We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.

We apply the inverse Gertsenshtein effect, i.e., the graviton-photon conversion in the presence of a magnetic field, to constrain high-frequency gravitational waves (HFGWs). Using existing astrophysical measurements, we compute upper limits on the GW energy densities Ω_GW at 16 different frequency bands. Given the observed magnetisation of galaxy clusters with field strength B ∼ μG correlated on (10) kpc scales, we estimate HFGW constraints in the (10²) GHz regime to be Ω_GW ≲ 10¹⁶ with the temperature measurements of the Atacama Cosmology Telescope (ACT). Similarly, we conservatively obtain Ω_GW ≲ 10¹³ (10¹¹) in the (10²) MHz ((10) GHz) regime by assuming uniform magnetic field with strength B ∼ 0.1 nG and saturating the excess signal over the Cosmic Microwave Background (CMB) reported by radio telescopes such as the Experiment to Detect the Global EoR Signature (EDGES), LOw Frequency ARray (LOFAR), and Murchison Widefield Array (MWA), and the balloon-borne second generation Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE2) with graviton-induced photons. The upcoming Square Kilometer Array (SKA) can tighten these constraints by roughly 10 orders of magnitude, which will be a step closer to reaching the critical value of Ω_GW = 1 or the Big Bang Nucleosynthesis (BBN) bound of Ω_GW ≃ 1.2 × 10^-6. We point to future improvement of the SKA forecast and estimate that proposed CMB measurement at the level of (10^0-2) nK, such as Primordial Inflation Explorer (PIXIE) and Voyage 2050, are needed to viably detect stochastic backgrounds of HFGWs.

We describe a novel proposal for inflationary magnetogenesis by identifying the non-Abelian sector of Spectator Chromo Natural Inflation (SCNI) with the SU(2)_L sector of the Standard Model. This mechanism relies on the recently discovered attractor of SCNI in the strong backreaction regime, where the gauge fields do not decay on super-horizon scales and their backreaction leads to a stable new trajectory for the rolling axion field. The large super-horizon gauge fields are partly transformed after the electroweak phase transition into electromagnetic fields. The strength and correlation length of the resulting helical magnetic fields depend on the inflationary Hubble scale and the details of the SCNI sector. For suitable parameter choices we show that the strength of the resulting magnetic fields having correlation lengths around 1 Mpc are consistent with the required intergalactic magnetic fields for explaining the spectra of high energy γ rays from distant blazars.

The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here, we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence – even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker. 

In decaying magnetohydrodynamic (MHD) turbulence with a strong magnetic field, the spectral magnetic energy density is known to increase with time at small wavenumbers k, provided the spectrum at low k is sufficiently steep. This process is called inverse cascading and occurs for an initial Batchelor spectrum, where the magnetic energy per linear wavenumber interval increases like k(4). For an initial Saffman spectrum that is proportional to k(2), however, inverse cascading has not been found in the past. We study here the case of an intermediate k(3) spectrum, which may be relevant for magnetogenesis in the early Universe during the electroweak epoch. This case is not well understood in view of the standard Taylor expansion of the magnetic energy spectrum for small k. Using high resolution MHD simulations, we show that, also in this case, there is inverse cascading with a strength just as expected from the conservation of the Hosking integral, which governs the decay of an initial Batchelor spectrum. Even for shallower k(alpha) spectra with spectral index alpha > 3/2, our simulations suggest a spectral increase at small k with time t proportional to t(4 alpha/9-2/3). The critical spectral index of alpha = 3/2 is related to the slope of the spectral envelope in the Hosking phenomenology. Our simulations with 2048(3) mesh points now suggest inverse cascading even for an initial Saffman spectrum.

The interconversion of axionlike particles (ALPs) and photons in magnetized astrophysical environments provides a promising route to search for ALPs. The strongest limits to date on light ALPs use galaxy clusters as ALP-photon converters. However, such studies traditionally rely on simple models of the cluster magnetic fields, with the state-of-the-art being Gaussian random fields (GRFs). We present the first systematic study of ALP-photon conversion in more realistic, turbulent fields from dedicated magnetohydrodynamic (MHD) simulations, which we compare with GRF models. For GRFs, we analytically derive the distribution of conversion ratios at fixed energy and find that it follows an exponential law. We find that the MHD models agree with the exponential law for typical, small-amplitude mixings but exhibit distinctly heavy tails for rare and large mixings. We explain how non-Gaussian features, e.g., coherent structures and local spikes in the MHD magnetic field, are responsible for the heavy tail. Our results suggest that limits placed on ALPs using GRFs are robust.

We study the gravitational wave (GW) spectrum produced by acoustic waves in the early universe, such as would be produced by a first order phase transition, focusing on the low-frequency side of the peak. We confirm with numerical simulations the Sound Shell model prediction of a steep rise with wave number k of k⁹  to a peak whose magnitude grows at a rate (H/k_p)H, where H is the Hubble rate and k_p the peak wave number, set by the peak wave number of the fluid velocity power spectrum. We also show that hitherto neglected terms give a shallower part with amplitude (H/k_p)²  in the range H ≲ k ≲ k_p, which in the limit of small H/k rises as k. This linear rise has been seen in other modelling and also in direct numerical simulations. The relative amplitude between the linearly rising part and the peak therefore depends on the peak wave number of the velocity spectrum and the lifetime of the source, which in an expanding background is bounded above by the Hubble time H^-1. For slow phase transitions, which have the lowest peak wave number and the loudest signals, the acoustic GW peak appears as a localized enhancement of the spectrum, with a rise to the peak less steep than k⁹. The shape of the peak, absent in vortical turbulence, may help to lift degeneracies in phase transition parameter estimation at future GW observatories.

Generation of magnetic field during inflation can explain its presence over a wide range of scales in the Universe. In [Sharma et al Phys. Rev. D 96, 083511 (2017)], we proposed a model to generate these fields during inflation. These fields have nonzero anisotropic stress which lead to the generation of a stochastic background of gravitational waves (GW) in the early universe. Here we show that for a scenario of magnetogenesis where reheating takes place around QCD epoch, this stochastic GW background lies in the 95% confidence region of the stochastic common spectrum process probed by NANOGrav collaboration. This is the case when the generated electromagnetic field (EM) energy density is 3%–10% of the background energy density at the end of reheating. For this case, the values of magnetic field strength B₀∼(0.7–1.4)×10⁻¹¹  G and its coherence length ∼3  kpc at the present epoch. These values are for the models in which EM fields are of nonhelical nature. For the helical nature of the fields, these values are B₀∼(2.1–3.8)×10⁻¹⁰  G and its coherence length ∼90  kpc.

Hydrodynamic and magnetohydrodynamic turbulence in the early Universe can drive gravitational waves (GWs) and imprint their spectrum onto that of GWs, which might still be observable today. We study the production of the GW background from freely decaying magnetohydrodynamic turbulence from helical and nonhelical initial magnetic fields. To understand the produced GW spectra, we develop a simple model on the basis of the evolution of the magnetic stress tensor. We find that the GW spectra obtained in this model reproduce those obtained in numerical simulations if we consider the detailed time evolution of the low frequency tail of the stress spectrum from numerical simulations. We also show that the shapes of the produced GW frequency spectra are different for helical and nonhelical cases for the same initial magnetic energy spectra. Such differences can help distinguish helical and nonhelical initial magnetic fields from a polarized background of GWs—especially when the expected circular polarization cannot be detected directly.

The Saffman helicity invariant of Hosking & Schekochihin (Phys. Rev. X, vol. 11, issue 4, 2021, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated non-helical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfven time.