Planck Length Scale Research Articles

Constraints on the mass spectrum of primordial black holes and braneworld parameters from the high-energy diffuse photon background

We investigate the spectral shape of a high-energy diffuse photon emitted by evaporating primordial black holes (PBHs) in the Randall-Sundrum type II (RS2) braneworld. In their braneworld scenario, the nature of small PBHs is drastically modified from the ordinary four-dimensional case for the following two reasons. (i) dropping Hawking temperature, which equivalently lengthens the lifetime of the individual PBH due to the change of space-time topology and (ii) the effective increase of the total amount of PBHs caused by accretion during the earliest part of the radiation-dominated epoch, the brane high-energy phase. From studies of the expected spectral shape and its dependence on braneworld parameters, we obtain two qualitatively distinctive possibilities of constraints on the braneworld PBHs from the observations of diffuse high-energy photon background. If the efficiency of accretion in the high-energy phase exceeds a critical value, the existence of the extra dimension gives a more stringent upper bound on the abundance of PBHs than the 4D case and a small length scale for the extra dimension is favored. On the contrary, in the case below the critical accretion efficiency, we find that the constraint on the PBH abundance can be relaxed by a few orders of magnitude in exchange for the existence of the large extra dimension; its size may be even bounded in the region above 10^{19} times 4D Planck length scale provided the rest mass energy density of the PBHs relative to energy density of radiation is actually larger than 10^{-27} (4D upper bound) at their formation time. The above analytical studies are also confirmed numerically, and an allowed region for braneworld parameters and PBH abundance is clearly obtained.

QUANTUM GRAVITY CORRECTIONS TO PARTICLE INTERACTIONS

An heuristic semiclassical procedure that incorporates quantum gravity induced corrections in the description of photons and spin 1/2 fermions is reviewed. Such modifications are calculated in the framework of loop quantum gravity and they arise from the granular structure of space at short distances. The resulting effective theories are described by power counting non-renormalizable actions which exhibit Lorentz violations at Planck length scale. The modified Maxwell an Dirac equations lead to corrections of the energy momentum relations for the corresponding particle at such scale. An action for the relativistic point particle exhibiting such modified dispersion relations is constructed and the first steps towards the study of a consistent coupling between these effective theories are presented.

Observer-independent quantum of mass

It has been observed recently by Amelino-Camelia that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this Letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the value of mass scale is the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed in the framework of the quantum κ-Poincaré symmetry. It follows that at the Planck scale the world may be non-relativistic.

Cosmogenesis and the origin of the fundamental length scale

The creation of the universe is regarded as a self-consistent process in which matter is engendered by the space-time varying cosmological gravitational field and vice versa. Abundant production can occur only if the mass of the particles so created is of the order of the Planck mass ( = κ − 1 2 . We conjecture that this is the origin of the fundamental length scale in field theory, as it is encountered, for example, in present efforts towards grandunification. The region of particle production is steady state in character. It ceases when the produced particles decay. The geometry of this steady state is characteristic of a de Sitter space. It permits one to estimate the number of ordinary particles presently observed, N. We find log N = O ( mτ decay) = O( g −2) = O(10 2) , with the usual estimate of g = O(10 − at the Planck length scale. This is not inconsistent with the experimental estimate N ⋍ O(10 90) . After production, cosmological history gives way to the more conventional scheme of free expansion. The present paper is a self-contained account of our view of cosmological history and the production of matter in a varying gravitational field. Special care has been taken to describe the vacuum correctly in the present context and to perform the necessary subtractions of zero-point effects.