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Cosmology has become an experimental science due to the high precision measurements of the Cosmic Microwave Background (CMB) radiation and an ever growing library of large scale structure surveys. String theory is the most promising candidate for the fundamental theory of nature which can potentially unify quantum mechanics and general relativity. The TPC's core strength lie at the interplay between theoretical and experimental aspects of cosmology and string theory .

Inflation, the accelerated expansion of the early universe, is the most successful framework to solve standard problems of the big bang, such as the horizon, flatness and relic problem. In addition, almost all inflationary models predict an almost scale invariant, highly Gaussian spectrum of adiabatic perturbations, which can be probed experimentally by measurements of temperature fluctuations in the CMB radiation as well as observations of large scale structure formation. In the center we have expertise in

- Model building: vector inflation, multi-field inflation, brane inflation, etc.
- Confronting different models with observations be extracting observational consequences, e.g. linear perturbations, non-Gaussianities.
- The consequences of the landscape in string theory; modeling landscape by random potentials.

Strings, one-dimensional objects that vibrate and fluctuate, are predicted by many models of symmetry breaking phase transitions and give rise to very distinct and detectable signatures such as gravitational lensing, CMB non-Gaussianities, gravitational waves, ultra-high energy cosmic rays, radio signals etc. It is also believed that cosmic super-strings can be formed at the end of brane inflation which opens a possibility of testing the models of string theory in the cosmological settings. In the center we have expertise in

- Field theory strings or string theory strings, their evolution and observational imprints.
- Non-equilibrium dynamic and statistical properties of networks of cosmic strings.
- Fluid description of multi-dimensional objects; Kinetic theory of strings.
- Effective filed theory of strings, Lagrangian description, quantization of strings, string gas cosmology.

Multiverse, an infinite collection of pocket universes, is a generic prediction of the most successful models of the early universe cosmologies including (but not limited) to cosmic inflation. The recent (possible) BICEP2 observation of the large tensor-to-scalar ratio in the CMB radiation suggests that the model of the large fields inflation (such as chaotic inflation) might be the most natural mechanism responsible for generation of primordial perturbations. In addition the chaotic inflation, due to the mechanism of eternal self-reproduction, generically leads to an infinite Multiverse. In most problems in physics very large is sufficient for all practical purposes, but in the case of eternal inflation the space-time is not only very large, but infinite which gives rise to the well known measure problem and consequently to many other problems and paradoxes. Evidently, these problems are essential for understanding not only the predictions of inflation, but also for understanding the effects of quantum gravity at much larger energy scales. In the center we have expertise in

- Problem of initial conditions; Quantum cosmology.
- Measure problem; Stochastic approach; Kolmogorov probability spaces.
- Paradoxes in eternal inflation; Markov random fields; Theory of initial conditions.
- Entropy problem; Non-equilibrium statistical mechanics; Dynamical systems.

Current research topics within these fields are explained in more detail below. More information, for example if you are an interested student, is available by contacting center members.

By far the most successful models of the early universe are realized in the context of the inflationary cosmology, yet we are still far from identifying the correct model from the multiplicity of proposed scenarios. A necessary ingredient of any standard inflationary paradigm is either a scalar field, as in chaotic inflation, or vector fields, as in vector inflation. For vector inflation the nearly isotropic evolution may be achieved by employing a triad of mutually orthogonal vector fields or alternatively by a large number of randomly oriented fields. From the point of view of the background dynamics, the proposed model is similar to the standard scalar field inflation, however, the evolution must not be completely isotropic which leads to distinct observational predictions. In this project we will study other cosmological models with vector and/or scalar fields and various stability issues discussed in the literature. In particular we are interested in models with scalar and vector fields described by non-canonical Lagrangians with only derivative terms. In such theories very anisotropic field configurations (i.e. the spatial gradients are greater than the temporal kinetic components) are capable of driving a nearly isotropic expansions of the background as in cosmic inflation or dark energy. It would be also interesting to investigate the possibility for such field theories to form stable solitonic configurations such as topological defects in the case where there are no symmetry breaking potential terms.

Recent developments in string theory and cosmology point towards a new picture where our observable universe is only one island in an infinite sea of eternally expanding space-time, known as the eternal inflation. Despite of the apparent simplicity a somewhat deeper analysis of the theory revealed a number of problems (e.g. measure problem, entropy problem, problem of observables, problem of initial conditions) that remain unsolved if not insolvable within the existing framework. To overcome the problems and/or to gain more insight we are now developing alternative approaches to eternal inflation using mathematical techniques including hyperbolic dynamical systems, Markov random fields, Kolmogorov probability theory, etc. For example, within the realm of Kolmogorov probabilities, one can show that the measure problem is caused by the countable additivity axiom applied to the maximal sigma-algebra of countably infinite sample spaces. This is a serious problem if the bulk space-time is treated as a sample space which is thought to be effectively countably infinite due to local quantum uncertainties. However, in semiclassical description of eternal inflation the physical space expands exponentially which makes the sample space of infinite trajectories uncountable and the (future) boundary space effectively continuous. Then the measure problem can be solved by defining a probability measure on the continuum of trajectories or holographically on the future boundary. This should enable us to analyze a variety of problems posed in the literature such as Youngness paradox, Boltzmann brains problem, Q-catastrophe, Guth-Vanchurin paradox, etc.

Model building in string theory led to the notion of a complicated field space: the landscape. Dynamics on this landscape in the early universe should determine our current state, e.g. the amount of dark energy. The trajectory on this multi-field potential to our vacuum needs to entail an inflationary phase to be consistent with current observations. Our aim is to test the internal consistency and predictiveness of inflation on specific landscapes. We model a given type of landscape, e.g. the swampland in supergravity, by random potentials which share global features such as the overall hilliness, statistical properties of the Hessian etc. with their fundamental counterparts. This modeling entails truncated Fourier series or the much more efficient method of creating random potentials by (generalized) Dyson Brownian motion. Once a large number of such potentials can be constructed efficiently, one can run numerical experiments to asses the duration of inflation, its type and observational consequences. A complementary theoretical tool we employ for higher dimensional landscapes is random matrix theory, which enables theoretical predictions without a detailed knowledge of the potential due to the central limit theorem. Our goal is to identify the most likely scenario within this framework and identify our history and vacuum. To this end the measure problem needs to be addressed, see above. We use mild anthropic reasoning to guarantee that only those histories are considered that allow for the subsequent formation of galaxies and thus observers. As future observations will only improve constraints on inflationary physics moderately, the theoretical assessment of this framework needs to take the spotlight. Possible research outcomes may support or weaken the idea of a landscape in string theory based on currently available observations.

Physical systems are usually analyzed by modeling the dynamics with either continuous or discrete degrees of freedom. Depending on the relevant energy and length scales the very same system may be better approximated using continuous wave-functions, discrete molecules, continuous fluids, discrete stars, etc. In quantum mechanics the interplay between continuum and discrete is often formulated as the wave-particle duality which states that the elementary particles can exhibit properties of both discrete particles and continuous waves. A classical illustration of the interplay is provided in the context of fluid mechanics, where a coarse-grained dynamics of discrete molecules gives rise to continuous fluids, or in the context of field theories, where particular solutions of the field equations give rise to discrete particles. Although the existence of particles and fields is well motivated both experimentally and theoretically, one might wonder whether there are any useful concepts between discrete and continuum that would be of interest for theoretical physics in general and for cosmology in particular. From the point of view of our three-dimensional world the discrete structures are effectively zero-dimensional (e.g. particles, galaxies) and continuous structures are three-dimensional (e.g. fields, fluids). In this project we are interested instead in the physical systems with one- or two-dimensional objects or, in other words, objects of codimension two or one respectively. These could be galactic filaments or walls in the large scale structure, cosmic strings or domain walls after cosmological phase transition, D-branes or fundamental strings near the Hagedorn temperature, topological strings or domain walls in liquid crystals or even more complicated objects such as polymer chains.

Over the coming decades, humanity will acquire the technological means to hear the ripples of space-time itself. These waves are generated by the motion of astrophysical systems such as compact stars and/or small black holes revolving around each other; or the same objects orbiting, and subsequently plunging into, the super-massive black holes residing at the center of galaxies. Such gravitational waves will not only contain information about the physical properties of these compact stars - for e.g., their nuclear equation of state - and of the geometry of black holes, but also allow us to further test whether Einstein's General Relativity is indeed the correct theory of gravity. This, in turn, has relevance for cosmology itself, since the same theory of gravity is what governs the evolution of the universe at large. Much effort is needed to predict the expected gravitational wave signals, understand how they travel through the space-times in which they were produced, and how gravity influences the motion of these astrophysical objects themselves. Theoretical tools borrowed from the study of quantum fields in both flat and curved geometries may prove useful in tackling these problems.

Electromagnetic-based cosmological observations have become so exquisite that, to understand them properly, it is no longer sufficient to regard the universe to be perfectly smooth. In the current era of precision cosmology, it is therefore worthwhile to develop a first principles description of how light travels through a realistic model of the universe that incorporates effects from the lumpiness of its matter distribution. This may either lead to previously overlooked effects on, say, the correlations of Cosmic Microwave Background temperature fluctuations, or at the very least, boost cosmologists' confidence that observational data is being correctly interpreted.