Starobinsky

Abstract : Recent observational data on supernovae at large redshifts, small-scal anisotropy of the cosmic microwave background (CMB) temperature and the powe spectrum of present density inhomogeneities in the Universe, as well a numerous previous arguments, prove the existence of a new type of dark matter in the Universe. This form of matter described by a positive Lambda-term ("dark energy") has a strongly negative pressure and remain unclustered at all scales where clustering of baryons and non-relativistic cold dark matter is seen. The simplest phenomenological way to describe it, borrowed from the inflationary scenario of the early Universe, is to introduce a scalar field (the Lambda-field, also sometimes called quintessence) with some self-interaction potential, minimally coupled to gravity and very weakly coupled (if at all) to matter fields. This is possible if and only if the weak energy condition is satisfied for this kind of matter (i.e., if the modulus of its pressure is less or equal to its positive energy density) that still has to be verified from observations. If so, then the required potential can be unambiguously determined from observational data, e.g., from the luminosity distance as a function of redshift (given the present density of non-relativistic matter in terms of the critical one additionally), or from the behaviour of density perturbations in the non-relativistic matter component as a function of redshift (given the Hubble constant). Generally, the potential need not be constant, so dark energy may be time-dependent. However, present observational data strongly restrict the variability of dark energy with an exact cosmological constant remaining the best fit to it. In terms of geometric properties of space-time, the latter fact (along with the absence of a noticeable spatial curvature of the Universe proved by recent CMB observations) means that the next basic cosmological parameter beyond the Hubble constant $H_0=(\dot a/a)_0$~and the deceleration parameter $q_0=-(a\ddot a/\dot a^2)_0$\,, where $a(t)$ is a scale factor of the Friedmann-Robertson-Walker cosmological model, $r=a^2{d^3a\over dt^3}/\dot a^3$ is close to unity both at the present time and in the whole past since the beginning of the matter dominated stage. Such a behaviour of dark energy may be understood in the scope of the inflationary scenario where it is natural for the Lambda-field to remain practically constant for a very long time due to initial conditions for it generated during inflation.

If future observations show that the weak energy condition is violated fo dark energy, more complicated models of it (e.g., based on scalar-tensor gravity) will be required. Thus, high quality cosmological data expected in near future will provide us with phenomenological knowledge about basic properties of this new kind of matter. In any case, it is clear already that properties of the present dark energy are remarkably qualitatively similar to properties of matter during inflation in the early Universe. So, the whole part of the Universe history which is accessible to observations may be considered as a transition from a high curvature de Sitter state to a low curvature one, with the power law radiation and matter dominated stages in
between.