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K. Adolf Mzer: Dark Energy and Dark Matter - Discovering their mysterious nature and discussing consequences. The model of adiabatic cold dark matter (LCDM) including Dark Matter and Dark Energy provides a viable description of the universe, albeit physical explanations of dark matter or dark energy are missing. Therefore an exploration of the nature of both phenomena on the basis of observable data was undertaken. Dark matter had been postulated for providing an energy field additional to the attraction of baryonic matter to counteract the centrifugal force of celestial bodies and to ensure a constant galaxy rotation speed. Accumulated cosmological energy around the black hole of galaxies was discovered to cause this energy field. By effect this accumulated cosmological energy is equivalent to dark matter. When applied to the Milky Way galaxy their peculiar rotation speed curve could be successfully reproduced. Similarly dark energy was postulated to be responsible for the accelerated escape velocity of celestial bodies towards the universe, evident in Hubble parameter values. Universal wide cosmological energy was identified for this dark energy. Taking pure cosmological as well as accumulated cosmological energy into account an equation for the speed of celestial bodies was developed, which match all data of a combination of updated H(z) datasets of the Pantheon and of the BAO data to a high accuracy. Based on these fundamental findings a new theoretical approach, named sigma (S) theory, was developed, which successfully describes the constant galaxy rotation speed as well as the accelerating recessional speed of celestial bodies and thus provides physically meaningful explanations for dark matter and for dark energy. A special example of the effect of accumulated cosmological energy is given by the approach speed of the Andromeda Galaxy, also known as their peculiar velocity. There the gravitational attraction of its accumulated cosmological energy or dark
