism has been inflation. A theory which assumes that the evolution of the Universe in the very early Universe , ~10-35 sec after the ‘big bang’, was driven by some yet unknown quantum field. This would lead to an exponential increase of the size of the Universe which in turn would blow up the very small causal connected regions present prior to the inflation to sizes much larger than what the causal regions would have been, had the inflation not happened. Those small causal regions would have initially small fluctuations of that primordial quantum field imprinted on them what would explain both the amplitudes of the primordial fluctuation as well as their Gaussianity. Moreover, as eventually all the components would be created via a decay of the quantum field in a process called a reheating, all of them would be perturbed in an analogous way and the fluctuations will be predominantly adiabatic.

Clearly, inflation really does fit the bill.

Worth noting that inflation was first proposed to address a very different set of problems (flatness, lack of magnetic monopoles, etc) so the very fact that it also explains the presence of the primordial fluctuations makes it particularly attractive …

What makes it less exciting is a number of different specific models, which could, in principle, lead to an inflation. The inflationary models have to rely on an extrapolation of the known physics laws to energies by orders (~10-12) of magnitude higher than the energies for which they were established and extensively tested. There is no clear and unique guidance how this should be done and very different proposals can be, and have been, put forward.

Deciding whether it is a correct theory and which one of the proposed models comes the closest to the actual model still requires more evidence and therefore data. While none of these questions is straightforward to answer, this seems to be a particularly worthwhile goal to strive for. A successful answer will not only address one of the key cosmological questions but will also shed some light on fundamental physics at energy scales well beyond those which can be produced in human-made laboratories. And whatever the answer here is going to be, this, no doubt, will be a remarkable achievement and a truly watershed moment for cosmology and fundamental physics.

A unique way to provide more information are gravitational waves … In addition to the density perturbations which lead to the structures in the Universe we observe today, inflationary models commonly lead to a generation of some very low level of primordial gravitational waves. These persist in the Universe and impact the polarisation properties of the cosmic microwave background photons, which are set free at the time when the Universe become neutral, at redshift around z ~ 1100. The way in which the gravitational waves affect the CMB photons polarization is such that the resulting pattern can not be, at least to first order, mimicked by the polarization pattern generated by the density perturbations. The former pattern is referred to as B-mode polarization and the latter as E-mode one. If a full sky observations are available there is no B-mode pattern which would look like the E-mode one and vice-versa. For small scale observations there are polarization patterns that are genuine B-like and not E-like. If we measure these genuine B-mode patterns this will then mean that we have detected a signature of primordial gravitational waves… If we can determine the amplitude of the B-mode signal precisely enough we could start differentiating between different proposed models and start rejecting some of them. We will also be able to say something about the properties of the quantum field which drives the inflation and thus the physics laws at the energies at which the inflationary expansion is taking place.