# The complete Brans–Dicke theories

## Abstract

Given that the simple wave equation of Brans–Dicke theory for the scalar field is preserved, we have investigated, through exhaustively analyzing the Bianchi identities, the consistent theories which violate the exact energy conservation equation. It is found that only three theories exist which are unambiguously determined from consistency, without imposing arbitrary functions by hand. Each of these theories possesses a specific interaction term which controls the energy exchange between the scalar field and ordinary matter. The theories contain new parameters (integration constants from the integration procedure) and when these are switched-off, Brans–Dicke theory emerges. As usually, the vacuum theories can be defined from the complete Brans–Dicke theories when the matter energy–momentum tensor vanishes.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617458

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 376; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENERGY-MOMENTUM TENSOR; GRAVITATION; SCALAR FIELDS; WAVE EQUATIONS

### Citation Formats

```
Kofinas, Georgios, E-mail: gkofinas@aegean.gr.
```*The complete Brans–Dicke theories*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2016.11.013.

```
Kofinas, Georgios, E-mail: gkofinas@aegean.gr.
```*The complete Brans–Dicke theories*. United States. doi:10.1016/J.AOP.2016.11.013.

```
Kofinas, Georgios, E-mail: gkofinas@aegean.gr. Sun .
"The complete Brans–Dicke theories". United States.
doi:10.1016/J.AOP.2016.11.013.
```

```
@article{osti_22617458,
```

title = {The complete Brans–Dicke theories},

author = {Kofinas, Georgios, E-mail: gkofinas@aegean.gr},

abstractNote = {Given that the simple wave equation of Brans–Dicke theory for the scalar field is preserved, we have investigated, through exhaustively analyzing the Bianchi identities, the consistent theories which violate the exact energy conservation equation. It is found that only three theories exist which are unambiguously determined from consistency, without imposing arbitrary functions by hand. Each of these theories possesses a specific interaction term which controls the energy exchange between the scalar field and ordinary matter. The theories contain new parameters (integration constants from the integration procedure) and when these are switched-off, Brans–Dicke theory emerges. As usually, the vacuum theories can be defined from the complete Brans–Dicke theories when the matter energy–momentum tensor vanishes.},

doi = {10.1016/J.AOP.2016.11.013},

journal = {Annals of Physics},

number = ,

volume = 376,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2017},

month = {Sun Jan 15 00:00:00 EST 2017}

}