How Sound Are Our Ultralight Axion Approximations?

Ultralight axions (ULAs) are a promising dark-matter candidate. ULAs may have implications for small-scale challenges to the ΛCDM model and arise in string scenarios. ULAs are already constrained by cosmic microwave background (CMB) experiments and large-scale structure surveys, and will be probed with much greater sensitivity by future efforts. It is challenging to compute observables in ULA scenarios with sufficient speed and accuracy for cosmological data analysis because the ULA field oscillates rapidly. In past work, an effective fluid approximation has been used to make these computations feasible. Here this approximation is tested against an exact solution of the ULA equations, comparing the induced error of CMB observables with the sensitivity of current and future experiments. In the most constrained mass range for a ULA dark-matter component (10−27  eV≤max≤10−25  eV), the induced bias on the allowed ULA fraction of dark matter from Planck data is less than 1σ. In the cosmic-variance limit (including temperature and polarization data), the bias is ≲2σ for primary CMB anisotropies, with more severe biases (as high as ∼4σ) resulting for less reliable versions of the effective fluid approximation. If all of the standard cosmological parameters are fixed by other measurements, the expected bias rises to 4−20σ (well beyond the validity of the Fisher approximation), though the required level of degeneracy breaking will not be achieved by any planned surveys

An improved estimator for non-Gaussianity in cosmic microwave background observations

An improved estimator for the amplitude fnl of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit. When applied to CMB maps which have a detectable level of non-Gaussianity the standard estimator is no longer optimal, possibly limiting the sensitivity of future observations to a non-Gaussian signal. Previous studies have proposed an improved estimator by using a realization-dependent normalization. Under the approximations of a flat sky and a vanishingly thin last-scattering surface, these studies showed that the variance of this improved estimator can be significantly smaller than the variance of the standard estimator when applied to non-Gaussian CMB maps. Here this technique is generalized to the full sky and to include the full radiation transfer function, yielding expressions for the improved estimator that can be directly applied to CMB maps. The ability of this estimator to reduce the variance as compared to the standard estimator in the face of a significant non-Gaussian signal is re-assessed using the full CMB transfer function. As a result of the late time integrated Sachs-Wolfe effect, the performance of the improved estimator is degraded. If CMB maps are first cleaned of the late-time ISW effect using a tracer of foreground structure, such as a galaxy survey or a measurement of CMB weak lensing, the new estimator does remove a majority of the excess variance, allowing a higher significance detection of fnl.Comment: 21 pages, 7 figure

Cosmological Implications Of Ultralight Axionlike Fields

Cosmological observations are used to test for imprints of an ultralight axionlike field (ULA), with a range of potentials V(ϕ)∝[1−cos(ϕ/f)]ⁿ set by the axion-field value ϕ and decay constant f. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For n=1, once dynamical, the axion energy density dilutes as matter; for n=2 it dilutes as radiation and for n=3 it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual n=1 case. ULA models are parametrized by the redshift z(c) when the field becomes dynamical, the fractional energy density f(z(c))≡Ωₐ(z(c))/Ωₜₒₜ(z(c)) in the axion field at zc, and the effective sound speed c²ₛ. Using Planck, BAO and JLA data, constraints on fzc are obtained. ULAs are degenerate with dark energy for all three potentials if 1+z(c)≲10. When 3×10⁴≳1+z(c)≳10, f(z(c)) is constrained to be ≲0.004 for n=1 and f(z(c))≲0.02 for the other two potentials. The constraints then relax with increasing zc. These results have implications for ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal

Baryons still trace dark matter: probing CMB lensing maps for hidden isocurvature

Compensated isocurvature perturbations (CIPs) are primordial fluctuations that balance baryon and dark-matter isocurvature to leave the total matter density unperturbed. The effects of CIPs on the cosmic microwave background (CMB) anisotropies are similar to those produced by weak lensing of the CMB: smoothing of the power spectrum, and generation of non-Gaussian features. Previous work considered the CIP effects on the CMB power-spectrum but neglected to include the CIP effects on estimates of the lensing potential power spectrum (though its contribution to the non-Gaussian, connected, part of the CMB trispectrum). Here, the CIP contribution to the standard estimator for the lensing potential power-spectrum is derived, and along with the CIP contributions to the CMB power-spectrum, Planck data is used to place limits on the root-mean-square CIP fluctuations on CMB scales, $\Delta_{\rm rms}^2(R_{\rm CMB})$. The resulting constraint of $\Delta_{\rm rms}^2(R_{\rm CMB}) < 4.3 \times 10^{-3}$ using this new technique improves on past work by a factor of $\sim 3$. We find that for Planck data our constraints almost reach the sensitivity of the optimal CIP estimator. The method presented here is currently the most sensitive probe of the amplitude of a scale-invariant CIP power spectrum placing an upper limit of $A_{\rm CIP}< 0.017$ at 95% CL. Future measurements of the large-scale CMB lensing potential power spectrum could probe CIP amplitudes as low as $\Delta_{\rm rms}^2(R_{\rm CMB}) = 8 \times 10^{-5}$ ($A_{\rm CIP} = 3.2 \times 10^{-4}$).Comment: 24 pages, 9 figures; comments welcome; v2 references correcte

Probing Spatial Variation Of The Fine-Structure Constant Using The CMB

The fine-structure constant, α, controls the strength of the electromagnetic interaction. There are extensions of the standard model in which α is dynamical on cosmological length and time scales. The physics of the cosmic microwave background (CMB) depends on the value of α. The effects of spatial variation in α on the CMB are similar to those produced by weak lensing: smoothing of the power spectrum, and generation of non-Gaussian features. These would induce a bias to estimates of the weak-lensing potential power spectrum of the CMB. Using this effect, Planck measurements of the temperature and polarization power spectrum, as well as estimates of CMB lensing, are used to place limits (95% C.L.) on the amplitude of a scale-invariant angular power spectrum of α fluctuations relative to the mean value (CαL=AαSI/[L(L+1)]) of AαSI≤1.6×10−5. The limits depend on the assumed shape of the α-fluctuation power spectrum. For example, for a white-noise angular power spectrum (CαL=AαWN), the limit is AαWN≤2.3×10−8. It is found that the response of the CMB to α fluctuations depends on a separate-universe approximation, such that theoretical predictions are only reliable for α multipoles with L≲100. An optimal trispectrum estimator can be constructed and it is found that it is only marginally more sensitive than lensing techniques for Planck but significantly more sensitive when considering the next generation of experiments. For a future CMB experiment with cosmic-variance limited polarization sensitivity (e.g., CMB-S4), the optimal estimator could detect α fluctuations with AαSI\u3e1.9×10−6 and AαWN\u3e1.4×10−9

Baryons Still Trace Dark Matter: Probing CMB Lensing Maps For Hidden Isocurvature

Compensated isocurvature perturbations (CIPs) are primordial fluctuations that balance baryon and dark-matter isocurvature to leave the total matter density unperturbed. The effects of CIPs on the cosmic microwave background (CMB) anisotropies are similar to those produced by weak lensing of the CMB: smoothing of the power spectrum and generation of non-Gaussian features. Here, an entirely new CIP contribution to the standard estimator for the lensing-potential power spectrum is derived. Planck measurements of the temperature and polarization power spectrum, as well as estimates of CMB lensing, are used to place limits on the variance of the CIP fluctuations on CMB scales, Δ2rms(RCMB). The resulting constraint of Δ2rms(RCMB)\u3c4.3×10−3 at 95% confidence level (CL) using this new technique improves on past work by a factor of ∼3. We find that for Planck data our constraints almost reach the sensitivity of the optimal CIP estimator. The method presented here is currently the most sensitive probe of the amplitude of a scale-invariant CIP power spectrum, ACIP, placing an upper limit of ACIP\u3c0.017 at 95% CL. Future measurements of the large-scale CMB lensing-potential power spectrum could probe CIP amplitudes as low as Δ2rms(RCMB)=8×10−5 at 95% CL (corresponding to ACIP=3.2×10−4)

On the approximation of the limit cycles function

We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x)$, which is based on the Newton scheme applied to the Poincar'e function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Li'enard system. The obtained result supports a conjecture by Lins, de Melo and Pugh

Pair-Breaking in Rotating Fermi Gases

We study the pair-breaking effect of rotation on a cold Fermi gas in the BCS-BEC crossover region. In the framework of BCS theory, which is supposed to be qualitatively correct at zero temperature, we find that in a trap rotating around a symmetry axis, three regions have to be distinguished: (A) a region near the rotational axis where the superfluid stays at rest and where no pairs are broken, (B) a region where the pairs are progressively broken with increasing distance from the rotational axis, resulting in an increasing rotational current, and (C) a normal-fluid region where all pairs are broken and which rotates like a rigid body. Due to region B, density and current do not exhibit any discontinuities.Comment: 4 pages, 2 figures; v2: discussion clarified, typos corrected, one reference adde

Dulac-Cherkas functions for generalized Liénard systems

Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems including criteria for the non-existence of limit cycles, at the same time they provide information about their stability and hyperbolicity. In this paper, we present a method to construct  a special class of Dulac-Cherkas functions for  generalized Liénard systems of the type $\frac{dx}{dt} = y, \quad  \frac{dy}{dt} = \sum_{j=0}^l h_j(x) y^j$ with $l \ge 1$. In case $1 \le l \le 3$,  linear differential equations play a key role in this process, for $l \ge 4$, we have to solve a system of linear differential and algebraic equations, where the number of equations is larger than the number of unknowns. Finally,  we show that Dulac-Cherkas functions can be used to construct generalized Liénard systems with any $l$ possessing limit cycles

Axion constraints in non-standard thermal histories

It is usually assumed that dark matter is produced during the radiation dominated era. There is, however, no direct evidence for radiation domination prior to big-bang nucleosynthesis. Two non-standard thermal histories are considered. In one, the low-temperature-reheating scenario, radiation domination begins as late as 1 MeV, and is preceded by significant entropy generation. Thermal axion relic abundances are then suppressed, and cosmological limits to axions are loosened. For reheating temperatures less than 35 MeV, the large-scale structure limit to the axion mass is lifted. The remaining constraint from the total density of matter is significantly relaxed. Constraints are also relaxed for higher reheating temperatures. In a kination scenario, a more modest change to cosmological axion constraints is obtained. Future possible constraints to axions and low-temperature reheating from the helium abundance and next-generation large-scale-structure surveys are discussed.Comment: 10 pages, 7 figures, revised to match version published in Phys. Rev. D. Fig. 7 and Eq. (20) modifie