UA Faculty Research
http://hdl.handle.net/10150/595873
2018-12-13T05:58:43ZUnpeeling a Homoclinic Banana in the FitzHugh--Nagumo System
http://hdl.handle.net/10150/631146
Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System
Carter, Paul; Sandstede, Björn
The FitzHugh Nagumo equations are known to admit fast traveling pulse solutions with monotone tails. It is also known that this system admits traveling pulses with exponentially decaying oscillatory tails. Upon numerical continuation in parameter space, it has been observed that the oscillations in the tails of the pulses grow into a secondary excursion resembling a second copy of the primary pulse. In this paper, we outline in detail the geometric mechanism responsible for this single-to-double-pulse transition, and we construct the transition analytically using geometric singular perturbation theory and blow-up techniques.
2018-01-01T00:00:00ZThe maximum angular-diameter distance in cosmology
http://hdl.handle.net/10150/631145
The maximum angular-diameter distance in cosmology
Melia, Fulvio; Yennapureddy, Manoj K.
Unlike other observational signatures in cosmology, the angular-diameter distance dA(z) uniquely reaches a maximum (at zmax) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use zmax inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing dA(z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of zmax can effectively discriminate between them. We find that zmax = 1.70 ± 0.20 – an important new probe of the Universe’s geometry. The most strongly favoured model is Rh = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the Rh = ct universe, which predicts zmax = 1.718, has a ∼92.8 per cent probability of being the correct cosmology. For consistency, we also carry out model selection based on dA(z) itself. This test confirms that Rh = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by zmax. The dA(z) comparison, however, is less discerning than that with zmax, due to the additional free parameter, H0. We find that H0 = 63.4 ± 1.2 km s−1 Mpc−1 for Rh = ct, and 69.9 ± 1.5 km s−1 Mpc−1 for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on zmax is independent of H0.
2018-07-23T00:00:00ZModel selection with strong-lensing systems
http://hdl.handle.net/10150/631144
Model selection with strong-lensing systems
Leaf, Kyle; Melia, Fulvio
In this paper, we use an unprecedentedly large sample (158) of confirmed strong lens systems for model selection, comparing five well-studied Friedmann–Robertson–Walker cosmologies: ΛCDM, wCDM (the standard model with a variable dark-energy equation of state), the Rh = ct universe, the (empty) Milne cosmology, and the classical Einstein-de Sitter (matter-dominated) universe. We first use these sources to optimize the parameters in the standard model and show that they are consistent with Planck, though the quality of the best fit is not satisfactory. We demonstrate that this is likely due to underreported errors, or to errors yet to be included in this kind of analysis. We suggest that the missing dispersion may be due to scatter about a pure single isothermal sphere (SIS) model that is often assumed for the mass distribution in these lenses. We then use the Bayes information criterion, with the inclusion of a suggested SIS dispersion, to calculate the relative likelihoods and ranking of these models, showing that Milne and Einstein-de Sitter are completely ruled out, while Rh = ct is preferred over ΛCDM/wCDM with a relative probability of ∼73percent versus ∼24percent. The recently reported sample of new strong lens candidates by the Dark Energy Survey, if confirmed, may be able to demonstrate which of these two models is favoured over the other at a level exceeding 3σ.
2018-05-24T00:00:00ZThe apparent (gravitational) horizon in cosmology
http://hdl.handle.net/10150/631143
The apparent (gravitational) horizon in cosmology
Melia, Fulvio
In general relativity, a gravitational horizon (more commonly known as the "apparent horizon") an imaginary surface beyond which all null geodesics recede from the observer. The Universe has an apparent (gravitational) horizon, but unlike its counterpart in the Schwarzschild and Kerr metrics, it is not static. It may eventually turn into an event horizon-an asymptotically defined membrane that forever separates causally connected events from those that are not-depending on the equation of state of the cosmic fluid. In this paper, we examine how and why an apparent (gravitational) horizon is manifested in the Friedmann-Robertson-Walker metric, and why it is becoming so pivotal to our correct interpretation of the cosmological data. We discuss its observational signature and demonstrate how it alone defines the proper size of our visible Universe. In so doing, we affirm its physical reality and its impact on cosmological models. (C) 2018 American Association of Physics Teachers.
2018-08-01T00:00:00Z