A Survey through Conformal Time
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911574059384832 |
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| author | Aeenehvand, Tahereh Shariati, Ahmad |
| author_facet | Aeenehvand, Tahereh Shariati, Ahmad |
| contents | We revisit conformal time $η$ in a spatially flat Friedmann--Robertson--Walker universe and use a $1+1$-dimensional setting as a technically transparent pedagogical arena. Our purpose is to clarify the relation among cosmic time $t$, conformal time $η$, and the scale factor $a(t)$, and then to follow how this relation governs the geodesics of freely moving particles and the curvature of the corresponding manifold. The radiation-dominated, matter-dominated, and exact vacuum-only de Sitter cases are treated separately, because each of them produces a distinct conformal-time dependence and therefore a distinct geodesic structure. We then write the affine-parameter formalism in a form that is genuinely general for any spatially flat conformal metric, and we record the straightforward extension to the spatially flat $3+1$ case. The presentation remains elementary in spirit, but the notation, the curvature formulas, and the de Sitter interpretation are kept explicit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06120 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Survey through Conformal Time Aeenehvand, Tahereh Shariati, Ahmad General Relativity and Quantum Cosmology We revisit conformal time $η$ in a spatially flat Friedmann--Robertson--Walker universe and use a $1+1$-dimensional setting as a technically transparent pedagogical arena. Our purpose is to clarify the relation among cosmic time $t$, conformal time $η$, and the scale factor $a(t)$, and then to follow how this relation governs the geodesics of freely moving particles and the curvature of the corresponding manifold. The radiation-dominated, matter-dominated, and exact vacuum-only de Sitter cases are treated separately, because each of them produces a distinct conformal-time dependence and therefore a distinct geodesic structure. We then write the affine-parameter formalism in a form that is genuinely general for any spatially flat conformal metric, and we record the straightforward extension to the spatially flat $3+1$ case. The presentation remains elementary in spirit, but the notation, the curvature formulas, and the de Sitter interpretation are kept explicit. |
| title | A Survey through Conformal Time |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.06120 |