[Paper Review] Axions in Cold Dark Matter and Inflation Models

Luca Visinelli|arXiv (Cornell University)|Nov 22, 2011

Dark Matter and Cosmic Phenomena204 references3 citations

TL;DR

This paper investigates the axion as a candidate for cold dark matter (CDM) in both standard and nonstandard cosmological models, using the misalignment mechanism and string decay scenarios. It demonstrates that axions with decay constants near the GUT scale ($f \sim 10^{16}$ GeV) can fully account for CDM in standard, LTR, and kination cosmologies, and proposes a warm natural inflation model where the axion decay constant is stabilized at the GUT scale, consistent with current CMB data and suppressing gravitational wave production.

ABSTRACT

The subjects of this thesis are the invisible axion and the more general family of axion-like particles. The invisible axion is a hypothetical elementary particle and a cold dark matter candidate. I present an improved computation of the constraints on the parameter space of the cold dark matter axion in the standard cosmology, that includes the contributions from anharmonicities in the axion potential and from the decay of axionic strings. In this scenario, I update the value of the mass of the cold dark matter axion, finding the value $(67\pm17){ m μeV}$, approximately one order of magnitude larger than previous computations. The effect of nonstandard cosmological scenarios on the parameter space of axion cold dark matter is studied for the first time. In particular, I consider the cases of low-temperature reheating and kination cosmologies, and I show that the mass of the cold dark matter axion can differ from the value in the standard cosmological scenario by orders of magnitude. Finally, I consider the family of axion-like particles, assuming that these particles serve as the inflaton in the context of warm inflation. I find that the axion energy scale $f$, which in the standard inflation scenario is of the order of the Planck mass, can be lowered to the much safer Grand Unification Theory scale $f \sim 10^{16}{ m GeV}$. I also constrain the parameter space and the amount of gravitational waves from this model, using results from the Wilkinson Microwave Anisotropy Probe 7-year data.

Motivation & Objective

• To assess the viability of the axion as the primary component of cold dark matter (CDM) in standard and nonstandard cosmological scenarios.
• To explore how nonstandard cosmologies—such as LTR and kination—affect axion production via the misalignment mechanism and string decay.
• To develop and constrain a warm natural inflation (NWI) model where axion-like particles with a GUT-scale decay constant ($f \sim 10^{16}$ GeV) are consistent with observational data.
• To compare the predictions of the NWI model with CMB observables, particularly the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, to distinguish it from standard natural inflation.

Proposed method

• Uses the misalignment mechanism to compute axion production in the early universe, solving the equation of motion on the FRW metric to determine oscillation temperature and energy density.
• Applies the axion potential $U(\phi) = f^2 \Lambda^2 \left[1 - \cos(\phi/f)\right]$ in slow-roll inflation, incorporating dissipation via $\Gamma$ in the Langevin-type equation.
• Derives slow-roll conditions and number of e-folds in the warm inflation framework, using the effective potential and dissipation rate $\Gamma \propto \alpha \phi^2$.
• Computes scalar and tensor power spectra using the curvature perturbation $\mathcal{R}$, deriving $n_s$ and $r$ as functions of $\alpha$ and $N_e$.
• Evaluates constraints from WMAP+BAO+SN data in the $r$-$n_s$ plane, using the bound $m_\phi < 2.7 \times 10^{12}$ GeV $(r/0.22)^{1/4} (N_e/60)^{-13/16} (g_*/228.75)^{5/48}$.
• Analyzes axion production from string decay and domain walls, computing the parameter space where axions constitute 100% of CDM in various cosmological models.

Experimental results

Research questions

• RQ1 Can axions produced via the misalignment mechanism fully account for cold dark matter in standard cosmology, and what is the required axion decay constant $f_a$?
• RQ2 How do nonstandard cosmologies—such as LTR and kination—alter the parameter space for axion CDM, and what are the resulting constraints on $f_a$ and initial misalignment angle $\theta_i$?
• RQ3 Can a warm natural inflation model with an axion-like field at the GUT scale ($f \sim 10^{16}$ GeV) be consistent with current CMB observations, particularly $n_s$ and $r$?
• RQ4 What are the observational differences between warm natural inflation and standard natural inflation, especially in terms of gravitational wave production and the tensor-to-scalar ratio $r$?

Key findings

• In standard cosmology, axions can constitute 100% of CDM when the axion decay constant is $f_a \sim 10^{12}$ GeV and the initial misalignment angle $\theta_i \sim 1$, with the parameter space constrained by the misalignment mechanism.
• In the LTR cosmology, the required PQ scale $f_a^{\rm LTR}$ is reduced compared to standard cosmology, allowing $f_a \sim 10^{16}$ GeV to still yield 100% CDM for $T_{\rm RH} \sim 10^9$ GeV.
• In the kination cosmology, the axion can be 100% CDM for $f_a \sim 10^{16}$ GeV when $T_{\rm kin} \sim 10^9$ GeV, with the parameter space depending on the reheating temperature and initial field value.
• The warm natural inflation (NWI) model allows the axion decay constant to be as low as $f \sim 10^{16}$ GeV (GUT scale), avoiding the Planck-scale fine-tuning of standard natural inflation.
• The model predicts a suppressed tensor-to-scalar ratio $r \ll 10^{-14}$ for $f \sim 10^{16}$ GeV, making it distinguishable from standard natural inflation via future $r$ measurements.
• For $f = 10^{16}$ GeV, the NWI model is consistent with WMAP+BAO+SN data, favoring $N_e \approx 40-50$ e-folds, with $r$ and $n_s$ predictions lying within the 95% C.L. region.