[Paper Review] Isentropic and Isocurvature Axion Perturbations in Inflationary Cosmology

Stephen D. Burns|arXiv (Cornell University)|Nov 25, 1997

Galaxies: Formation, Evolution, Phenomena3 references6 citations

TL;DR

This paper investigates isentropic and isocurvature perturbations from axions in inflationary cosmology, showing that COBE data constrains the inflationary Hubble scale to $ H_I \lesssim 10^{12} $ GeV if isocurvature modes are present. Using Saskatoon microwave background data and $ \sigma_8 $, it finds isocurvature perturbations are not ruled out, with amplitude limits of $ \lesssim 0.1 $ times adiabatic at $ \ell = 87 $ and $ \lesssim 10^{-3} \text{--} 10^{-2} $ at $ \ell = 237 $.

ABSTRACT

Isentropic and isocurvature axion inflationary perturbations are studied in detail. If isocurvature perturbations are present, COBE requires the inflationary Hubble constant to be rather small, $H_{I} \stackrel{

Motivation & Objective

• Examine the impact of axion-induced isocurvature and isentropic perturbations on cosmic microwave background (CMB) anisotropies.
• Constrain the amplitude of isocurvature perturbations using observational data from COBE and the Saskatoon experiment.
• Determine the consistency of mixed axion and supersymmetric cold dark matter (CDM) models with CMB power spectra.
• Evaluate the implications for the inflationary Hubble scale $ H_I $ when isocurvature modes are included.
• Assess the viability of axion dark matter in models with mixed adiabatic and isocurvature initial conditions.

Proposed method

• Calculate the angular power spectrum of CMB anisotropies in CDM models with a mixture of axion and supersymmetric CDM components.
• Use linear perturbation theory to model both isentropic (adiabatic) and isocurvature axion fluctuations during inflation.
• Apply constraints from COBE-DMR data on the normalization of the primordial power spectrum to limit $ H_I $.
• Compare theoretical CMB power spectra with Saskatoon data at multipoles $ \ell = 87 $ and $ \ell = 237 $ to constrain isocurvature amplitudes.
• Integrate $ \sigma_8 $ measurements to further restrict the allowed parameter space for isocurvature contributions.
• Employ a transfer function formalism to compute the evolution of perturbations from horizon entry to recombination.

Experimental results

Research questions

• RQ1 How do isocurvature axion perturbations affect the angular power spectrum of the cosmic microwave background?
• RQ2 What upper bounds can be placed on the amplitude of isocurvature perturbations using Saskatoon CMB data and $ \sigma_8 $?
• RQ3 To what extent does the presence of isocurvature modes constrain the inflationary Hubble scale $ H_I $?
• RQ4 How do mixed axion and supersymmetric CDM models compare with observational CMB anisotropy data?
• RQ5 Are isocurvature axion perturbations still viable given current CMB and large-scale structure constraints?

Key findings

• COBE data requires the inflationary Hubble scale to be $ H_I \lesssim 10^{12} $ GeV if isocurvature perturbations are present, regardless of the inflation model.
• At $ \ell = 87 $, the square of the isocurvature perturbation amplitude must be $ \lesssim 0.1 $ times that of the adiabatic component to be consistent with Saskatoon data.
• At $ \ell = 237 $, the isocurvature amplitude is constrained to $ \lesssim 10^{-3} \text{--} 10^{-2} $ times the adiabatic amplitude.
• Although not dominant, isocurvature perturbations are not ruled out by current CMB and $ \sigma_8 $ data.
• The CMB angular power spectrum depends not only on the amplitude of the isocurvature spectrum but also on the axion density parameter $ \Omega_a $.
• Consistency with observations allows for non-negligible contributions from axion isocurvature modes, particularly at intermediate multipoles.