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<p>The gravitational path-integral of Gauss–Bonnet gravity is investigated and the transition from one spacelike boundary configuration to another is analyzed. Of particular interest is the case of Neumann and Robin boundary conditions which is known to lead to a stable Universe in Einstein–Hilbert gravity in four spacetime dimensions. After setting up the variational problem and computing the necessary boundary terms, the transition amplitude is computed <i>exactly</i> in the mini-superspace approximation. The <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3369_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbar \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ħ</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> limit brings out the dominant pieces in the path-integral which is traced to an initial configuration corresponding to Hartle–Hawking no-boundary Universe. A deeper study involving Picard–Lefschetz methods not only allow us to find the integration contour along which the path-integral becomes convergent but also aids in understanding the crossover from Euclidean to Lorentzian signature. Saddle analysis further highlights the boundary configurations giving dominant contribution to the path-integral which is seen to be those corresponding to Hartle–Hawking no-boundary proposal and agrees with the exact computation. To ensure completeness, a comparison with the results from Wheeler–DeWitt equation is done.</p>

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Lorentzian Robin Universe of Gauss-Bonnet Gravity

  • 期刊论文

  • 发表日期：

    2025年1月31日

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  • Manishankar Ailiga,
  • Shubhashis Mallik,
  • Gaurav Narain

摘要

The gravitational path-integral of Gauss–Bonnet gravity is investigated and the transition from one spacelike boundary configuration to another is analyzed. Of particular interest is the case of Neumann and Robin boundary conditions which is known to lead to a stable Universe in Einstein–Hilbert gravity in four spacetime dimensions. After setting up the variational problem and computing the necessary boundary terms, the transition amplitude is computed exactly in the mini-superspace approximation. The \(\hbar \rightarrow 0\) ħ → 0 limit brings out the dominant pieces in the path-integral which is traced to an initial configuration corresponding to Hartle–Hawking no-boundary Universe. A deeper study involving Picard–Lefschetz methods not only allow us to find the integration contour along which the path-integral becomes convergent but also aids in understanding the crossover from Euclidean to Lorentzian signature. Saddle analysis further highlights the boundary configurations giving dominant contribution to the path-integral which is seen to be those corresponding to Hartle–Hawking no-boundary proposal and agrees with the exact computation. To ensure completeness, a comparison with the results from Wheeler–DeWitt equation is done.