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Exploring Phenomenological Aspects of Loop Quantum Cosmology and Inflation

This study delves into the intricate relationship between Loop Quantum Cosmology (LQC), inflation, and corrections to the cosmological background. By analyzing holonomy and inverse-volume effects, the research aims to resolve paradoxes and test the viability of combining LQC and inflation. The incorporation of corrections to the background leads to intriguing findings such as modified field equations and the evolution of physical modes during inflation. Computed primordial power spectra reveal unique features like suppressed power in the infra-red regime and characteristic oscillations associated with the bounce moment. Furthermore, the analysis of Bogoliubov transformations uncovers essential details about the frequency and amplitude of oscillations, shedding light on the impact of initial conditions on the Cosmic Microwave Background (CMB). As the research progresses towards a comprehensive loop-inflation paradigm, insights from these investigations could potentially revolutionize our understanding of the early universe.

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Exploring Phenomenological Aspects of Loop Quantum Cosmology and Inflation

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  1. Some phenomenological aspects ofLoop Quantum Cosmology Aurélien Barrau Work with J. Grain, T. Cailleteau, J. Mielczarek Laboratoire de Physique Subatomique et de Cosmology CNRS/IN2P3 – University Joseph Fourier – Grenoble, France

  2. The IR World is easy to see ! WMAP, 5 ans SNLS, Astier et al. SDSS, Eisenstein et al. 2005

  3. Alam et al., MNRAS 344 (2003) 1057

  4. Not the UV one… • High energy gamma-ray (Amélino-Camelia et al.) Not very conclusive however • Cosmology !

  5. LQC & inflation • Inflation • success (paradoxes solved, perturbations, etc.) • difficulties (no fundamental theory, initial conditions, etc.) • LQC • success (background-independant quantization of GR, BB • Singularity resolution, good IR limit) • difficulties (very hard to test !) • Could it be that considering both LQC and inflation within the same framework allows to cure simultaneously all the problems ?

  6. I. TOY MODEL • Let’s see what happens in a standard inflationnary background… • (tensor modes only)

  7. Holonomy corrections • « standard » inflation • decouples the effects • happens after superinflation Bojowald & Hossain, Phys. Rev. D 77, 023508 (2008)

  8. dS background Which translates, in a cosmological framework, in: Redifining the field: Which should be compared (pure general relativity) to: A.B. & Grain, Phys. Rev. Lett. , 102, 081321, 2009

  9. Grain & A.B., Phys. Rev. Lett. 102,081301 (2009)

  10. Inverse volume corrections in dS background (or in slow-roll inflation) IV Holonomy Grain, A.B., Gorecki, Phys. Rev. D. 79, 084015 (2009)

  11. Case κ(1+ε)=2 with S(q)=1+λ*q^(-κ/2)

  12. Excellent numerical / analytical agreement

  13. Holonomy + inverse volume   J. Grain, A.B., A. Gorecki, Phys. Rev. D , 79, 084015, 2009 

  14. Holonomies dominate the background and inverse-volume dominate the modes

  15. II. More seriously Including corrections to the background (still tensor modes)

  16. Taking into account the background modifications H changes sign in the KG equation ϕ’’+3Hϕ’+m2ϕ=0  Inflation inevitably occurs ! Mielczarek, Cailleteau, Grain, A.B., Phys. Rev. D, 81, 104049, 2010

  17. A tricky horizon history… Physical modes may cross he horizon several times… • Computation of the primordial power spectrum: • Bogolibov transformations • Full numerical resolution • -The power is suppressed in the infra-red (IR) regime. This is a characteristic feature associated with the bounce • -The UV behavior agrees with the standard general relativistic picture. • Damped oscillations are superimposed with the spectrum around the ”transition” momentum k∗ between the suppressed regime and the standard regime. • The first oscillation behaves like a ”bump” that can substantially exceed the UV asymptotic value. Mielczarek, Cailleteau, Grain, A.B., Phys. Rev. D, 81, 104049, 2010

  18. Effective description with a Bogoliubov transformation : • - Frequency of the oscillations controlled by Delta(eta), the width of the bounce • - Amplitude of the oscillations controlled by k0, the effective mass at the bounce • Fundamental description : • R driven my the field mass • k* driven by initial conditions Initial conditions are critical

  19. CMB consequences… Grain, A.B., Cailleteau, Mielczarek, Phys. Rev. D, 82, 123520 (2010)

  20. A.B., Grain et al.

  21. Grain & A.B., preliminary

  22. CMB consequences Grain, A.B., Cailleteau, Mielczarek, Phys. Rev. D, 82, 123520 (2010)

  23. If the scalar spectrum is assumed not to be affected : one needs x<2E-6 to probe the model If the scalar spectrum is assumed to follow the tensor one : x>2E-6 Most of the parameter space is compatible with the model Grain, A.B., Cailleteau, Mielczarek, Phys. Rev. D, 82, 123520 (2010)

  24. Is a N>78 inflation probable ?What is the probability to be compatible with WMAP data ? Good news from Ashtekar and Sloan ! Can B-mode be used to distinguised with string inflation ? I think yes.

  25. Anomaly-free vector algebra for holonomy corrections • Counter terms • Free v1 integer • Free v2 integer (even in • The diffeo constraint) • Mielczarek, Cailleteau, AB, Grain, in preparation

  26. Without counter terms : Anomaly free to the 4th order only. OK with counter-terms but the parameters cannot be fixed.

  27. Including matter The counterterms can be computed together with the integers. As expected v2=0 (no diffo correction).  The algerbra is determined (on need B=0 – and of course A=0)

  28. Perspective I : closing the algebra for scalar modes (with holonomy corrections) The solution seems to be uniquely determined. Complementary to Bojowald, Hossain, Kagan and Shankaranarayanan Cailleteau, Mielczarek, A.B., Grain, preliminary

  29. Perpsectices II (tensor modes) :IV + holonomy for background + modes Simulation in progress A.B., Cailleteau, Grain, in progress

  30. Toward a loop – inflation paradigm ?

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