# Scientific Goals

## The scientific objectives of the STAR cluster are:

- Studying possible modifications of general relativity, especially f(R) gravity and scalar-tensor theories (including scalar fields non-minimally coupled to the spacetime curvature) with regard to stability, cosmological implications, weak-field limit, spherical exact solutions, initial value problem, and other aspects.
- Studying cosmology in the framework of extended gravitational theories, including the early universe inflationary era and the generation of primordial gravitational waves (spectrum and amplitudes) possibly detectable in the current PLANCK satellite experiment of the European Space Agency and in future experiments; early universe nucleosynthesis during the radiation-dominated era of the universe; the growth of structures ( galaxies, galaxy clusters, voids) during the matter-dominated era following the radiation era; and searching for explanations of the present acceleration of the cosmic expansion.
- Studying astrophysics in the framework of these extended theories of gravity, including exact spherically symmetric solutions and black holes in these theories, the thermodynamics of black hole and cosmological apparent horizons, and the generation of gravitational waves (scalar modes, etc.).
- Studying compact objects (both in standard and in alternative gravity) as they relate to questions in high-energy astrophysics, including:
- population synthesis of Cataclysmic Variables and Low-Mass X-ray Binaries
- a model explaining Type Ia supernova progenitors and their role as standard candles in cosmology
- the structure and nature of compact objects such as neutron stars and white dwarfs as predicted by these extended theories of gravity
- the role of binary tidal heating and ablation by close binary millisecond pulsars
- the investigation of unsolved problems such as elemental abundance anomalies associated with stellar evolution in close binary systems
- the modeling the nature and properties of soft gamma-ray repeaters
- the detection and determination of extragalactic dark matter.

## Specifically, the open problems that we want to address include:

- What modifications to general relativity are reasonable to expect given a few basic assumptions about gravity? What are their effects on cosmology (expansion history, evolution of voids, growth of density perturbations and formation of galaxies/clusters)?
- What is the gravitational wave content of extended gravity, how are gravitational waves generated, and what signatures of the theory should we look for in experiments aiming to detect these waves?
- How would different descriptions of the gravitational radiation reaction affect the evolution of close interacting binary systems and other systems, and how could these differences be detected?
- What model can be proposed that would explain the salient observations of Type Ia supernova explosions and also account for their observed frequency? Are these models consistent with the frequencies for all galaxy morphologies?

Planned research for the short term includes: constraining extended gravity with Solar System experiments; studying the stability of the theory (a more difficult issue than in GR because there are more degrees of freedom and, hence, channels for decay); studying the initial value problem, which must be well-posed for the theory to have any predictive power; understanding exact solutions and finding whether there are “generic” ones or attractors.

On the astrophysics side, the 1998 revolution in cosmology came from the study of Type Ia supernovae and the relation between their redshift and luminosity distance, which depends strongly on the background universe. These supernovae were initially believed to originate in interacting binary stellar systems for which the white dwarf accretor is pushed over the Chandrasekhar Limit and explodes by detonation/deflagration leaving behind a somewhat ablated companion (i.e., the donor star). One of the main problems with this scenario is that the putative progenitors are very difficult to create in nature. We study interacting binaries containing compact objects which are expected to be the likely progenitors of Type Ia supernovae. Using sophisticated Monte Carlo simulations (Population Synthesis) the current models cannot explain the observed frequency. However, the Common Envelope phase of the evolution is extremely difficult to evaluate precisely, and it may be possible that nature favours the formation of extremely close detached binaries. This issue and an analysis of the ablation of the putative donor stars in these systems are currently active areas of investigation.

The dynamics and lifetime of these stellar systems are affected by the rate at which they lose energy by radiating gravitational waves, which generally depend on the theory of gravity (extra modes can be generated in certain theories, or they can be radiated at different rates).

The present accelerated era of the universe is a major puzzle which could be a manifestation of deviations from general relativity on the largest scales. We plan to expand our study of exact cosmological solutions, their stability and attractor behaviour, and to study the generation and growth of density perturbations which formed the seed for the galaxies and galaxy clusters that we observe today. The confrontation with supernovae and data from cosmic microwave background experiments will contribute to this study.

The mathematical challenges encountered in solving these problems stimulate the development of more sophisticated analytical and numerical tools. Mathematical physics that is not available needs to be laid down and massive computations stimulate progress in the numerical approaches.

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Bishop's University - All Rights Reserved

Bishop's University

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Sherbrooke, QC, Canada

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