Exact general solutions for cosmological scalar field evolution in a vacuum-energy dominated expansion
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| Format: | Preprint |
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2026
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| author | Hu, Patrick Scherrer, Robert J. |
| author_facet | Hu, Patrick Scherrer, Robert J. |
| contents | We derive exact general solutions (as opposed to attractor particular solutions) for the evolution of a scalar field $ϕ$ in a universe dominated by a background fluid with equation of state parameter $w_B = -1$, extending earlier work on exact solutions with $w_B > -1$. Straightfoward exact solutions exist when the evolution is described by a linear differential equation, corresponding to constant, linear, and quadratic potentials. In the nonlinear case, exact solutions are derived for $V = V_0\ln ϕ$, $V = V_0 ϕ^{1/2}$ and $V = V_0/ϕ$, and the logarithmic potential also yields an exact first integral. These complicated parametric solutions are considerably less useful than those derived previously for a universe dominated by a barotropic fluid such as matter or radiation with $w_B > -1$. However, we generalize the slow-roll approximation and show that it applies to all sufficiently flat potentials in the case of a vacuum-dominated expansion, while it never applies when the universe is dominated by a background fluid with $w_B > -1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact general solutions for cosmological scalar field evolution in a vacuum-energy dominated expansion Hu, Patrick Scherrer, Robert J. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics We derive exact general solutions (as opposed to attractor particular solutions) for the evolution of a scalar field $ϕ$ in a universe dominated by a background fluid with equation of state parameter $w_B = -1$, extending earlier work on exact solutions with $w_B > -1$. Straightfoward exact solutions exist when the evolution is described by a linear differential equation, corresponding to constant, linear, and quadratic potentials. In the nonlinear case, exact solutions are derived for $V = V_0\ln ϕ$, $V = V_0 ϕ^{1/2}$ and $V = V_0/ϕ$, and the logarithmic potential also yields an exact first integral. These complicated parametric solutions are considerably less useful than those derived previously for a universe dominated by a barotropic fluid such as matter or radiation with $w_B > -1$. However, we generalize the slow-roll approximation and show that it applies to all sufficiently flat potentials in the case of a vacuum-dominated expansion, while it never applies when the universe is dominated by a background fluid with $w_B > -1$. |
| title | Exact general solutions for cosmological scalar field evolution in a vacuum-energy dominated expansion |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2601.15226 |