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In this paper we consider the Cauchy problem for semi-linear de Sitter models. The model of interest is \(\displaystyle \phi _{tt} - e^{-2t} \varDelta \phi + n\phi _t+m^2\phi =F_p(\phi ),\quad (\phi (0,x),\phi _t(0,x))=(f(x),g(x)), \) where n is the space dimension, \(m^2\) is a non-negative constant and p is a positive parameter. Our main goal is to verify that, in general, one cannot observe a critical exponent \(p_{crit}=p_{crit}(n)\) in the family of non-linearities \(\{F_p(\phi )\}_{p >1}=\{|\phi |^p\}_{p >1}\) .

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About Critical Exponents in Semi-Linear de Sitter Models

  • 会议论文

  • 发表日期：

    2025年

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  • M. R. Ebert,
  • J. Marques,
  • M. Reissig

摘要

In this paper we consider the Cauchy problem for semi-linear de Sitter models. The model of interest is \(\displaystyle \phi _{tt} - e^{-2t} \varDelta \phi + n\phi _t+m^2\phi =F_p(\phi ),\quad (\phi (0,x),\phi _t(0,x))=(f(x),g(x)), \) where n is the space dimension, \(m^2\) is a non-negative constant and p is a positive parameter. Our main goal is to verify that, in general, one cannot observe a critical exponent \(p_{crit}=p_{crit}(n)\) in the family of non-linearities \(\{F_p(\phi )\}_{p >1}=\{|\phi |^p\}_{p >1}\) .