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 ΩGW at 16 different frequency bands. Given the observed magnetisation of galaxy clusters with field strength B ∼ μG correlated on O(10) kpc scales, we estimate HFGW constraints in the O(102) GHz regime to be ΩGW ≲ 1016 with the temperature measurements of the Atacama Cosmology Telescope (ACT). Similarly, we conservatively obtain ΩGW ≲ 1013 (1011) in the O(102) MHz (O(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 ΩGW = 1 or the Big Bang Nucleosynthesis (BBN) bound of ΩGW ≃ 1.2 × 10-6. We point to future improvement of the SKA forecast and estimate that proposed CMB measurement at the level of O(100-2) nK, such as Primordial Inflation Explorer (PIXIE) and Voyage 2050, are needed to viably detect stochastic backgrounds of HFGWs.

We study the propagation of cosmological gravitational wave (GW) backgrounds from the early radiation era until the present day in modified theories of gravity. Comparing to general relativity (GR), we study the effects that modified gravity parameters, such as the GW friction & alpha;M and the tensor speed excess & alpha;T, have on the present-day GW spectrum. We use both the WKB estimate, which provides an analytical description but fails at superhorizon scales, and numerical simulations that allow us to go beyond the WKB approximation. We show that a constant & alpha;T makes relatively insignificant changes to the GR solution, especially taking into account the constraints on its value from GW observations by the LIGO-Virgo collaboration, while & alpha;M can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of & alpha;M. The latter effect is additional to the damping or growth occurring equally at all scales that can be predicted by the WKB approximation. In light of the recent observations by pulsar timing array (PTA) collaborations, and the potential observations by future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most of the cases, constraints cannot be placed on the effects of & alpha;M and the initial GW energy density E*GW separately, but only on the combined effects of the two, unless the signal is observed at different frequency ranges. In particular, we provide some constraints on the combined effects from the reported PTA observations.

We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about 10(-9) of the critical energy density in the nHz range today and may already have been observed by the NANOGrav Collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions.

Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3 x 10(5) GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one. Both in the helical and nonhelical cases, the GW spectrum is followed by a sharp drop for frequencies above the respective peak frequency. In this magnetogenesis scenario, the presence of a helical term extends the peak of the GW spectrum and therefore also the position of the aforementioned drop toward larger frequencies compared to the case without helicity. This might make a difference in it being detectable with space interferometers. The efficiency of GW production is found to be almost the same as in the nonhelical case, and independent of the reheating temperature, provided the electromagnetic energy at the end of reheating is fixed to be a certain fraction of the radiation energy density. Also, contrary to the case without helicity, the electric energy is now less than the magnetic energy during reheating. The fractional circular polarization is found to be nearly 100% in a certain range below the peak frequency range.

We consider a generic dispersive massive gravity theory and numerically study its resulting modified energy and strain spectra of tensor gravitational waves (GWs) sourced by (i) fully developed turbulence during the electroweak phase transition (EWPT) and (ii) forced hydromagnetic turbulence during the QCD phase transition (QCDPT). The GW spectra are then computed in both spatial and temporal Fourier domains. We find, from the spatial spectra, that the slope modifications are weakly dependent on the eddy size at QCDPT, and, from the temporal spectra, that the modifications are pronounced in the 1-10 nHz range the sensitivity range of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) for a graviton mass mg in the range 2 x 10(-23) eV ,less than or similar to m(g)c(2) less than or similar to 7 x 10(-22) eV.