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Isotropic LQC and LQC-inspired models with a massless scalar field as generalised Brans–Dicke theories

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Abstract

We explore whether generalised Brans–Dicke theories, which have a scalar field \(\Phi \) and a function \(\omega (\Phi )\), can be the effective actions leading to the effective equations of motion of the LQC and the LQC-inspired models, which have a massless scalar field \(\sigma \) and a function f(m). We find that this is possible for isotropic cosmology. We relate the pairs \((\sigma , f)\) and \((\Phi , \omega )\) and, using examples, illustrate these relations. We find that near the bounce of the LQC evolutions for which \(f(m) = sin \; m\), the corresponding field \(\Phi \rightarrow 0\) and the function \(\omega (\Phi ) \propto \Phi ^2\). We also find that the class of generalised Brans–Dicke theories, which we had found earlier to lead to non singular isotropic evolutions, may be written as an LQC-inspired model. The relations found here in the isotropic cases do not apply to the anisotropic cases, which perhaps require more general effective actions.

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Notes

  1. In the following, the convention of summing over repeated indices is not always applicable. Hence we will write explicitly the indices to be summed over.

  2. See the review [13] for a complete description of the various LQG/C terms and concepts mentioned here and in the following.

  3. In LQC, \((3 + 1)\) dimensional effective actions have been constructed in [19,20,21,22,23,24] by generalising Einstein’s term R to F(R) and finding an appropriate function F which will give the isotropic LQC evolution. Any F(R)-theory, including that for LQC, can be written as a scalar–tensor theory with the Brans–Dicke constant \(\omega = 0\) and with a potential that depends on F [16,17,18]. Similar approach may also work for the present \((d + 1)\) dimensional LQC-inspired models for any arbitrary function \(f \;\), but we will not pursue it in this paper.

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Acknowledgements

We thank the referee for her/his suggestions and for pointing out the references [32,33,34, 47, 48].

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  1. Institute of Mathematical Sciences, HBNI, C. I. T. Campus, Tharamani, Chennai, 600 113, India

    S. Kalyana Rama

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Rama, S.K. Isotropic LQC and LQC-inspired models with a massless scalar field as generalised Brans–Dicke theories. Gen Relativ Gravit 50, 56 (2018). https://doi.org/10.1007/s10714-018-2378-0

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