3,692 research outputs found
Palatini approach to bouncing cosmologies and DSR-like effects
It is shown that a quadratic gravitational Lagrangian in the Palatini
formulation is able to capture different aspects of quantum gravity
phenomenology in a single framework. In particular, in this theory field
excitations propagating with different energy-densities perceive different
background metrics, a fundamental characteristic of the DSR and Rainbow Gravity
approaches. This theory, however, avoids the so-called soccer ball problem.
Also, the resulting isotropic and anisotropic cosmologies are free from the big
bang singularity. This singularity avoidance occurs non-perturbatively and
shares some similitudes with the effective dynamics of loop quantum cosmology.Comment: 4 pages. Proceedings of Loops'11, Madrid. To appear in Journal of
Physics: Conference Series (JPCS
Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms
Quantum Mechanics and Signal Processing in the line R, are strictly related
to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition
of a new discrete variable that measures the degree of the Hermite functions
and allows to obtain the projective algebra io(2). A Rigged Hilbert space is
found and a new discrete basis in R obtained. The operators {O[R]} defined on R
are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in
this way, their algebraic discussion. Introducing in the half-line a
Fourier-like Transform, the procedure is extended to R^+ and can be easily
generalized to R^n and to spherical reference systems.Comment: 12 pages, Contribution to the 30th International Colloquium on Group
Theoretical Methods in Physics, July 14-18, 2014, Gent (Belgium
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