527 research outputs found
Evolution of a Primordial Black Hole Population
We reconsider in this work the effects of an energy absorption term in the
evolution of primordial black holes (hereafter PBHs) in the several epochs of
the Universe. A critical mass is introduced as a boundary between the accreting
and evaporating regimes of the PBHs. We show that the growth of PBHs is
negligible in the Radiation-dominated Era due to scarcity of energy density
supply from the expanding background, in agreement with a previous analysis by
Carr and Hawking, but that nevertheless the absorption term is large enough for
black holes above the critical mass to preclude their evaporation until the
universe has cooled sufficiently. The effects of PBH motion are also discussed:
the Doppler effect may give rise to energy accretion in black-holes with large
peculiar motions relative to background. We discuss how cosmological
constraints are modified by the introduction of the critical mass since that
PBHs above it do not disturb the CMBR. We show that there is a large range of
admissible masses for PBHs above the critical mass but well below the
cosmological horizon. Finally we outline a minimal kinetic formalism, solved in
some limiting cases, to deal with more complicated cases of PBH populationsComment: RevTex file, 8 pp., 3 .ps figures available upon request from
[email protected]
Bounds from Primordial Black Holes with a Near Critical Collapse Initial Mass Function
Recent numerical evidence suggests that a mass spectrum of primordial black
holes (PBHs) is produced as a consequence of near critical gravitational
collapse. Assuming that these holes formed from the initial density
perturbations seeded by inflation, we calculate model independent upper bounds
on the mass variance at the reheating temperature by requiring the mass density
not exceed the critical density and the photon emission not exceed current
diffuse gamma-ray measurements. We then translate these results into bounds on
the spectral index n by utilizing the COBE data to normalize the mass variance
at large scales, assuming a constant power law, then scaling this result to the
reheating temperature. We find that our bounds on n differ substantially
(\delta n > 0.05) from those calculated using initial mass functions derived
under the assumption that the black hole mass is proportional to the horizon
mass at the collapse epoch. We also find a change in the shape of the diffuse
gamma-ray spectrum which results from the Hawking radiation. Finally, we study
the impact of a nonzero cosmological constant and find that the bounds on n are
strengthened considerably if the universe is indeed vacuum-energy dominated
today.Comment: 24 pages, REVTeX, 5 figures; minor typos fixed, two refs added,
version to be published in PR
Viability of primordial black holes as short period gamma-ray bursts
It has been proposed that the short period gamma-ray bursts, which occur at a
rate of , may be evaporating primordial black holes
(PBHs). Calculations of the present PBH evaporation rate have traditionally
assumed that the PBH mass function varies as . This mass
function only arises if the density perturbations from which the PBHs form have
a scale invariant power spectrum. It is now known that for a scale invariant
power spectrum, normalised to COBE on large scales, the PBH density is
completely negligible, so that this mass function is cosmologically irrelevant.
For non-scale-invariant power spectra, if all PBHs which form at given epoch
have a fixed mass then the PBH mass function is sharply peaked around that
mass, whilst if the PBH mass depends on the size of the density perturbation
from which it forms, as is expected when critical phenomena are taken into
account, then the PBH mass function will be far broader than . In this paper we calculate the present day PBH evaporation rate,
using constraints from the diffuse gamma-ray background, for both of these mass
functions. If the PBH mass function has significant finite width, as recent
numerical simulations suggest, then it is not possible to produce a present day
PBH evaporation rate comparable with the observed short period gamma-ray burst
rate. This could also have implications for other attempts to detect
evaporating PBHs.Comment: 5 pages, 2 figures, version to appear in Phys. Rev. D with additional
reference
Constraints on diffuse neutrino background from primordial black holes
We calculated the energy spectra and the fluxes of electron neutrino emitted
in the process of evaporation of primordial black holes (PBHs) in the early
universe. It was assumed that PBHs are formed by a blue power-law spectrum of
primordial density fluctuations. We obtained the bounds on the spectral index
of density fluctuations assuming validity of the standard picture of
gravitational collapse and using the available data of several experiments with
atmospheric and solar neutrinos. The comparison of our results with the
previous constraints (which had been obtained using diffuse photon background
data) shows that such bounds are quite sensitive to an assumed form of the
initial PBH mass function.Comment: 18 pages,(with 7 figures
Robust pricing and hedging of double no-touch options
Double no-touch options, contracts which pay out a fixed amount provided an
underlying asset remains within a given interval, are commonly traded,
particularly in FX markets. In this work, we establish model-free bounds on the
price of these options based on the prices of more liquidly traded options
(call and digital call options). Key steps are the construction of super- and
sub-hedging strategies to establish the bounds, and the use of Skorokhod
embedding techniques to show the bounds are the best possible.
In addition to establishing rigorous bounds, we consider carefully what is
meant by arbitrage in settings where there is no {\it a priori} known
probability measure. We discuss two natural extensions of the notion of
arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are
needed to establish equivalence between the lack of arbitrage and the existence
of a market model.Comment: 32 pages, 5 figure
Primordial black holes in braneworld cosmologies: astrophysical constraints
In two recent papers we explored the modifications to primordial black hole
physics when one moves to the simplest braneworld model, Randall--Sundrum type
II. Both the evaporation law and the cosmological evolution of the population
can be modified, and additionally accretion of energy from the background can
be dominant over evaporation at high energies. In this paper we present a
detailed study of how this impacts upon various astrophysical constraints,
analyzing constraints from the present density, from the present high-energy
photon background radiation, from distortion of the microwave background
spectrum, and from processes affecting light element abundances both during and
after nucleosynthesis. Typically, the constraints on the formation rate of
primordial black holes weaken as compared to the standard cosmology if black
hole accretion is unimportant at high energies, but can be strengthened in the
case of efficient accretion.Comment: 17 pages RevTeX4 file with three figures incorporated; final paper in
series astro-ph/0205149 and astro-ph/0208299. Minor changes to match version
accepted by Physical Review
Multidimensional collaboration; reflections on action research in a clinical context
This paper reflects on the challenges and benefits of multidimensional collaboration in an action research study to evaluate and improve preoperative education for patients awaiting colorectal surgery. Three cycles of planning, acting,observing and reflecting were designed to evaluate practice and implement change in this interactive setting, calling for specific and distinct collaborations. Data collection includes: observing educational interactions; administering patient evaluation questionnaires; interviewing healthcare staff, patients and carers; patient and carer focus groups; and examining written and audiovisual educational materials. The study revolves around and depends on multi-dimensional collaborations. Reflecting on these collaborations highlights the diversity of perspectives held by all those engaged in the study and enhances the action research lessons. Successfully maintaining the collaborations recognises the need for negotiation, inclusivity, comprehension, brokerage,and problem-solving. Managing the potential tensions is crucial to the successful implementation of changes introduced to practice and thus has important implications for patients’ well-being. This paper describes the experiences from an action research project involving new and specific collaborations, focusing on a particular healthcare setting. It exemplifies the challenges of the collaborative action research process and examines how both researchers and practitioners might reflect on the translation of theory into educational practices within a hospital colorectal department. Despite its context-specific features, the reflections on the types of challenges faced and lessons learned provide implications for action researchers in diverse healthcare settings across the world
Primordial black holes in braneworld cosmologies: Accretion after formation
We recently studied the formation and evaporation of primordial black holes
in a simple braneworld cosmology, namely Randall-Sundrum Type II. Here we study
the effect of accretion from the cosmological background onto the black holes
after formation. While it is generally believed that in the standard cosmology
such accretion is of negligible importance, we find that during the high-energy
regime of braneworld cosmology accretion can be the dominant effect and lead to
a mass increase of potentially orders of magnitude. However, unfortunately the
growth is exponentially sensitive to the accretion efficiency, which cannot be
determined accurately. Since accretion becomes unimportant once the high-energy
regime is over, it does not affect any constraints expressed at the time of
black hole evaporation, but it can change the interpretation of those
constraints in terms of early Universe formation rates.Comment: 6 pages RevTeX4 file. Extension to discussion of thermal balance and
grey-body factor
Football in the community schemes: Exploring the effectiveness of an intervention in promoting healthful behaviour change
This study aims to examine the effectiveness of a Premier League football club’s Football in the Community (FitC) schemes intervention in promoting positive healthful behaviour change in children. Specifically, exploring the effectiveness of this intervention from the perspectives of the participants involved (i.e. the researcher, teachers, children and coaches). A range of data collection techniques were utilized including the principles of ethnography (i.e. immersion, engagement and observations), alongside conducting focus groups with the children. The results allude to the intervention merely ‘keeping active children active’ via (mostly) fun, football sessions. Results highlight the important contribution the ‘coach’ plays in the effectiveness of the intervention. Results relating to working practice (i.e. coaching practice and coach recruitment) are discussed and highlighted as areas to be addressed. FitC schemes appear to require a process of positive organizational change to increase their effectiveness in strategically attending to the health agenda
Brans-Dicke Theory and primordial black holes in Early Matter-Dominated Era
We show that primordial black holes can be formed in the matter-dominated era
with gravity described by the Brans-Dicke theory. Considering an early
matter-dominated era between inflation and reheating, we found that the
primordial black holes formed during that era evaporate at a quicker than those
of early radiation-dominated era. Thus, in comparison with latter case, less
number of primordial black holes could exist today. Again the constraints on
primordial black hole formation tend towards the larger value than their
radiation-dominated era counterparts indicating a significant enhancement in
the formation of primordial black holes during the matter-dominaed era.Comment: 9 page
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