Einstein's Cosmological Constant and the Vacuum Energy Enigma
Earth was already several billion years old, so to bring everything back to a more acceptable date, Eddington reintroduced the cosmological constant. With a small modification to the value introduced by Einstein, Eddington managed to obtain a satisfactory result for the age of the Universe, thus saving the situation. For more than half a century, the cosmological constant appeared and disappeared alternately until, at a certain point, towards the end of the 1960s, for fear of some implications that we will mention later, it was totally abandoned and forgotten until the fateful year 1998, when its presence was again required. Faced with the acceleration of the universe, perhaps the cosmological constant could still play an important role. The cosmological constant $\Lambda$ could, indeed, acting contrary to the force of gravity, gather within itself the cause of the unexpected acceleration of the universe. Was the ballet of the cosmological constant thus beginning again? In reality, the matter was much more complicated; after the 1960s, no one would have dreamed of reintroducing such a constant with impunity except for a valid reason. Indeed, in those years, some works by Zel'dovich highlighted a problem so central to the use of the cosmological constant that the scientific landscape of the time preferred to steer clear rather than have to confront it. The cosmological constant, in fact, did not appear only in General Relativity Theory, but also in its irreconcilable companion, Quantum Field Theory, and the agreement between the two theories was extremely turbulent. The cosmological constant, from a physical point of view, indeed has a very precise meaning: it can be simply considered as an energy density of the vacuum. In simple words, an energy cost to be assigned to the simple existence of space-time. In particle physics, the vacuum has never been properly considered as devoid of energy, but always associated with a certain degree of energy indeterminacy capable of producing some fluctuations. Since the late 1940s, physicists Casimir and Polder proposed an experiment to determine the quantum fluctuations of the vacuum. Now, although this experiment could only be verified recently in 1997, such vacuum energy did not constitute any theoretical problem on paper. The origin of the conflict, instead, was a purely numerical gap with the calculation performed through Quantum Field Theory. A gap, however, of considerable importance given that numerically the cosmological constant calculated in this way carried an error of 120 orders of magnitude compared to that observed (roughly the difference between the smallest hypothesized elementary particle and the estimated radius of the Universe). For good reason, this was called the worst prediction of theoretical physics and left pending awaiting improvements. It must be said, however, that this flaw regarding vacuum energy is specific only to the Standard Model; by imposing minimal supersymmetric behavior on it (thus adding a series of mirror partner particles to those ordinarily studied), the value obtained from theoretical calculation approaches considerably that observed. To supersymmetric theories must then be added numerous theories belonging to the String theory environment that seek to incorporate this observation among their theoretical results, so it can be said that, despite the unpromising premises, this still remains a promising avenue of investigation at the moment. Alongside the introduction of dark energy, there is another current and line of investigation that must be taken into account: simply, General Relativity is wrong at large distances. The argument in this case is fairly simple: after all, we have a theory of gravitation that, while perfectly describing the life of our solar system, when it has to interpret gravitational motion external to it must introduce two new types of energy. First, it is forced to introduce dark matter that allows it to agree with the observed rotation of galaxies, subsequently it must introduce another form of energy that causes their expansion. And as if that were not enough, at the end of the day, adding these energy sources together we realize that they amount to 96% of the energy existing in the universe. One could therefore turn the tables by saying that General Relativity has a 4% experimental agreement with observations relating to distant galaxies and that the remaining 96% is an ad hoc addition to save the theory. This is perhaps a merciless vision of General Relativity; indeed, at the moment no alternative theory to General Relativity has been found consistent with astronomical data internal and external to the solar system. The underlying problem is due to the fact that General Relativity is extremely precise in relation to motions within the solar system. Every alternative candidate must therefore be very close to General Relativity for small astronomical distances, but distance itself from it for large distances. The most obvious corrections in this sense have proved equivalent to other approaches and thus abandoned in a short time. In general, efforts to modify General Relativity theory can be framed in two distinct strands: those that aim at a modification of the Friedman equations relating to the evolution of the cosmic scale factor; those that aim to modify the equations governing the growth of perturbations that subsequently evolve into large-scale structure. Both of these strands, while arousing keen interest in the scientific community, have not yet achieved any result such as to draw general attention to them. With strings, we do not have a big bang because singularities are limited by the Planck length. The modern origin of this cosmological principle derives from the analysis of cosmic radiation.