[Paper Review] Cosmic microwave background polarization in Noncommutative space-time

S. Batebi, M. Haghighat+2 more|arXiv (Cornell University)|May 29, 2016

Cosmology and Gravitation Theories15 references3 citations

TL;DR

This paper investigates how non-commutative (NC) space-time modifies Compton scattering to generate circular and B-mode polarization in the cosmic microwave background (CMB) via scalar metric perturbations. It shows that NC corrections can produce detectable V-mode and B-mode power spectra even at NC energy scales up to 10 TeV, implying that the observed r-parameter may have contributions beyond primordial gravitational waves.

ABSTRACT

In the standard model of cosmology (SMC) the B-mode polarization of the CMB can be explained by the gravitational effects in the inflation epoch. However, this is not the only way to explain the B-mode polarization for the CMB. It can be shown that the Compton scattering in presence of a background besides generating a circularly polarized microwave, can leads to a B-mode polarization for the CMB. Here we consider the non-commutative (NC) space time as a background to explore the CMB polarization at the last scattering surface. We obtain the B-mode spectrum of the CMB radiation by scalar perturbation of metric via a correction on the Compton scattering in NC-space-time in terms of the circular polarization power spectrum and the non-commutative energy scale. It can be shown that even for the NC-scale as large as $10TeV$ the NC-effects on the CMB polarization and the r-parameter is significant. We show that the V-mode power spectrum can be obtained in terms of linearly polarized power spectrum in the range Micro to Nano-Kelvin squared for the NC-scale about $1TeV$ to $10TeV$, respectively.

Motivation & Objective

• To investigate whether non-commutative (NC) space-time can generate circular and B-mode polarization in the CMB via modified Compton scattering.
• To assess the viability of NC effects as an alternative source for the observed B-mode polarization, especially given the tension between BICEP2 and Planck results.
• To estimate the range of the NC energy scale Λ consistent with current CMB polarization data, particularly the V-mode and B-mode power spectra.
• To quantify the impact of NC corrections on the tensor-to-scalar ratio r, considering scalar-mode contributions.

Proposed method

• Formalism of Stokes parameters (Q, U, V) is used to describe CMB polarization, with V representing circular polarization.
• The Boltzmann equation for photon transport is modified to include NC corrections in Compton scattering cross-sections.
• A scalar mode perturbation of the metric is introduced to model density inhomogeneities during recombination.
• The time evolution of Stokes parameters is computed under NC space-time, leading to a non-zero V-mode power spectrum.
• The B-mode power spectrum is derived from the circular polarization power spectrum via a proportionality involving the NC correction parameter κ̃.
• The V-mode and B-mode power spectra are estimated using the linearly polarized CMB power spectrum and bounds on the NC scale Λ.

Experimental results

Research questions

• RQ1 Can non-commutative space-time generate circular polarization in the CMB through modified Compton scattering?
• RQ2 To what extent can scalar-mode perturbations in NC space-time produce B-mode polarization, contrary to the standard model?
• RQ3 What is the range of the non-commutative energy scale Λ consistent with observed CMB polarization power spectra?
• RQ4 How significant are NC effects on the tensor-to-scalar ratio r, especially at Λ ~ 1 TeV to 10 TeV?
• RQ5 Can the observed B-mode signal be explained by NC-induced effects rather than primordial gravitational waves?

Key findings

• The circular polarization power spectrum C_Vl is estimated to be in the range 0.1 nK² to 0.1 μK² for an NC scale Λ ~ 10 TeV.
• For Λ ~ 1 TeV, C_Vl lies between 10⁻³ μK² and 10³ μK², which is within the sensitivity range of current and future CMB experiments.
• The B-mode power spectrum C_Bl^S due to scalar-mode NC effects is bounded by 0.1 pK² to 0.1 μK² for Λ ~ 10 TeV and 10 nK² to 10 mK² for Λ ~ 1 TeV.
• These B-mode levels are comparable to the observed C_Bl^ob ~ 0.01 μK² for l < 250, suggesting NC effects could contribute significantly to the measured r-parameter.
• The NC correction parameter κ̃² scales as (10 TeV/Λ)², indicating that even at Λ ~ 10 TeV, NC effects on CMB polarization remain significant.
• The study implies that the observed B-mode signal may not solely originate from primordial gravitational waves, as NC effects can mimic tensor-mode contributions through scalar perturbations.