8 Part I. Introduction solving Eq. (1.28) using Eq. (1.18), the energy density of a fluid with an equation of state parameter ω behaves like ρ ∝ a −3(1+ω) . (1.29) The Friedmann equation can thus be restated in terms of separate densities for radiation ρ r and matter ρ m as ( H 2 ρr = κ a + ρ ) m − kc2 4 a 3 a + Λc2 2 3 . (1.30) Assuming the universe at a certain time to be dominated by a fluid with equation of state parameter ω, the Friedmann equation reduces to (ȧ ) 2 H 2 = = κ a −3(1+ω) . (1.31) a Solving this differential equation for a(t) is straightforward, and results in 2 a(t) ∝ t 3(1+ω) . (1.32) For a radiation-dominated universe, the scale factor expands like a r (t) ∝ t 1/2 , while for matter-dominance, one finds a m (t) ∝ t 2/3 . Another situation worth investigating is the case of a negative equation of state parameter. Assuming an equation of state of p = −ρ leads to a scaling ofthe energy density of such a fluid of ρ ∝ a −3(1+ω) = a 0 ∼ const., (1.33) i.e. the energy density ofthe fluid remains constant with the expansion ofthe universe. This is called de Sitter behaviour, and by solving Eq. (1.31) we see that the scale factor grows exponentially in this case, a dS (t) ∝ e t . (1.34) It corresponds to the behaviour of a cosmological constant inthe Friedmann equation, and so Λ is equivalent to a fluid with ω = −1. In 1998 and 1999, the astrophysical observations of two separate groups of scientists, the High-z Supernova Search Team , andthe Supernova Cosmology Project , were published indicating the fact that the universe is currently expanding at an accelerating pace. This conclusion was extracted from the observations of Type Ia supernovae events at various redshifts, measuring the luminosity ofthese supernovae as a function oftheir redshift. The findings made quite an impact on the astrophysical and cosmological community, since up to that point of time the universe was believed to be in a matter-dominated stage, which drives the expansion ofthe universe with a constant or decelerating pace, and depending on the total amount of matter and radiation admits an open, flat or closed evolution of
1. Basic Foundations and Outlook 9 the universe. However, the data are hinting at an on-going transition from a matterdominated into another stage of evolution, dominated by an as of yet unknown substance with constant energy density and a negative equation of state parameter ω = −1, resulting in dynamics which a matter-dominated universe could not explain. In the years following the publications [5, 6], other experiments confirmed and consolidated the discoveries ofthe earlier analyses, and by today the acceleration ofthe expansion ofthe universe is an accepted feature of current cosmological models, including the ΛCDM. Evidence and discussions can be found inthe publications [7–9], from the WMAP collaboration  or the Planck collaboration . There are several works [12–16], which aim at quantitatively extracting the exact dynamics and kinematics ofthe accelerated expansion from data, withinthe framework of a branch of cosmology called cosmography. The analysis strives to describe the kinematical features ofthe expansion ofthe universe without the assumption of a particular model a priori; i.e. carrying out the analysis of data from a viewpoint which is as neutral as possible, and avoiding the need to choose an underlying model of cosmology. From such investigations, it is possible to obtaininformation on the equation of state ofthe universe, and constraining the specific properties ofthe underlying mechanism for the accelerated expansion. From those cosmographic analyses, which are in detail described in Part III of this thesis, the current equation of state parameter ofthe total universe is predicted to be ω = −0.7174 +0.0922 −0.0964 . This is a value that describes the universe as one single ideal fluid, being a mixture of radiation, matter and some unknown, but, as it seems, pre-dominant, substance. More model-dependent analyses, as e.g. the one ofthe Planck collaboration , predict similar values for the parameter ω, assuming the validity ofthe ΛCDM model. As already described, the ΛCDM model features a cosmological constant in order to explainthe dark energy phenomenon, and matter contributions described by the Lagrangian L m , containing the standard model particle content ofthe universe representing the small amount of baryonic matter and an unknown substance dubbed dark matter, whose existence was postulated in order to explainthe observed rotation curves of galaxies andthe acoustic peaks ofthe CMB temperature spectrum. Dark matter is, besides dark energy, yet another unexplained feature ofthe ΛCDM, introduced ad hoc to account for observations, but without microphysical motivation. It is assumed to consist of particles which are only weakly or non-interacting with normal matter, and is therefore hard to detect. It is postulated to form large lumps at the center of galaxies and large scale structures, thus explaining the observed innergalactic dynamics. Since both dark energy and dark matter seem to be needed on an observational level but are yet unknown in nature and origin, their combined existence is dubbed the dark sector of cosmology. The contributions of baryonic and dark
The universe is not a world of separate things and events but is a cosmos that is connected, coherent, and bears a profound resemblance to the visions held in the earliest spiritual traditions in which the physical world and spiritual experience were both aspects of the same reality and man and the universe were one. The findings that justify this new vision of the underlying logic of the universe come from almost all of the empirical sciences: physics, cosmology, the life sciences, and consciousness research. They explain how interactions lead to interconnections that produce instantaneous and multifaceted coherence–what happens to one part also happens to the other parts, and hence to the system as a whole. The sense of sacred oneness experienced by our ancestors that was displaced by the unyielding material presumptions of modern science can be restored, and humanity can once again feel at home in the universe.