Introduction to new bimetric models

• Grant number: 17/12655-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2017
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Denis Dalmazi
• Grantee: Felipe Augusto da Silva Barbosa
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

In the late 1990s, through the observation of supernovae light, the accelerated expansion of the universe (2011 Nobel prize) was observed. The fact that the universe is expanding was already known since the beginning of the XX century, thanks to E. Hubble. In order to explain its acceleration the concept of dark energy has been created. It represents a "repulsive force" between matter, thus playing the inverse role of the gravitational force. Presumably, dark energy fills most of the universe however, no plausible explanation has been found so far to clarify its origin and what it is. On the other hand, one believes that gravitational interactions are intermediated by elementary particles called gravitons. Late gravitational wave detection experiments are consistent with massless spin-2 gravitons however, there is still some room for masses below 10 -22 ev. Massive gravitons would make long distance gravitational interaction weaker which would contribute to the accelerated expansion of the universe. Eventually, massive gravitons dispense the existence of dark energy. The purpose of the present research plan is to address the issue of the accelerated expansion of the universe by means of massive gravity in spaces of D=2+1 dimensions, working as toy models. In D=3+1 dimensions a viable covariant massive gravity model requires two metrics, one massive graviton plus a massless one, whereas in D=2+1 it is possible to describe massive gravitons with only one metric, the so called "New Massive Gravity" (NMG). Recently however, it appeared in the literature a bimetric version of such model. We have also suggested a bimetric NMG model in D=2+1 which we believe to be even more interesting than the existing models of the literature. In the present work, after an introduction to gravitation and its techniques, the student will analyze both the models in the literature and our suggestions, from the point of view of the stability of maximally symmetric solutions and its relations with the free parameters of the model. (AU)