PyCOOL - a Cosmological Object-Oriented Lattice code written in Python

Sainio, Jani

doi:10.48550/arxiv.1201.5029

Cited by 9 publications

(12 citation statements)

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“…However, most of them can be applied only to models with canonical kinetic term in the Lagrangian (e.g. [39][40][41]). One exception is GABE [42], designed to make simulations for models with non-canonical kinetic terms.…”

Section: Description Of Simulationsmentioning

confidence: 99%

On preheating in alpha-attractor models of inflation

Krajewski,

Turzyński,

Wieczorek

2018

Preprint

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We study (p)reheating in α-attractor T-models of inflation, taking into account both scalar fields present in these models: the inflaton and the spectator. The two-field model has a negative field-space curvature which, at the end of inflation, may lead to geometrical destabilization of the spectator for small values of α < ∼ 10 −3 . We perform the instability (Floquet) analysis of the linear dynamics and a fully non-linear lattice computations with our numerical code, which we specifically designed for a class of two-field models with noncanonical kinetic terms. We find that the perturbations of the spectator field are much more unstable than the perturbations of the inflaton field, so the dynamics of the early stages of preheating is dominated by the evolution of the spectator perturbations. As a result, the transition from the inflationary era to radiation domination era is practically instantaneous and much faster than previously found in an effective theory including only the inflaton field.

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Section: Description Of Simulationsmentioning

confidence: 99%

On preheating in alpha-attractor models of inflation

Krajewski,

Turzyński,

Wieczorek

2018

Preprint

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“…We will consider the simplest Fourier NN with 1 hidden layer and 1 neuron per input variable. [7] Poisson equation 1:…”

Section: A Comments On α Hyperparametersmentioning

confidence: 99%

“…Finite difference methods are clearly more straightforward to be implemented. This is the main reason why they are widespread in the scientific community, see for instance [3][4][5][6][7][8][9][10][11][12] for some examples of early universe, general relativity and large scale structure simulations. On the other hand finite difference methods do not work well if the domain is irregular, which is a standard situation in many engineering contexts, in which one has to deal for instance with structural analysis of buildings or deformation and stresses of solid bodies.…”

Section: Introductionmentioning

confidence: 99%

dNNsolve: an efficient NN-based PDE solver

Guidetti,

Muia,

Welling

et al. 2021

Preprint

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Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be solved and of the initial/boundary conditions. A feed forward NN is trained to minimise this loss function evaluated on a set of collocation points sampled from the domain where the problem is defined. A compact and smooth solution, that only depends on the weights of the trained NN, is then obtained. This approach is often referred to as 'PINN', from Physics Informed Neural Network [1,2]. Despite the success of the PINN approach in solving various classes of PDEs, an implementation of this idea that is capable of solving a large class of ODEs and PDEs with good accuracy and without the need to finely tune the hyperparameters of the network, is not available yet. In this paper, we introduce a new implementation of this concept -called dNNsolve -that makes use of dual Neural Networks to solve ODEs/PDEs. These include: i) sine and sigmoidal activation functions, that provide a more efficient basis to capture both secular and periodic patterns in the solutions; ii) a newly designed architecture, that makes it easy for the the NN to approximate the solution using the basis functions mentioned above. We show that dNNsolve is capable of solving a broad range of ODEs/PDEs in 1, 2 and 3 spacetime dimensions, without the need of hyperparameter fine-tuning.Preprint. Under review.

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“…A favored integration scheme involves finite-difference techniques on a spatial lattice, in the presence of a spatially homogeneous and isotropic spacetime. 6 This is the case of codes such as LatticeEasy [51], Defrost [52], PyCool [53],…”

Section: Back-reactionmentioning

confidence: 99%

Freeze-in from Preheating

Garcia,

Kaneta,

Mambrini

et al. 2021

Preprint

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We consider the production of dark matter during the process of reheating after inflation. The relic density of dark matter from freeze-in depends on both the energy density and energy distribution of the inflaton scattering or decay products composing the radiation bath. We compare the perturbative and non-perturbative calculations of the energy density in radiation. We also consider the (likely) possibility that the final state scalar products are unstable. Assuming either thermal or non-thermal energy distribution functions, we compare the resulting relic density based on these different approaches. We show that the present-day cold dark matter density can be obtained through freeze-in from preheating for a large range of dark matter masses.

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PyCOOL - a Cosmological Object-Oriented Lattice code written in Python

Cited by 9 publications

References 0 publications

On preheating in alpha-attractor models of inflation

On preheating in alpha-attractor models of inflation

dNNsolve: an efficient NN-based PDE solver

Freeze-in from Preheating

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