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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Michał Artymowski Loop Quantum Cosmology holonomy corrections to inflationary models University of Warsaw Warszawa 15-06-2009 In colaboration with L. Szulc and Z. Lalak

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Outline Backgroud evolution in the FRW cosmology with the holonomy loop correction Initial conditions for the accelerated expansion Evolution of the scalar metric perturbations Effective comoving sonic horizon The power spectrum of the initial energy density perturbations Phenomenology of loop corrections

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 The loop correction and Ashtekar variables Ashtekar variables in the FRW Universe: The hamiltonian gives us Friedmann equations The parallel transport around the loop changes the vector. If we would shrink the loop to the smallest possible size we would get the elementary correction

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Quantum of length By considering the loop quantum gravity modifications to the we get, where is the quantum of length. This is an extremely important variable! No specific value of j chosen by nature! Critical (maximal) energy density of the Universe For and big values of j we have The holonomy loop correction does not changes p!

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Friedmann equations Effective variables normal FRW

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Initial conditions for inflation Accelerated expansion always appears when Initial conditions for the accelerated expansion much more natural than in the standard FRW but we have to count e-folds from the moment of anyway

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Perturbations in LQC We can write Hamilton equations for, where We consider k 0 so perturbations are functions of time only. We do not have any anisotropic pressure and from perturbated Friedmann equations we have For the adiabatic perturbations we obtain This equation is almoust identical with the one from the standard FRW. Perturbations are frozen outside the effective sonic horizon.

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 The effective speed of sound In LQC the effective speed of sound becomes infinite for No conserved information left over from the period The effective Big Bang scenario! is not a physical velocity!!!

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 The power spectrum Equations for the inflaton and its perturbation are not changed by the loop correction where is the inflaton perturbation For the slow-roll approximation, The power spectrum of the curvature perturbations is then in form of From the COBE normalization we know, that if we want to avoid fine tuning we need to have This gives us the limit for j. For big values of j The spectral index is changed by the LQC to

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Loop Quantum Cosmology corrections to inflationary models Michał Artymowski, University of Warsaw2009-06-15 Conclusions FRW Universe in the low energy limit for LQC No information about the scalar perturbations can cross the energy regime untouched We can limit the quantum of length by the COBE normalization More models fit the data for strong LQC holonomy effects

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