$δn$ formalism: A new formulation for the probability density of the curvature perturbation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910976080609280 |
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| author | Cruces, Diego Pi, Shi Sasaki, Misao |
| author_facet | Cruces, Diego Pi, Shi Sasaki, Misao |
| contents | $δN$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $δN$ formalism by using the $e$-folding number $n$ counted forward in time. For a fixed initial time $\bar{n}_0$, the probability density function (PDF) of the initial conditions $δϕ_0$ and $δπ_0$ are specified by the solutions of the perturbation equation on subhorizon scales. As $δπ_0$ is fully correlated with $δϕ_0$ after horizon exit, we find a simple formula to calculate the curvature perturbation as well as its PDF by using the $δN$ method reformulated in terms of $n$, the $δn$ formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_24590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $δn$ formalism: A new formulation for the probability density of the curvature perturbation Cruces, Diego Pi, Shi Sasaki, Misao Cosmology and Nongalactic Astrophysics $δN$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $δN$ formalism by using the $e$-folding number $n$ counted forward in time. For a fixed initial time $\bar{n}_0$, the probability density function (PDF) of the initial conditions $δϕ_0$ and $δπ_0$ are specified by the solutions of the perturbation equation on subhorizon scales. As $δπ_0$ is fully correlated with $δϕ_0$ after horizon exit, we find a simple formula to calculate the curvature perturbation as well as its PDF by using the $δN$ method reformulated in terms of $n$, the $δn$ formalism. |
| title | $δn$ formalism: A new formulation for the probability density of the curvature perturbation |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2505.24590 |