In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG) and in 2002 the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Ten graduate students obtained their PhD under her supervision between 20. She has collaborated with several other mathematicians and physicists, among them Yuri I. Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology, algebraic-geometric structures in quantum field theory, noncommutative geometry with applications to number theory and to physics models, especially related to particle physics, quantum gravity and cosmology, and to the quantum Hall effect. She held visiting positions at the Tata Institute of Fundamental Research in Mumbai, the Kavli Institute for Theoretical Physics in Santa Barbara, the Mittag-Leffler Institute in Stockholm, the Isaac Newton Institute in Cambridge, and the Mathematical Sciences Research Institute in Berkeley, California. Since 2008 she is full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology in Pasadena. She also held an honorary professorship at the University of Bonn. Between 20 she held a C3 position (German equivalent of associate professor) at the Max Planck Institute for Mathematics in Bonn and held an associate professor position (courtesy) at Florida State University in Tallahassee. Moore instructor in the Department of Mathematics. Between 19 she worked at the Massachusetts Institute of Technology (MIT) as a C.L.E. She moved to the USA in 1994, where she obtained a master's degree (1994) and a PhD (1997) in Mathematics from the University of Chicago, under the supervision of Melvin Rothenberg, with a thesis on Three dimensional aspects of Seiberg-Witten Gauge Theory. Our method is a general tool to contrast the predictions of several scenarios of fluctuation generation regarding large scale structures in the Universe.Marcolli obtained her Laurea in Physics in 1993 summa cum laude from the University of Milan under the supervision of Renzo Piccinini, with a thesis on Classes of self equivalences of fibre bundles. We develope our argument in such a way that the formulae are valid for any shape of the primordial spectrum, and choose a scale invariant one to compare with actual observations. In the second one we calculate the CMBR anisotropies at large angular scales produced by the density contrast and by the asymmetry of the observer's location, up to first order in the perturbations. In the first case we find expressions to evaluate the density contrast and the number count and luminosity distance vs redshift relationships up to second order in the perturbations. We solve perturbatively a Hamilton Jacobi equation for a timelike geodesic and obtain the null one as a limiting case in two situations: for an observer located in the center of symmetry and for a non centered one. We assume no a priori profile for them, instead we find it through a matching procedure of the Tolman Universe to a flat Friedmann Robertson Walker Universe plus perturbations originated during Inflation. We present an analytical method to extract observational predictions about non linear evolution of perturbations in a Tolman Universe. Its mathematical exposition will be addressed in Part II with a generalization of the emergent spacetime picture to matrix string theory. In Part I we will focus on the physical foundation of cosmic inflation from the emergent spacetime picture to highlight the main idea. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis. The emergent spacetime picture admits a background-independent formulation so that the inflation can be described by a conformal Hamiltonian system characterized by an exponential phase space expansion without introducing any inflaton field as well as an inflation potential. We observe that the cosmic inflation is triggered by the condensate of Planck energy into vacuum responsible for the dynamical emergence of spacetime and must be a single event according to the exclusion principle of noncommutative spacetime caused by the Planck energy condensate in vacuum. The inflation in this picture corresponds to a dynamical process to generate space and time while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We propose a background-independent formulation of cosmic inflation.
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