Noncommutative spacetime, stringy spacetime uncertainty principle, and density fluctuations

Abstract

We propose a variation of spacetime noncommutative field theory to realize the stringy spacetime uncertainty relation without breaking any of the global symmetries of the homogeneous isotropic universe. We study the spectrum of metric perturbations in this model for a wide class of accelerating background cosmologies. Spacetime noncommutativity leads to a coupling between the fluctuation modes and the background cosmology which is nonlocal in time. For each mode, there is a critical time at which the spacetime uncertainty relation is saturated. This is the time when the mode is generated. These effects lead to a spectrum of fluctuations whose spectral index is different from what is obtained for commutative spacetime in the infrared region, but is unchanged in the ultraviolet region. In the special case of an exponentially expanding background, we find a scale-invariant spectrum. but with a different magnitude than in the context of commutative spacetime if the Hubble constant is above the string scale.

Consistency relations and degeneracies in (non)commutative patch inflation

“…We are going to confirm this result in quite a general manner and pave the way to the classification of eventual * Electronic address: calcagni@fis.unipr.it future braneworld scenarios. The nondegeneracy of the consistency relations is then substantially confirmed in the case of a noncommutative brane with a realization of the noncommutative algebra preserving the FRW symmetry; see [4,5] and references therein. The introduction of the new degree of freedom provided by a noncommutative parameter slightly complicates the analysis but does not trigger further degeneracies in any of the concrete (non)commutative braneworlds.…”

“…Here, σ is a nonnegative function encoding the dependence on the string scale; in the commutative limit or UV region of the spectrum, it is σ ∝ (H/M s ) 4 , where H is evaluated at horizon crossing. In the far IR regime, one finds that either σ = 6 or σ = 2 for class 1 (FRWsphere factored out) and class 2 (one single effective scale factor) models, respectively.…”

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

“…A tool that has been used in order to address this issue is to confront the trans-Planckian power spectra to the CMB data. The trans-Planckian problem originates from the fact that, due to the exponential expansion during inflation, the scales of astrophysical interest today were below the Planck length at the beginning of inflation [91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117]. In this regime, the framework utilised to derive the inflationary predictions (namely quantum field theory in curved space-time) breaks down.…”

Inflationary universe in loop quantum cosmology

“…Still, it is expected that the imprint of quantum effects should be left on the primordial power spectrum which can be investigated through observation on the CMB sky. It should be mentioned that the stringy imprint in the primordial perturbations has been discussed in the noncommutative inflation models, see e.g., [27]. While cosmological scales are leaving the horizon, the slow-roll paradigm of inflation is practically mandatory in order to account for the near scale invariance of spectrum of the primordial curvature perturbation.…”