Cosmological simulations with disformally coupled symmetron fields

We investigate statistical properties of the distribution of matter at redshift zero in disformal gravity by using N-body simulations. The disformal model studied here consists of a conformally coupled symmetron field with an additional exponential disformal term. We conduct cosmological simulations to discover the impact of the new disformal terms in the matter power spectrum, halo mass function, and radial profile of the scalar field. We calculated the disformal geodesic equation and the equation of motion for the scalar field. We then implemented these equations into the N-body code ISIS, which is a modified gravity version of the code RAMSES. The presence of a conformal symmetron field increases both the power spectrum and mass function compared to standard gravity on small scales. Our main finding is that the newly added disformal terms tend to counteract these effects and can make the evolution slightly closer to standard gravity. We finally show that the disformal terms give rise to oscillations of the scalar field in the centre of the dark matter haloes.Comment: Updated version to reflect the journal accepted paper. Added one figure. 7 pages, 7 figure

Very large scale structures in growing neutrino quintessence

A quintessence scalar field or cosmon interacting with neutrinos can have important effects on cosmological structure formation. Within growing neutrino models the coupling becomes effective only in recent times, when neutrinos become non-relativistic, stopping the evolution of the cosmon. This can explain why dark energy dominates the universe only in a rather recent epoch by relating the present dark energy density to the small mass of neutrinos. Such models predict the presence of stable neutrino lumps at supercluster scales (~200 Mpc and bigger), caused by an attractive force between neutrinos which is stronger than gravity and mediated by the cosmon. We present a method to follow the initial non-linear formation of neutrino lumps in physical space, by integrating numerically on a 3D grid non-linear evolution equations, until virialization naturally occurs. As a first application, we show results for cosmologies with final large neutrino average mass ~2 eV: in this case, neutrino lumps indeed form and mimic very large cold dark matter structures, with a typical gravitational potential 10^{-5} for a lump size ~10 Mpc, and reaching larger values for lumps of about 200 Mpc. A rough estimate of the cosmological gravitational potential at small k in the non-linear regime, Phi_nu = 10^{-6} (k/k_0)^{-2}, 1.2x10^{-2} h/Mpc < k_0 < 7.8x10^{-2} h/Mpc, turns out to be many orders of magnitude smaller than an extrapolation of the linear evolution of density fluctuations. The size of the neutrino-induced gravitational potential could modify the spectrum of CMB anisotropies for small angular momenta.Comment: 17 pages, 16 figures, accepted for publication in Physical Review D, minor changes and correction

Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.Comment: 10 pages, no figure

Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two dimensional square spin ice model as an effective model. Using an extension of the model presented in ref. [Scientific Reports 5, 15875 (2015)], considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the monopoles and string densities dependence as a function of the temperature.Comment: 11 pages, 8 figure

A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals