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<p>Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global <i>dS</i> preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass.</p>

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No-boundary extremal surfaces in slow-roll inflation and other cosmologies

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月26日

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  • Kaberi Goswami,
  • K. Narayan,
  • Gopal Yadav

摘要

Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global dS preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass.