Nearly scale-invariant power spectrum and quantum cosmological perturbations in the gravity’s rainbow scenario

Abstract We modify the procedure to estimate PBH abundance proposed in Ref. [1] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation △ ζ and use the values of △ ζ and △ △ ζ at each peak to specify the profile of ζ as a function of the radial coordinate while the values of ζ and △ ζ are used in Ref. [1]. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in Ref. [1]. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the k-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the k-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

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HAWKING RADIATION VIA TUNNELING OF MASSIVE PARTICLES FROM A GRAVITY'S RAINBOW

Modern Physics Letters A ◽

10.1142/s0217732310034341 ◽

2010 ◽

Vol 25 (38) ◽

pp. 3229-3240 ◽

Cited By ~ 5

Author(s):

CHENG-ZHOU LIU

Keyword(s):

Black Holes ◽

Hawking Radiation ◽

Quantum Effect ◽

Massive Particle ◽

Planck Scale ◽

Gravity’S Rainbow ◽

Gravity's Rainbow ◽

Corrected Entropy ◽

Massive Particles ◽

Massive Particle Tunneling

In the tunneling framework of Hawking radiation, the quantum tunneling of massive particles in the modified Schwarzschild black holes from gravity's rainbow is investigated. While the massive particle tunneling from the event horizon, the metric fluctuation is taken into account, not only due to energy conservation but also to the Planck scale effect of spacetime. The obtained results show that, the emission rate is related to changes of the black hole's quantum corrected entropies before and after the emission. This implies that, considering the quantum effect of spacetime, information conservation of black holes is probable. Meanwhile, the quantum corrected entropy of the modified black hole is obtained and the leading correction behave as log-area type. And that, the emission spectrum with Planck scale correction is obtained and it deviates from the thermal spectrum.

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De Nostalgia

Cultural Politics an International Journal ◽

10.1215/17432197-3342008 ◽

2015 ◽

Vol 11 (3) ◽

pp. 395-406

Author(s):

Friedrich Kittler

Keyword(s):

Technology Transfer ◽

Second World War ◽

Discursive Construction ◽

World War ◽

Gravity’S Rainbow ◽

Gravity's Rainbow ◽

Complete Destruction ◽

Second World ◽

Home Territory

The essay presents a reading of three war-related texts: Friedrich Schiller’s Wilhelm Tell, Heinrich von Kleist’s The Battle of Hermann, and Thomas Pynchon’s Gravity’s Rainbow. Written against the background of the Revolutionary Wars and the Prussian Wars of Liberation, respectively, the plays by Schiller and Kleist engage in the discursive construction of an emphatic sense of heimat (home), either by way of creating the new sentiment of homesickness (originally called nostalgia) or by advocating the complete destruction of the very home territory you are trying to defend. Gravity’s Rainbow, in turn, decodes the Second World War as a massive exercise in technology transfer. It effectively presents a deconstruction of heimat in an age in which the imperative to merge technologies supersedes all national agendas.

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