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Axion isocurvature fluctuations with extremely blue spectrum

Shinta Kasuya, Masahiro Kawasaki

TL;DR

The paper addresses the possibility of isocurvature fluctuations with a blue spectrum in the early universe, motivated by analyses allowing independent spectral indices for adiabatic and isocurvature modes. It develops a concrete SUSY axion model in which the PQ scale $F_a$ is a dynamical field $\varphi$ that starts near the Planck scale $M_P$ during inflation and evolves toward $F_a$, with Hubble-induced masses shaping a blue tilt $n_{\rm iso}-1 = 3 - 3\sqrt{1 - \frac{4}{9} c_+}$ for $0 < c_+ \le \tfrac{9}{4}$, while the spectrum becomes scale-invariant after settling. The axion isocurvature amplitude scales as $A_{\rm iso} \simeq H^2/(2\pi^2 \varphi_+^2 \theta_+^2)$ and the tilt transitions from $n_{\rm iso}>1$ to unity; numerical results confirm blue indices up to $n_{\rm iso}=4$ for representative parameters and illustrate the connection to a later scale-invariant regime. This mechanism links axion dark matter to early-universe perturbations and suggests possible PLANCK/large-scale structure signatures from a temporally blue isocurvature component.

Abstract

We construct an axion model for generating isocurvature fluctuations with blue spectrum, n_{iso}=2-4, which is suggested by recent analyses of admixture of adiabatic and isocurvature perturbations with independent spectral indices, n_{ad} \ne n_{iso}. The distinctive feature of the model is that the spectrum is blue at large scales while scale invariant at small scales. This is naturally realized by the dynamics of the Peccei-Quinn scalar field.

Axion isocurvature fluctuations with extremely blue spectrum

TL;DR

The paper addresses the possibility of isocurvature fluctuations with a blue spectrum in the early universe, motivated by analyses allowing independent spectral indices for adiabatic and isocurvature modes. It develops a concrete SUSY axion model in which the PQ scale is a dynamical field that starts near the Planck scale during inflation and evolves toward , with Hubble-induced masses shaping a blue tilt for , while the spectrum becomes scale-invariant after settling. The axion isocurvature amplitude scales as and the tilt transitions from to unity; numerical results confirm blue indices up to for representative parameters and illustrate the connection to a later scale-invariant regime. This mechanism links axion dark matter to early-universe perturbations and suggests possible PLANCK/large-scale structure signatures from a temporally blue isocurvature component.

Abstract

We construct an axion model for generating isocurvature fluctuations with blue spectrum, n_{iso}=2-4, which is suggested by recent analyses of admixture of adiabatic and isocurvature perturbations with independent spectral indices, n_{ad} \ne n_{iso}. The distinctive feature of the model is that the spectrum is blue at large scales while scale invariant at small scales. This is naturally realized by the dynamics of the Peccei-Quinn scalar field.

Paper Structure

This paper contains 5 sections, 28 equations, 1 figure.

Table of Contents

  1. Introduction
  2. How to get the blue spectrum
  3. Axion model in SUSY
  4. Dynamics of the fields and isocurvature fluctuations
  5. Conclusions

Figures (1)

  • Figure 1: Evolution of the fields $\Phi_+$ (upper thick lines) and $\Phi_-$ (lower thin lines) for $c_-=9/4$ and $c_+=9/4$ ($n_{\rm iso}=4$, red solid), 2 ($n_{\rm iso}=3$, green dashed), and $5/4$ ($n_{\rm iso}=2$, blue dotted-dashed). The inset shows the minima where the fields settle down.