Stochastic Inflation in Compact Extra Dimensions

While moving down the potential on its classical slow roll trajectory, the inflaton field is subject to quantum jumps, which take it up or down the potential at random. In "stochastic inflation", the impact of these quantum jumps is modeled by smoothing out the field over (at least) Hubble-patch sized domains and treating fluctuations on smaller scales as noise. The inflaton thus becomes a stochastic process whose values at a given time are calculated using its probability distribution. We generalize this approach for non-canonic kinetic terms of Dirac Born Infeld (DBI) type and investigate the resulting modifications of the field's trajectory. Since models of DBI inflation arise from string-inspired scenarios in which the scalar field has a geometric interpretation, we insist that field value restrictions imposed by the model's string origin must be respected at the quantum level.Comment: Proceedings of the ERE 2010 conference, 4 pages, 1 figur

Exact solution of inflationary model with minimum length

Within the inflationary scenario, Planck scale physics should have affected the comoving modes' initial conditions and early evolution, thereby potentially affecting the inflationary predictions for the cosmic microwave background (CMB). This issue has been studied extensively on the basis of various models for how quantum field theory (QFT) is modified and finally breaks down towards the Planck scale. In one model, in particular, an ultraviolet cutoff was implemented into QFT through generalized uncertainty relations which have been motivated from general quantum gravity arguments and from string theory. Here, we improve upon prior numerical and semi-analytical results by presenting the exact mode solutions for both de Sitter and power-law inflation in this model. This provides an explicit map from the modes' initial conditions, which are presumably set by quantum gravity, to the modes' amplitudes at horizon crossing and thus to the inflationary predictions for the CMB. The solutions' particular behaviour close to the cutoff scale suggests unexpected possibilities for how the degrees of freedom of QFT emerge from the Planck scale.Comment: 19 pages, LaTe

Constraints on Kinetically Modified Inflation from WMAP5

Single field inflationary models with a non-minimal kinetic term (also called k-inflationary models) can be characterised by the so-called sound flow functions, which complete the usual Hubble flow hierarchy. These parameters appear in the primordial power spectra of cosmological perturbations at leading order and, therefore, affect the resulting Cosmic Microwave Background (CMB) anisotropies. Using the fifth year Wilkinson Microwave Anisotropy Probe (WMAP5) data, we derive the marginalised posterior probability distributions for both the sound and Hubble flow parameters. In contrast to the standard situation, these parameters remain separately unbounded, and notably there is no longer any upper limit on epsilon_1, the first Hubble flow function. Only special combinations of these parameters, corresponding to the spectral index and tensor-to-scalar ratio observables, are actually constrained by the data. The energy scale of k-inflation is nevertheless limited from above to Hinf/mpl < 6x10^(-6) at two-sigma level. Moreover, for the sub-class of Dirac-Born-Infeld models, by considering the non-gaussianity bounds on the sound speed, we find a weak limit epsilon_1 < 0.08 at 95% confidence level.Comment: 7 pages, 6 figures, uses RevTe

Reheating in a Brane Monodromy Inflation Model

We study reheating in a recently proposed brane "monodromy inflation" model in which the inflaton is the position of a D4 brane on a "twisted torus". Specifically, we study the repeated collisions between the D4 brane and a D6 brane (on which the Standard Model fields are assumed to be localized) at a fixed position along the monodromy direction as the D4 brane rolls down its potential. We find that there is no trapping of the rolling D4 brane until it reaches the bottom of its potential, and that reheating is entirely described by the last brane encounter. Previous collisions have negligible effect on the brane velocity and hence on the reheat temperature. In the context of our setup, reheating is efficient and the reheat temperature is therefore high.Comment: 13 pages, reference adde

Daylight design exploration using parametric processes and Artificial Neural Networks

The integration of Artificial Neural Networks (ANNs) as surrogates for daylight simulation models within parametric design environments promises greater computational efficiency in the exploration and optimisation of design solutions. This thesis demonstrates how ANNs can be integrated in design exploration processes, specifically focusing on the investigation of design solutions for the central atrium of a school building. ANNs are validated as surrogates for climate-based-performance metrices including Daylight Autonomy (DA) and spatial Daylight Autonomy (sDA) for thresholds of 100 lux (DA100) and 300 lux (DA300). The presented work discusses the prediction accuracies and sensitivities of the developed ANN models, the efficacy of the method, and atrium design strategies aimed at improving daylight conditions in atrium adjacent spaces. The research also critically evaluates daylight performance metrices and their implications on the design outcome of optimisation. Contributions are made in terms of validating ANN prediction accuracies for annual climate-based-daylight metrices, presenting a workflow for the selection and optimisation of input features from parametric models, and identifying limitations of ANN predictions related to model complexity and number of design variables. The work also contributes to the field of atrium design research by analysing the impact of atrium design changes on daylight performance, and by employing and comparing multiple daylight performance metrices. Thesis results showed that robust predictions could be achieved by optimising the network architecture of ANN ensembles, optimising input features, and employing cross-validation and early stopping. Overall, high accuracies were achieved for performance metrices predicting both % of occupied hours in a year and the % of space. For %time metrices, mean absolute errors were around 0.6% DA MAE (for DA ranging from 0 to 100%) for the 100 lux and 300 lux thresholds. For %space metrices, mean absolute errors were around 0.3% sDA MAE for both the 100 lux and 300 lux thresholds (for sDA ranging between 0 and 100%). Daylight simulation time was reduced by up to 71% by integrating ANNs within the design process. The design results showed that optimum atrium design solutions varied between the sDA300/50% and sDA100/50% metric. Additionally, the favorable design solutions also varied depending on whether design solutions were explored via the %space results of the sDA metric or the %time visualisations of the DA metric. Hence, this work discusses both the target thresholds employed in daylight performance metrices and bias that can be introduced by careless implementation of them. In terms of design strategy, southward orientations of the atrium well and reducing WWR towards the top floors increased daylight in atrium adjacent spaces on lower floors, but was met by a tradeoff, as this also reduced daylight on upper floors. The interdependencies of atrium design changes and the value and interpretability of the applied daylight performance metrices are further elaborated on in this thesis

Geometrically Consistent Approach to Stochastic DBI Inflation

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for a inflaton field with Dirac Born Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's Probability Density Function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the distance-inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.Comment: 20 pages, 3 figure

Predicting daylight autonomy metrics using machine learning

This study analyses the efficacy of using machine learning though artificial neural networks (ANN) to predict daylight autonomy metrics in typical office spaces. Based on a literature review of the use of ANN for non-linear problems, the chosen approach was deemed promising for its use in predicting daylight performance with the assumption that previous training data can be provided. The ANN approach, while empirical, has advantages when compared to conducting full simulations in the areas of speed and computing resources. In this study, several network architectures were analysed against several test cases. The accuracy of the obtained results mirror those in other studies when applied to daylight autonomy metrics. In addition, accuracy improved with the addition of a larger set of training data as well as the enhancement of the network architecture itself