# Brief introduction to the dark energy puzzle

Cosmology is a young and rapidly changing discipline. It is evolving at such a pace that the last decade has witnessed deep and crucial advances in our understanding of physics on large scales. In particular, the arrival of the first high-precision data of the Cosmic Microwave Background and the large-scale distribution of matter has turned Cosmology into a high-precision science.

In the era of precision Cosmology, our model of the Universe at large can finally be confronted to the real complexity of Nature. Despite the astonishing match between this model and the data, one must not forget that it is a simplified, mathematical representation that still leaves numerous questions and observations unresolved. In particular, our understanding of gravity and how it connects to quantum physics is very limited. This issue is now arising as one of the biggest Physics challenges of our time.

Without doubt, General Relativity, which has now been tested on a wide range of scales and energies, remains incredibly accurate for explaining gravity on large scales. This makes it one of the best models in Physics, and leads to a beautiful, consistent model of the Universe viewed as an evolving structure whose dynamic is determined by its content. However, although observational data has confirmed the GR-driven picture of an expanding flat Universe, this model is only compatible with data when Einstein’s equation of GR include a constant term. This term, known as Dark Energy, is extremely mysterious for two reasons.

First, it must have been extremely small in all cosmic history to avoid a ‘cosmic crunch’ and allow classical structure formation as we observe it. It is particularly unsettling as we know its value is stricly non-zero and causing today’s Universe to fall into a new accelerated phase.

Second, Dark Energy cannot simply be waved away by extending GR or fine tuning some aspects of the current model. More precisely, it is extremely hard (i.e. theoretically irrelevant or already ruled out by current data) to design a model of the Universe which is consistent with observational data and that does not include a cosmological constant.

Hence Dark Energy is likely to be a much deeper issue than just a constant term in Einstein’s equation, and it jeopardizes our understanding of Nature at large. Even worse, it seems to be a part of a greater puzzle that relates to our inability to unify General Relativity with Quantum Field Theory (QFT), our best model for small scale physics. Intriguingly, the two theories differ in one crucial aspect: QFT is only sensitive to differences in energies, whereas in GR vacuum energy gravitates. If Dark Energy is indeed a vacuum energy, we do not yet understand how quantum fluctuations can source it, and for this reason we do not have a good understanding of the physics of the early univers where Quantum Physics and General Relativity are strongly coupled.

Another riddle for the GR-based standard model of the Universe was revealed by the homogeneity of the CMB (homogeneous at $10^{-5}$), that indicated that all points must have been in causal contact at some point before the last scattering surface was emitted. One way to incorporate this observational fact in the previous picture of the Universe was to introduce a phase of extremely fast expansion called cosmological inflation. Naturally, since it takes place in the very early universe, this phase of inflation cannot be fully understood without a viable candidate for a quantum theory of gravity, and Dark Energy is again a part of the picture.

String Theory is currently the best candidate for such a theory, and could explain the inflationary phase and the origin of dark energy. Unluckily, both inflation and string theory involve an incredible (almost untractable) theoretical complexity and exist in a wide variety of versions, which complexifies the task of constraining the models from observation. Fortunately, our best current data favor initial conditions which are extremely close to Gaussian. This enables us to focus on inflationary models that predict –or are at least compatible– with Gaussian initial conditions for the CMB and the large scale structure. Even better, it appears that inflation must be highly fine-tuned in order to predict such conditions, and various models for inflation predict different amounts of non-gaussianity. Since non-gaussanity can be measured in a variety of observational data, it is currently one of the most powerful probe of the early universe, potentially permitting us to rule out and favor models of inflation and quantum gravity.