Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch
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| Format: | Preprint |
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2024
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| _version_ | 1866914816285736960 |
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| author | Nojiri, Shin'ichi Odintsov, S. D. |
| author_facet | Nojiri, Shin'ichi Odintsov, S. D. |
| contents | We formulate the convenient and mimetic $f(Q)$ gravities in terms of the metric and four scalar fields with the $Q$ being the non-metricity scalar. As a result, it is shown that the obtained field equations are well-defined. By using the field equations, we show how the $f(Q)$ models which realise any given FLRW spacetime may be reconstructed. We construct convenient $f(Q)$ gravity and mimetic $f(Q)$ gravity, which describe the inflation and dark energy epochs and even unify the inflation and dark energy. Moreover, a radiation-dominated epoch and early dark energy may be easily included in the above theories as is explicitly shown. It is shown that the inflationary spectral index $n_s$ and the tensor-to-scalar ratio $r$ are consistent with Planck data for some models of $f(Q)$ gravity. Corresponding asymptotic forms of $f(Q)$ and mimetic $f(Q)$ are given. Finally, some remarks on possible reconstruction for spherically symmetric spacetime are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch Nojiri, Shin'ichi Odintsov, S. D. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory We formulate the convenient and mimetic $f(Q)$ gravities in terms of the metric and four scalar fields with the $Q$ being the non-metricity scalar. As a result, it is shown that the obtained field equations are well-defined. By using the field equations, we show how the $f(Q)$ models which realise any given FLRW spacetime may be reconstructed. We construct convenient $f(Q)$ gravity and mimetic $f(Q)$ gravity, which describe the inflation and dark energy epochs and even unify the inflation and dark energy. Moreover, a radiation-dominated epoch and early dark energy may be easily included in the above theories as is explicitly shown. It is shown that the inflationary spectral index $n_s$ and the tensor-to-scalar ratio $r$ are consistent with Planck data for some models of $f(Q)$ gravity. Corresponding asymptotic forms of $f(Q)$ and mimetic $f(Q)$ are given. Finally, some remarks on possible reconstruction for spherically symmetric spacetime are given. |
| title | Well-defined $f(Q)$ Gravity, Reconstruction of FLRW Spacetime and Unification of Inflation with Dark Energy Epoch |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.18427 |