Density fluctuations in $\kappa$-deformed inflationary universe

Abstract

We study the spectrum of metric fluctuation in $\kappa$-deformed inflationary universe. We write the theory of scalar metric fluctuations in the $\kappa -$deformed Robertson-Walker space, which is represented as a non-local theory in the conventional Robertson-Walker space. One important consequence of the deformation is that the mode generation time is naturally determined by the structure of the $\kappa -$deformation. We expand the non-local action in $H^2/{\kappa }^2$, with $H$ being the Hubble parameter and $\kappa$ the deformation parameter, and then compute the power spectra of scalar metric fluctuations both for the cases of exponential and power law inflations up to the first order in $H^2/{\kappa }^2$. We show that the power spectra of the metric fluctuation have non-trivial corrections on the time dependence and on the momentum dependence compared to the commutative space results. Especially for the power law inflation case, the power spectrum for UV modes is weakly blue shifted early in the inflation and its strength decreases in time. The power spectrum of far-IR modes has cutoff proportional to $k^3$ which may explain the low CMB quadrupole moment.

final revision; 19 pages, 3 figures; to appear in Phys. Rev. D

References in corpus (32)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Testable scenario for Relativity with minimum-length
• The Trans-Planckian Problem of Inflationary Cosmology
• Dumb Holes and the Effects of High Frequencies on Black Hole Evaporation
• Hawking Spectrum and High Frequency Dispersion
• The Robustness of Inflation to Changes in Super-Planck-Scale Physics
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Noncommutative Spacetime, Stringy Spacetime Uncertainty Principle, and Density Fluctuations
• Deformed Special Relativity as an effective flat limit of quantum gravity
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• 2+1 gravity and Doubly Special Relativity
• CMB Power Spectrum from Noncommutative Spacetime
• Possible Explanation to Low CMB Quadrupole
• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• Hopf-algebra description of noncommutative-spacetime symmetries
• Noncommutative Inflation and the CMB Multipoles
• Testing Dispersion Relations of Quantum $\kappa$-Poincaré Algebra on Cosmological Ground
• Generalized Quantum Relativistic Kinematics: a Stability Point of View
• Theoretical tools for CMB physics
• A Canonical Formalism For Lagrangians With Nonlocality Of Finite Extent
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• On the Tensor/Scalar Ratio in Inflation with UV Cutoff
• Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator
• A Note on Curvature Fluctuation of Noncommutative Inflation
• Physics of Deformed Special Relativity
• Problem of Unitarity and Quantum Corrections in Semiclassical Quantum Gravity
• Classical Spacetime from Quantum Gravity
• Measuring the cosmological density perturbation

Cited by in corpus (11)

• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• $\kappa -$Minkowski spacetime and a uniformly accelerating observer
• A Note on Noncommutative Brane Inflation
• Field Theory on Curved Noncommutative Spacetimes
• Noncommutative KKLMMT Model
• Trans-Planckian Physics from a Nonlinear Dispersion Relation
• Blackbody radiation in κ-Minkowski spacetime
• Slow-roll reconstruction for running spectral index
• Trans-Planckian Physics and Non-Commutative Inflation