Axion Density Research Articles

Radiation constraints from cosmic strings

We show that it is possible to evolve a network of global strings numerically including the effects of radiative backreaction, using the renormalised equations for the Kalb-Ramond action. We calculate radiative corrections to the equations of motion and deduce the effect on a network of global strings. We also discuss the implications of this work for the cosmological axion density.

Anharmonic evolution of the cosmic axion density spectrum.

We present analytic solutions to the spatially homogeneous axion field equation, using a model potential which strongly resembles the standard anharmonic (1-cosN\ensuremath{\theta}) potential, but contains only a piecewise second order term. Our model for \ensuremath{\theta}(x,t) spans the entire range [-\ensuremath{\pi}/N,\ensuremath{\pi}/N] and is exactly soluble for homogeneous initial conditions. For nearly homogeneous initial conditions, as would naturally occur after inflation, we are able to confirm semianalytically (i) Turner's numeric correction factors to the adiabatic and harmonic analytic treatments of homogeneous axion oscillations, and (ii) Lyth's estimate valid near the metastable misalignment angle \ensuremath{\pi}/N at the peak at the potential. We compute the enhancement of axion density fluctuations that occurs when the axion mass becomes significant at T\ensuremath{\sim}1 GeV. We find that the anharmonicity amplifies density fluctuations, but only significantly for relatively large initial misalignment angles. The enhancement factor is \ensuremath{\sim} (2,3,4,13) for ${\mathrm{\ensuremath{\theta}}}_{\mathrm{in}\mathrm{\ensuremath{\sim}}}$(0.85,0.90,0.95,0.99)\ifmmode\times\else\texttimes\fi{}\ensuremath{\pi}.

Dilution of cosmological densities by saxino decay.

Saxino decay can generate significant cosmological entropy, and hence dilute theoretical estimates of the present mass density of a given particle species. The dilution factor depends on the saxino and axion masses, and is constrained by the requirement that saxino decay should not affect nucleosynthesis, as well as by the usual requirement that the axion density be less than the critical density. The latter constraint is evaluated carefully, under both the Harari-Sikivie and Davis proposals about the emission spectrum from axionic strings. Uncertainties are carefully evaluated, points of principle are addressed, and with an eye to future numerical simulation the spacing and typical oscillation wavelength of the strings are represented by parameters varying in the range 1 to 3. Within the constraints, the entropy dilution varies from 1 to ${10}^{\ensuremath{-}4}$. Only saxions originating from thermal equilibrium are considered, so that more dilution might arise from nonthermal saxinos.

Axion miniclusters and Bose stars.

Evolution of inhomogeneities in the axion field around the QCD epoch is studied numerically, including for the first time important nonlinear effects. It is found that perturbations on scales corresponding to causally disconnected regions at T\ensuremath{\sim}1 GeV can lead to very dense axion clumps, with present density ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}}$\ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}8}$ g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. This is high enough for the collisional 2a\ensuremath{\rightarrow}2a process to lead to Bose-Einstein relaxation in the gravitationally bound clumps of axions, forming Bose stars.

Hadronic axion window and the big-bang nucleosynthesis

Hadronic axions with the decay constant ƒ a⋍10 6 GeV may fulfil all astrophysical and laboratory constraints discussed so far. In this paper, we reexamine the possibility of the hadronic axion window while taking into account the uncertainties of some parameters describing low energy axion dynamics. It is found that ƒ a in the range 3×10 5−3×10 6GeV can not be excluded by existing arguments. We then examine the implication of this hadronic axion window for the big-bang nucleosynthesis (NS) by evaluating the energy density of thermal axions at the nucleosynthesis epoch. Our analysis yields ( ϱ a / ϱ v ) NS=0.4−0.5 which exceeds slightly the current best bound ( ϱ a / ϱ v ) NS⩽0.3.

Planck-scale corrections to axion models.

It has been argued that quantum gravitational effects will violate all nonlocal symmetries. Peccei-Quinn symmetries must therefore be an "accidental" or automatic consequence of local gauge symmetry. Moreover, higher-dimensional operators suppressed by powers of ${M}_{\mathrm{Pl}}$ are expected to explicitly violate the Peccei-Quinn symmetry. Unless these operators are of dimension $d\ensuremath{\ge}10$, axion models do not solve the strong $\mathrm{CP}$ problem in a natural fashion. A small gravitationally induced contribution to the axion mass has little if any effect on the density of relic axions. If $d=10,11,or 12$ these operators can solve the axion domain-wall problem, and we describe a simple class of Kim-Shifman-Vainshtein-Zakharov axion models where this occurs. We also study the astrophysics and cosmology of "heavy axions" in models where $5\ensuremath{\le}d\ensuremath{\le}10$.

Constraining the inflationary energy scale from axion cosmology

If the temperature after inflation is below the Peccei-Quinn energy scale ƒ a, the microwave background constraint on the spectrum P a of the primeval isocurvature axion density inhomogeneity can provide an upper bound on the inflationary potential V 1 (the subscript 1 denotes the epoch when the observable universe leaves the horizon). Recent work evaluates this bound for the entire regime of parameter space and the essential results are reported here. The crucial new finding is that during inflation the PQ field may be kicked out of the vacuum by its quantum fluctuation, leading to the production of strings which remove the bound. This typically happens if H 1≳ƒ a , where H 1 is the Hubble parameter. In the opposite case, the only degree of freedom during inflation is the axion field, whose quantum fluctuation is gaussian. In that case the bound on P a is evaluated, taking into account the non-gaussian part of the density inhomogeneity (quadratic in the field) as well as the gaussian part (linear in the field).

Axions and inflation: Vacuum fluctuations.

Cosmological consequences of the Peccei-Quinn field \ensuremath{\psi}=${\mathit{re}}^{\mathit{i}\mathrm{\ensuremath{\theta}}}$/ \ensuremath{\surd}2 are explored. It has a Mexican-hat potential W=1/4\ensuremath{\lambda}(${\mathit{r}}^{2}$-${\mathit{f}}_{\mathit{a}}^{2}$${)}^{2}$. During inflation the potential may be modified so that ${\mathit{f}}_{\mathit{a}}$ has a different effective value ${\mathit{f}}_{\mathit{a}1}$; it is assumed that r sits in the vacuum at r=${\mathit{f}}_{\mathit{a}1}$. After inflation the temperature is supposed to be less than ${\mathit{f}}_{\mathit{a}}$ so that r=${\mathit{f}}_{\mathit{a}}$, and the only degree of freedom is the axion field ${\mathit{f}}_{\mathit{a}}$\ensuremath{\theta}. It has a Gaussian inhomogeneity coming from the vacuum fluctuation of \ensuremath{\theta} during inflation. When the axion mass ${\mathit{m}}_{\mathit{a}}$(T) becomes significant at T\ensuremath{\sim}1 GeV, \ensuremath{\theta} has dispersion ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{\theta}}}$\ensuremath{\simeq}(4/2\ensuremath{\pi})(${\mathit{H}}_{1}$/${\mathit{f}}_{\mathit{a}1}$) and some mean \ensuremath{\theta}\ifmmode\bar\else\textasciimacron\fi{} (in the observable Universe). The axion potential is U(\ensuremath{\theta})=(79 MeV${)}^{4}$(1-cosN\ensuremath{\theta}), and the ensuing cosmology is determined by the three parameters ${\mathit{f}}_{\mathit{a}}$/N, N\ensuremath{\theta}\ifmmode\bar\else\textasciimacron\fi{}, and N${\mathrm{\ensuremath{\sigma}}}_{\mathrm{\ensuremath{\theta}}}$. The entire domain of parameter space is considered, including the regime where the axion density perturbation is non-Gaussian and the regime where axionic domain walls are produced. Observational constraints on the parameters are established. At the end of the paper the additional assumption is made that during inflation the vacuum is at r=${\mathit{f}}_{\mathit{a}}$. Unless ${\mathit{f}}_{\mathit{a}}$/N is near the Planck scale and axions make up only a small fraction of the dark matter, this leads to the bound ${\mathit{V}}_{1}^{1/4}$2\ifmmode\times\else\texttimes\fi{}${10}^{15}$ GeV, where ${\mathit{V}}_{1}$ is the energy density during inflation, at the epoch when the observable Universe leaves the horizon.

Dilution of cosmological axions by entropy production

The usual cosmological bound on axions can be significantly relaxed if the universe experienced a period of entropy production between the time axions were produced and nucleosynthesis. We discuss a scenario in which a large amount of entropy is generated by decaying particles of mass 1–10 TeV. We find that nucleosynthesis constraints the decay lifetimes to be less than about 0.03 seconds. Using this limiting lifetime, we derive cosmological limits on the axion mass and find that m a ≳ 9 × 10 −8 eV if the axion density is dominated by radiation from strings. This limit is far from the limit m a ≲ 10 −3 based on supernova 1987A, thus showing clearly a case where axionic strings do not need to be inflated away. If the strings were inflated away, we can relax the axion mass bound to m a ≳ 5 × 10 −9 eV.

A limit on the inflationary energy density from axion isocurvature fluctuations

It is shown that the existence of axions arising from a Peccei-Quinn symmetry which is already broken at the onset of inflation implies an upper limit on the energy density V during inflation V 1 4 < 5 × 10 −5m Pl , where m Pl is the Planck energy. The limit comes from requiring that isocurvature perturbations in the axion density should not produce a microwave background anisotropy in excess of the observational limit.

Do axions need inflation?

Without inflation the energy density of relic axions in a Robertson-Walker universe arises not from coherent oscillations of a zero-momentum mode but from radiative decay of axion strings. An estimate of the upper bound on the PQ scale coming from these axions is in conflict with the lower bound from SN1987a. We present analytical and numerical evidence supporting this estimate. If true, then the axion needs inflation. With inflation the axion is safe, but the motivation for axion search experiments is weakened.

Axions and the anthropic principle.

We consider the possibility that the axion density in the Universe today may be constrained by the anthropic requirement that life should have evolved. If this were the case, the force of the usual cosmological bound on the axion decay constant would be greatly lessened. However, we find no mechanism by which excessive axion energy density could prevent the condensation of matter into potentially life-nurturing structures.

Axion miniclusters

The formation of cold dark matter in the form of coherent axion fields is expected to produce large-amplitude (δϱ≅) isocurvature fluctuations in axion density. These are later the first fluctuations to collapse, forming tiny bound “miniclusters” of axions which cluster in a gravitational hierarchy until the standard inflationary fluctuations become non-linear. The existence of these miniclusters can have observable consequences for gravitational lensing, may have a role in seeding the collapse of the first stars, and could affect the signal observed in axion-detection experiments.

Cosmic and local mass density of "invisible" axions.

If the Universe is axion dominated it may be possible to detect the axions which comprise the bulk of the mass density of the Universe. The feasibility of the proposed experiments depends crucially upon knowing the axion mass (or equivalently, the Peccei-Quinn symmetry-breaking scale) and the local mass density of axions. In an axion-dominated universe our galactic halo should be comprised primarily of axions. We calculate the local halo density to be at least 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}25}$ g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and at most a factor of 2 larger. Unfortunately, it is not possible to pin down the axion mass, even to within an order of magnitude. In an axion-dominated universe we place an upper limit to the axion mass of about ${10}^{\mathrm{\ensuremath{-}}4}$ eV. We give precise formulas for the axion mass in an axion-dominated universe, and clearly point out all the uncertainties involved in determining the precise value of the mass.

Questions about Gravitational Instability of Axion Density Fluctuations in an Axion Dominated Universe

It has recently been suggested that the axion with its spontaneous symmetry breaking mass scale of IA'10 12 GeV would dominate the energy density of the present universe and possibly explain the observed structure of the universe.') However most of previous analyses on this topic seem to rely on a too simplified argument on the development of density fluctuations in an axion dominated universe (e.g. treating axions as a ,usual bosonic fluid). Since in the scenario of our interest, the energy density of the universe is not dominated by an axion fluid but by a coherent energy of the axion field, we must take account of its coherent nature when considering the development of density fluctuations. Keeping this point in mind, we investigate perturbations of the coherent axion fi~ld in this letter. The result strongly indicates that the coherent nature of the axion field restrains the growth of density fluctuations. Although only the case of the axion is considered here explicitly, our result applies to other cosmologically possible coherent fields if they have a chance to dominate the energy density of the universe. When the Peccei-Quinn symmetry breaks down spontaneous1y at cosmic time t = to, the corresponding' U(1)PQ angle 1J (modulo 2ir) would attain some finite expectation value which would be coherent over at least the horizon size of the universe (Hubble radius) to. Although the expectation value of If at this epoch is not quite physical, it will eventually affect the physics at later times and hence should be regarded as a physical quantity. Therefore the axion field, which is defined by ? = fA If, should be considered as being materialized classically and its energy momentum tensor as contributing to the r.h.s. of the Einstein equations directly. This is in' contrast with the case when the field' is highly incoherent and its expectation value is essentially zero; in such a case we know that a fluid picture becomes more adequate. Now, since rp= is realized at least over the horizon scale at t = to, spatial fluctuations of rp on scales l~to are real classical (observable) fluctuations. Hence their Fourier amplitudes rp k (where k is the comoving wavenumber) are classically observable. Although the phases of rp k cannot be predicted a priori, this probabilistic nature of rp k is completely classical and nothing to do with quantum uncertainty. Note that the same is true in the usual case of cosmological density fluctuations where each Fourier component 8p k represents an observable density fluctuation though fluctuations may be quite incoherent as a whole. This is a characteristic feature in cosmology where scales of fluctuations are so large. The energy momentum tensor of the field is expressed as

Can Galactic Halos Be Made of Axions?

If axions exist, they contribute significantly to the present energy density. These axions have been collisionless and nonrelativistic since their appearance at \ensuremath{\sim} 1 GeV. Hence axion density perturbations survive on essentially all scales, and once the axions are dominant, grow and in turn create and amplify baryon fluctuations. Axions can cluster into galactic halos even though the axion mass \ensuremath{\lesssim}${10}^{\ensuremath{-}2}$ eV. If galactic halo matter is mainly axions, the Peccei-Quinn order parameter \ensuremath{\gtrsim}${10}^{10}$ GeV.