Diffuse $γ$-ray background and primordial black hole constraints on the spectral index of density fluctuations

Details Diffuse $γ$-ray background and primordial black hole constraints on the spectral index of density fluctuations Diffuse $γ$-ray background and primordial black hole constraints on the spectral index of density fluctuations

1999-01-05

arxiv.org/abs/astro-ph/9901030v1

Phys.Rev. D59 (1999) 063004

Astronomy and Astrophysics

Astrophysics

To be published in the Feb 15, 1999 issue of Phys. Rev. D (22 pages, 3 figures)

Scientific paper

10.1103/PhysRevD.59.063004

We calculate the flux of $\gamma$-rays emitted from primordial black holes (PBHs) which are formed by a ``blue'' power-law spectrum of density fluctuations in the early universe. Gamma-ray emission from such PBHs may contribute significantly to the observed extragalactic diffuse $\gamma$-ray background (DGB). Using the observed DGB flux from the imaging Compton Telescope (COMPTEL) and the Energetic Gamma Ray Experiment Telescope (EGRET) as the upper limit of $\gamma$-ray flux from PBHs, we derive the upper limit on the spectral index $n$ of the density fluctuations. The range of initial PBH masses which can contribute to the DGB is $2\times 10^{13}\g - 5\times 10^{14}\g$, corresponding to a cosmic reheating temperature of $7\times 10^{7}\gev - 4\times 10^{8} \gev$. In this range, we find the upper limit to be $n \lsim 1.23-1.25$. This limit is stronger than those derived from the energy density in PBHs or PBH relics and matches the value of $n$ required to explain the cosmic microwave background anisotropy.

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