Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band

The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA) Collaborations have reported evidence for a common-spectrum process that can potentially correspond to a stochastic gravitational wave background (SGWB) in the 1-100 nHz frequency range. We consider the scenario in which this signal is produced by magnetohydrodynamic (MHD) turbulence in the early Universe, induced by a nonhelical primordial magnetic field at the energy scale corresponding to the quark confinement phase transition. We perform MHD simulations to study the dynamical evolution of the magnetic field and compute the resulting SGWB. We show that the SGWB output from the simulations can be very well approximated by assuming that the magnetic anisotropic stress is constant in time, over a time interval related to the eddy turnover time. The analytical spectrum that we derive under this assumption features a change of slope at a frequency corresponding to the GW source duration that we confirm with the numerical simulations. We compare the SGWB signal with the PTA data to constrain the temperature scale at which the SGWB is sourced, as well as the amplitude and characteristic scale of the initial magnetic field. We find that the generation temperature is constrained to be in the 1-200 MeV range, the magnetic field amplitude must be >1% of the radiation energy density at that time, and the magnetic field characteristic scale is constrained to be >10% of the horizon scale. We show that the turbulent decay of this magnetic field will lead to a field at recombination that can help to alleviate the Hubble tension and can be tested by measurements in the voids of the Large Scale Structure with gamma-ray telescopes like the Cherenkov Telescope Array.

Energetics of turbulence generated by chiral MHD dynamos

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, PrM. In particular, we determine the ratio of kinetic to magnetic energy, Υ, in chiral magnetically driven turbulence. Within the parameter space explored in this study, Υ reaches a value of approximately 0.064–0.074–independently of the initial chiral asymmetry and for PrM=1. Our simulations suggest, that Υ decreases as a power law when increasing PrM by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of Υ(PrM)=0.1 Pr−0.4M is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.

TAYLOR & FRANCIS LTD2019

Ability of LIGO and LISA to probe the equation of state of the early Universe

Daniel Garcia Figueroa

The expansion history of the Universe between the end of inflation and the onset of radiation-domination (RD) is currently unknown. If the equation of state during this period is stiffer than that of radiation, w > 1/3, the gravitational wave (GW) background from inflation acquires a blue-tilt d log rho GW/d log f = 2(w-1/3)/(w+1/3) > 0 at frequencies f >> f(RD) corresponding to modes re-entering the horizon during the stiff-domination (SD), where f(RD) is the frequency today of the horizon scale at the SD-to-RD transition. We characterized in detail the transfer function of the GW energy density spectrum, considering both 'instant' and smooth modelings of the SD-to-RD transition. The shape of the spectrum is controlled by w, f(RD), and H-inf (the Hubble scale of inflation). We determined the parameter space compatible with a detection of this signal by LIGO and LISA, including possible changes in the number of relativistic degrees of freedom, and the presence of a tensor tilt. Consistency with upper bounds on stochastic GW backgrounds, however, rules out a significant fraction of the observable parameter space. We find that this renders the signal unobservable by Advanced LIGO, in all cases. The GW background remains detectable by LISA, though only in a small island of parameter space, corresponding to scenarios with an equation of state in the range 0.46 less than or similar to w less than or similar to 0.56 and a high inflationary scale H-inf greater than or similar to 10(13) GeV, but low reheating temperature 1 MeV less than or similar to T-RD less than or similar to 150 MeV (equivalently, 10(-11) Hz less than or similar to f(RD) less than or similar to 3.6.10(-9) Hz). Implications for early Universe scenarios resting upon an SD epoch are briefly discussed.

IOP PUBLISHING LTD2019

Potential of Radio Telescopes as High-Frequency Gravitational Wave Detectors

Valerie Fiona Domcke

In the presence of magnetic fields, gravitational waves are converted into photons and vice versa. We demonstrate that this conversion leads to a distortion of the cosmic microwave background (CMB), which can serve as a detector for MHz to GHz gravitational wave sources active before reionization. The measurements of the radio telescope EDGES can be cast as a bound on the gravitational wave amplitude, h(c) < 10(-21) (10(-12)) at 78 MHz, for the strongest (weakest) cosmic magnetic fields allowed by current astrophysical and cosmological constraints. Similarly, the results of ARCADE 2 imply h(c) < 10(-24) (10(-14)) at 3-30 GHz. For the strongest magnetic fields, these constraints exceed current laboratory constraints by about 7 orders of magnitude. Future advances in 21 cm astronomy may conceivably push these bounds below the sensitivity of cosmological constraints on the total energy density of gravitational waves.

2021