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Detecting the Stochastic Gravitational Wave Background from Primordial Black Hole Formation

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 Added by Sebastien Clesse
 Publication date 2018
  fields Physics
and research's language is English




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Primordial Black Holes (PBH) from peaks in the curvature power spectrum could constitute today an important fraction of the Dark Matter in the Universe. At horizon reentry, during the radiation era, order one fluctuations collapse gravitationally to form black holes and, at the same time, generate a stochastic background of gravitational waves coming from second order anisotropic stresses in matter. We study the amplitude and shape of this background for several phenomenological models of the curvature power spectrum that can be embedded in waterfall hybrid inflation, axion, domain wall, and boosts of PBH formation at the QCD transition. For a broad peak or a nearly scale invariant spectrum, this stochastic background is generically enhanced by about one order of magnitude, compared to a sharp feature. As a result, stellar-mass PBH from Gaussian fluctuations with a wide mass distribution are already in strong tension with the limits from Pulsar Timing Arrays, if they constitute a non negligible fraction of the Dark Matter. But this result is mitigated by the uncertainties on the curvature threshold leading to PBH formation. LISA will have the sensitivity to detect or rule out light PBH down to $10^{-14} M_{odot}$. Upcoming runs of LIGO/Virgo and future interferometers such as the Einstein Telescope will increase the frequency lever arm to constrain PBH from the QCD transition. Ultimately, the future SKA Pulsar Timing Arrays could probe the existence of even a single stellar-mass PBH in our Observable Universe.



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We investigate the stochastic gravitational wave background produced by primordial black hole binaries during their early inspiral stage while accreting high-density radiation surrounding them in the early universe. We first show that the gravitational wave amplitude produced from a primordial black hole binary has correction terms because of the rapid rate of increase in masses of the primordial black holes. These correction terms arise due to non-vanishing first and second time derivatives of the masses and their contribution to the overall second time derivative of quadrupole moment tensor. We find that some of these correction terms are not only significant in comparison with the main term but even dominant over the main term for certain ranges of time in the early Universe. The significance of these correction terms is not only for the gravitational wave amplitude produced from an individual PBH-binary, but persists for the overall stochastic gravitational wave background produced from them. We show that the spectral density produced from such accreting primordial black hole binaries lie within the detectability range of some present and future gravitational wave detectors.
The black hole merging rates inferred after the gravitational-wave detection by Advanced LIGO/VIRGO and the relatively high mass of the progenitors are consistent with models of dark matter made of massive primordial black holes (PBH). PBH binaries emit gravitational waves in a broad range of frequencies that will be probed by future space interferometers (LISA) and pulsar timing arrays (PTA). The amplitude of the stochastic gravitational-wave background expected for PBH dark matter is calculated taking into account various effects such as initial eccentricity of binaries, PBH velocities, mass distribution and clustering. It allows a detection by the LISA space interferometer, and possibly by the PTA of the SKA radio-telescope. Interestingly, one can distinguish this background from the one of non-primordial massive binaries through a specific frequency dependence, resulting from the maximal impact parameter of binaries formed by PBH capture, depending on the PBH velocity distribution and their clustering properties. Moreover, we find that the gravitational wave spectrum is boosted by the width of PBH mass distribution, compared with that of the monochromatic spectrum. The current PTA constraints already rule out broad-mass PBH models covering more than three decades of masses, but evading the microlensing and CMB constraints due to clustering.
83 - Tomohiro Harada 2016
Primordial black holes (PBHs) are those which may have formed in the early Universe and affected the subsequent evolution of the Universe through their Hawking radiation and gravitational field. To constrain the early Universe from the observational constraint on the abundance of PBHs, it is essential to determine the formation threshold for primordial cosmological fluctuations, which are naturally described by cosmological long-wavelength solutions. I will briefly review our recent analytical and numerical results on the PBH formation.
The merger rate of black hole binaries inferred from the detections in the first Advanced LIGO science run, implies that a stochastic background produced by a cosmological population of mergers will likely mask the primordial gravitational-wave background. Here we demonstrate that the next generation of ground-based detectors, such as the Einstein Telescope and Cosmic Explorer, will be able to observe binary black hole mergers throughout the universe with sufficient efficiency that the confusion background can potentially be subtracted to observe the primordial background at the level of $Omega_{mathrm{GW}} simeq 10^{-13}$ after five years of observation.
We do a complete calculation of the stochastic gravitational wave background to be expected from cosmic strings. We start from a population of string loops taken from simulations, smooth these by Lorentzian convolution as a model of gravitational back reaction, calculate the average spectrum of gravitational waves emitted by the string population at any given time, and propagate it through a standard model cosmology to find the stochastic background today. We take into account all known effects, including changes in the number of cosmological relativistic degrees of freedom at early times and the possibility that some energy is in rare bursts that we might never have observed.
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