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Register a new userNew constraints on quantum foam models from X-ray and gamma-ray observations of distant quasars
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Astronomical observations of distant quasars may be important to test models for quantum gravity, which posit Planck-scale spatial uncertainties (spacetime foam) that would produce phase fluctuations in the wavefront of radiation emitted by a source, which may accumulate over large path lengths. We show explicitly how wavefront distortions cause the image intensity to decay to the point where distant objects become undetectable if the accumulated path-length fluctuations become comparable to the wavelength of the radiation. We also reassess previous efforts in this area. We use X-ray and gamma-ray observations to rule out several models of spacetime foam, including the interesting random-walk and holographic models.
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One aspect of the quantum nature of spacetime is its foaminess at very small scales. Many models for spacetime foam are defined by the accumulation power $alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $alpha$ is defined by theexpression for the path-length fluctuations, $delta ell$, of a source at distance $ell$, wherein $delta ell simeq ell^{1 - alpha} ell_P^{alpha}$, with $ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {em Chandra} to set the constraint $alpha gtrsim 0.58$, which rules out the random walk model (with $alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $alpha gtrsim 0.67$ and $alpha gtrsim 0.72$, respectively. These limits on $alpha$ seem to rule out $alpha = 2/3$, the model of some physical interest.
The fraction of the Universe going into primordial black holes (PBHs) with initial mass M_* approx 5 times 10^{14} g, such that they are evaporating at the present epoch, is strongly constrained by observations of both the extragalactic and Galactic gamma-ray backgrounds. However, while the dominant contribution to the extragalactic background comes from the time-integrated emission of PBHs with initial mass M_*, the Galactic background is dominated by the instantaneous emission of those with initial mass slightly larger than M_* and current mass below M_*. Also, the instantaneous emission of PBHs smaller than 0.4 M_* mostly comprises secondary particles produced by the decay of directly emitted quark and gluon jets. These points were missed in the earlier analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass function, with initial mass (1+mu) M_* and mu << 1, the current mass is (3mu)^{1/3} M_* and the Galactic background constrains the fraction of the Universe going into PBHs as a function of mu. However, the initial mass function cannot be precisely monochromatic and even a tiny spread of mass around M_* would generate a current low-mass tail of PBHs below M_*. This tail would be the main contributor to the Galactic background, so we consider its form and the associated constraints for a variety of scenarios with both extended and nearly-monochromatic initial mass functions. In particular, we consider a scenario in which the PBHs form from critical collapse and have a mass function which peaks well above M_*. In this case, the largest PBHs could provide the dark matter without the M_* ones exceeding the gamma-ray background limits.
Aims. The small-scale nature of spacetime can be tested with observations of distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533, 71) which claims that Hubble Space Telescope observations of the most distant quasars place severe constraints on models of foamy spacetime. Methods. If space is foamy on the Planck scale, photons emitted from distant objects will accumulate uncertainties in distance and propagation directions thus affecting the expected angular size of a compact object as a function of redshift. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We also address the mechanics of carrying out such a test. We draw upon our previously published work on this subject (Christiansen et al. 2011), which carried out similar tests as Tamburini et al. and also went considerably beyond their work in several respects. Results. When calculating the path taken by photons as they travel from a distant source to Earth, one must use the comoving distance rather than the luminosity distance. This then also becomes the appropriate distance to use when calculating the angular broadening expected in a distant source. The use of the wrong distance measure causes Tamburini et al. to overstate the constraints that can be placed on models of spacetime foam. In addition, we consider the impact of different ways of parametrizing and measuring the effects of spacetime foam. Given the variation of the shape of the point-spread function (PSF) on the chip, as well as observation-specific factors, it is important to select carefully -- and document -- the comparison stars used as well as the methods used to compute the Strehl ratio.
We use measurements of the peak photon energy and bolometric fluence of 119 gamma-ray bursts (GRBs) extending over the redshift range of $0.3399 leq z leq 8.2$ to simultaneously determine cosmological and Amati relation parameters in six different cosmological models. The resulting Amati relation parameters are almost identical in all six cosmological models, thus validating the use of the Amati relation in standardizing these GRBs. The GRB data cosmological parameter constraints are consistent with, but significantly less restrictive than, those obtained from a joint analysis of baryon acoustic oscillation and Hubble parameter measurements.
The Hubble constant, $H_0$, sets the scale of the size and age of the Universe and its determination from independent methods is still worthwhile to be investigated. In this article, by using the Sunyaev-Zel`dovich effect and X-ray surface brightness data from 38 galaxy clusters observed by Bonamente {it{et al.}} (2006), we obtain a new estimate of $H_0$ in the context of a flat $Lambda$CDM model. There is a degeneracy on the mass density parameter ($Omega_{m}$) which is broken by applying a joint analysis involving the baryon acoustic oscillations (BAO) as given by Sloan Digital Sky Survey (SDSS). This happens because the BAO signature does not depend on $H_0$. Our basic finding is that a joint analysis involving these tests yield $H_0= 0.765^{+0.035}_{-0.033}$ km s$^{-1}$ Mpc$^{-1}$ and $Omega_{m}=0.27^{+0.03}_{-0.02}$. Since the hypothesis of spherical geometry assumed by Bonamente {it {et al.}} is questionable, we have also compared the above results to a recent work where a sample of triaxial galaxy clusters has been considered.
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