Red or Blue Tensor Spectrum from GW170817-compatible Einstein-Gauss-Bonnet Theory: A Detailed Analysis
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arXiv
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| Format: | Preprint |
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2024
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| author | Oikonomou, V. K. Tsyba, Pyotr Razina, Olga |
| author_facet | Oikonomou, V. K. Tsyba, Pyotr Razina, Olga |
| contents | In this work we shall prove that the tensor spectral index of the primordial tensor perturbations for GW170817-compatible Einstein-Gauss-Bonnet theories, takes the approximate simplified form $n_{\mathcal{T}}\simeq 2\left(-1+\frac{1}{λ(ϕ)} \right)ε_1$ at leading order, with $λ(ϕ)$ being a function of the scalar field which depends on the scalar field potential and the second derivative of the scalar-Gauss-Bonnet coupling $ξ''(ϕ)$. With our analysis we aim to provide a definitive criterion for selecting Einstein-Gauss-Bonnet models that can provide a blue-tilted inflationary phenomenology, by simply looking at the scalar potential and the scalar-Gauss-Bonnet coupling. We shall prove this using two distinct approaches and as we show the tilt of the tensor spectral index is determined by the values of the potential $V(ϕ)$ and of scalar-Gauss-Bonnet coupling at first horizon crossing. Specifically the blue-tilted tensor spectral index can occur when $ξ''(ϕ_*)V(ϕ_*)>0$ at first horizon crossing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Red or Blue Tensor Spectrum from GW170817-compatible Einstein-Gauss-Bonnet Theory: A Detailed Analysis Oikonomou, V. K. Tsyba, Pyotr Razina, Olga General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory In this work we shall prove that the tensor spectral index of the primordial tensor perturbations for GW170817-compatible Einstein-Gauss-Bonnet theories, takes the approximate simplified form $n_{\mathcal{T}}\simeq 2\left(-1+\frac{1}{λ(ϕ)} \right)ε_1$ at leading order, with $λ(ϕ)$ being a function of the scalar field which depends on the scalar field potential and the second derivative of the scalar-Gauss-Bonnet coupling $ξ''(ϕ)$. With our analysis we aim to provide a definitive criterion for selecting Einstein-Gauss-Bonnet models that can provide a blue-tilted inflationary phenomenology, by simply looking at the scalar potential and the scalar-Gauss-Bonnet coupling. We shall prove this using two distinct approaches and as we show the tilt of the tensor spectral index is determined by the values of the potential $V(ϕ)$ and of scalar-Gauss-Bonnet coupling at first horizon crossing. Specifically the blue-tilted tensor spectral index can occur when $ξ''(ϕ_*)V(ϕ_*)>0$ at first horizon crossing. |
| title | Red or Blue Tensor Spectrum from GW170817-compatible Einstein-Gauss-Bonnet Theory: A Detailed Analysis |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.02049 |