Testing modified gravity with globular clusters: the case of NGC 2419

The dynamics of globular clusters has been studied in great detail in the context of general relativity as well as with modifications of gravity that strongly depart from the standard paradigm such as MOND. However, at present there are no studies that aim to test the impact that less extreme modifications of gravity (e.g. models constructed as alternatives to dark energy) have on the behaviour of globular clusters. This Letter presents fits to the velocity dispersion profile of the cluster NGC 2419 under the symmetron modified gravity model. The data shows an increase in the velocity dispersion towards the centre of the cluster which could be difficult to explain within general relativity. By finding the best fitting solution associated with the symmetron model, we show that this tension does not exist in modified gravity. However, the best fitting parameters give a model that is inconsistent with the dynamics of the Solar System. Exploration of different screening mechanisms should give us the chance to understand if it is possible to maintain the appealing properties of the symmetron model when it comes to globular clusters and at the same time recover the Solar System dynamics properly.Comment: 6 pages, 2 figures. Accepted for publication in MNRAS Letter

Releasing scalar fields: cosmological simulations of scalar-tensor theories for gravity beyond the static approximation

Several extensions of General Relativity and high energy physics include scalar fields as extra degrees of freedom. In the search for predictions in the non-linear regime of cosmological evolution, the community makes use of numerical simulations in which the quasi-static limit is assumed when solving the equation of motion of the scalar field. In this Letter, we propose a method to solve the full equations of motion for scalar degrees of freedom coupled to matter. We run cosmological simulations which track the full time and space evolution of the scalar field, and find striking differences with respect to the commonly used quasi-static approximation. This novel procedure reveals new physical properties of the scalar field and uncovers concealed astrophysical phenomena which were hidden in the old approach.Comment: 5 Pages, 3 figures, matches version accepted for publication in PR

Cosmological simulations of screened modified gravity out of the static approximation: effects on matter distribution

In the context of scalar tensor theories for gravity, there is a universally adopted hypothesis when running N-body simulations that time derivatives in the equation of motion for the scalar field are negligible. In this work we propose to test this assumption for one specific scalar-tensor model with a gravity screening mechanism: the symmetron. To this end, we implemented the necessary modifications to include the non-static terms in the N-body code Ramses. We present test cases and results from cosmological simulations. Our main finding when comparing static vs. non-static simulations is that the global power spectrum is only slightly modified when taking into account the inclusion of non-static terms. On the contrary, we find that the calculation of the local power spectrum gives different measurements. Such results imply one must be careful when assuming the quasi-static approximation when investigating the environmental effects of modified gravity and screening mechanisms in structure formation of halos and voids distributions.Comment: 12 pages, 8 figures, matches version accepted for publication in PR

Shape of Clusters as a Probe of Screening Mechanisms in Modified Gravity

Scalar fields are crucial components in high energy physics and extensions of General Relativity. The fact they are not observed in the solar system may be due to a mechanism which screens their presence in high dense regions. We show how observations of the ellipticity of galaxy clusters can discriminate between models with and without scalar fields and even between different screening mechanisms. Using nowadays X-ray observations we put novel constraints on the different models.Comment: 4 pages, 3 figures, matches version accepted for publication in PR

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

ISIS: a new N-body cosmological code with scalar fields based on RAMSES. Code presentation and application to the shapes of clusters

Several extensions of the standard cosmological model include scalar fields as new degrees of freedom in the underlying gravitational theory. A particular class of these scalar field theories include screening mechanisms intended to hide the scalar field below observational limits in the solar system, but not on galactic scales, where data still gives freedom to find possible signatures of their presence. In order to make predictions to compare with observations coming from galactic and clusters scales (i.e. in the non-linear regime of cosmological evolution), cosmological N-body simulations are needed, for which codes that can solve for the scalar field must be developed. We present a new implementation of scalar-tensor theories of gravity which include screening mechanisms. The code is based in the already existing code RAMSES, to which we have added a non-linear multigrid solver that can treat a large class of scalar tensor theories of modified gravity. We present details of the implementation and the tests that we made to it. As application of the new code, we have studied the influence that two particular modified gravity theories, the symmetron and $f(R)$ gravity, have on the shape of cluster sized dark matter halos and found consistent results with previous estimations made with a static analysis.Comment: 13 pages, 6 figures, matches version accepted for publication in A&

Tareas matemáticas en la formación de maestros. Caracterizando perspectivas

El diseño de tareas en los programas de formación de maestros se vincula al desarrollo del conocimiento necesario para realizar diferentes tareas profesionales- organizar el contenido matemático, interpretar el aprendizaje, gestionar la enseñanza. Se ejemplifica esta perspectiva en el caso del diseño de tareas matemáticas considerando la tarea profesional del maestro de analizar libros de texto