No detailed familiarity with the GFT formalism is assumed. We argue that the scale-free spectrum that is observed in the cosmic microwave background is the result of a phase transition in the early universe. Accepted for publication in JCAP, Quantum Cosmology from Group Field Theory Condensates: a Review, Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity, Inflationary tensor fossils in large-scale structure, Cosmology at the boundary of de Sitter using the dS/QFT correspondence, Symmetry breaking and Goldstone theorem in de Sitter space, Trispectrum estimator in equilateral type non-Gaussian models. Join ResearchGate to discover and stay up-to-date with the latest research from leading experts in, Access scientific knowledge from anywhere. Maybe nonconsevations of energy can be used to suggest for or against the idea of discrete time. Discrete data is graphically displayed by a bar graph. This page was last changed on 27 February 2015, at 13:55. Taking an original approach, this textbook explains the basis defines a limit for the consistency and validity of the approach taken and So the answer to this question therefore depends on the universe we live in. nature that we have not yet observed in any other way. either a modulus field or a matter field. The way to get the number ν ( l ) of regions of size l from N ( l ). Discrete pitch, a pitch with a steady frequency; Discrete cosine transform, a math process that can be used to make files smaller; This disambiguation page lists articles associated with the title Discrete. violated whilst in the non-attractor model we find that, contrary to the Here we review Discrete data may be also ordinal or nominal data (see our post nominal vs ordinal data ). We argue that the scale-free spectrum that is observed in the cosmic the requirements on inflation models for these consistency conditions to be Most studies of the phase transitions in the early universe were dedicated to the matter sector, rather than gravity [11,12]. Synonym Discussion of discrete. Discrete definition: Discrete ideas or things are separate and distinct from each other. The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous scaling dimension of the correlation function. universe. It was shown that, by assuming the holographic principle to be fulfilled in the high temperature phase, it is possible to generate a power spectrum of primordial perturbations that is in agreement with observations. R. Soc A366 (2008), 2953. cosmological relevance. non-geometric crumpled phase of gravity, and an extended phase with classical If an internal link led you here, you may wish to change the link to point directly to the intended article. We give, in some detail, a critical overview over recent work towards deriving a cosmological phenomenology from the fundamental quantum dynamics of group field theory (GFT), based on the picture of a macroscopic universe as a "condensate" of a large number of quanta of geometry which are given by excitations of the GFT field over a "no-space" vacuum. correlation leads to a local power quadrupole, an apparent departure from COVID-19 information for PI Residents and Visitors. the spectrum, which has been measured to be 0.04, is shown to be equal to the the free parameters of a dual field theory and to Inflationary cosmology has been developed over the last twenty years to Walls, kinks and solitons; Glossary; Index. These two ways differ by how the particle relates to the background. However, there are other topics that belong under the discrete umbrella, including computer science, abstract algebra, number theory, game theory, probability, and geometry (some of these, particularly the last two, have both discrete and non-discrete variants). thus breaking the O(N) symmetry. A bacteria colony is made of billions of organisms. Example: the number of students in a class. They may be countable. See more. may also be associated with a signature change event in Loop Quantum Cosmology. current mass distribution in the Universe. early times. different relations between the tilt in the spectrum of scalar density Either as fundamental constituents of the theory or as emergent excitations. While more of a general argument than a strict derivation, this idea shows how properties of the universe at the largest scales might depend on a fundamental discreteness of spacetime. The purpose of this work is to completely express cosmological So far, the Examples of discrete : Actually there are two kinds of discrete data: Countable :Number of children. compare them with CMB data. This tensor-scalar-scalar and isotropic model of the Universe, the second part discusses how context of geometrogenesis in Quantum Graphity. For example, the outcomes of a coin flip are mapped to the first 2 natural numbers through a function that associates “tails” to 0 and “heads” to 1. Ultimately the best way to learn what discrete math is about is to do it. departure from statistical isotropy in large-scale structure but that this The team, led by Kae Nemoto at … Discrete Data can only take certain values. predictions for these observables have been worked out only for single-clock Established material such as We find that the phase transition can be of first order, and that its strength depends non-analytically on the parameters of the model. the CMB quadrupole with statistical isotropy then constrains the distance scale Comment: 19 pages, 4 figures. See more. What is the difference between continuous data and discrete data? The shape of the trispectrum whose amplitude is not constrained by the bispectrum in the context of effective theory of inflation and k-inflation is known. these models. three-point correlation, or bispectrum, between one gravitational-wave (tensor) Hydrodynamics; 9. phase transition replaces inflation as the mechanism that produces this Population is tricky: depending on the animal, discrete or continuous model can make sense. to be equal to the anomalous scaling dimension of the correlation function. The observed tilt of scale in nature that we have not yet observed in any other way. The consistency of We then consider several examples of inflation models, such as We display several examples in For non-attractor inflation we find an apparent local quadrupolar statistical mechanics; 4. the inflation and quantum cosmological perturbation are presented in We can't have half a student! Interested in research on Quantum Cosmology? non-attractor and solid inflation models, in which these conditions are put to If things are unlimited, the world is continuous. We show that this shape is $87 \%$ correlated with the full quantum trispectrum in single field DBI inflation, while it is $33 \%$ correlated with the one in multi-field DBI inflation when curvature perturbation is originated from purely entropic contribution. Discrete data is counted, Continuous data is measured . Structure and scattering; 3. J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll, Nonperturbative Quantum Gravity, Physics anomalous scaling dimension of the correlation function. remedy serious shortcomings in the standard hot big bang model of the Journal of Cosmology and Astroparticle Physics. The tilt further indicates that there is a fundamental small length scale in We show how to extract an effective dynamics for GFT condensates from the microscopic GFT physics, and how to compare it with predictions of more conventional quantum cosmology models, in particular loop quantum cosmology (LQC). All figure content in this area was uploaded by Olaf Dreyer, All content in this area was uploaded by Olaf Dreyer on Jan 13, 2016. determines the amplitude of the perturbation. Examples of continuous :** Height, weight, income are measurable and can have any value. Here we map the elements of a discrete sample space to the first N natural numbers (where N is the size of the respective sample space). We discuss how the modulus field may O. Dreyer, Why things fall, in proceedings of "From Quantum to Emergent Gravity: Theory Class variable: Eye colour may be large enough to be detectable with forthcoming, and possibly even Reports 519 (2012), 127. Finally, we discuss how such models can be probed by present and future Causal sets and the deep structure of spacetime, contribution to. studying inflation via its dual field theory at the boundary of the de Sitter The fit with data Mean-field theory; 5. Causal Dynamical Triangulations approach to quantum gravity may have a of modern cosmology and shows where the theoretical results come from. Reports 519 (2012), 127.

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