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• W1984127945 abstract "We study cosmological self-reproduction in models of inflation driven by a scalar field $ensuremath{phi}$ with a noncanonical kinetic term ($k$-inflation). We develop a general criterion for the existence of attractors and establish conditions selecting a class of $k$-inflation models that admit a unique attractor solution. We then consider quantum fluctuations on the attractor background. We show that the correlation length of the fluctuations is of order ${c}_{s}{H}^{ensuremath{-}1}$, where ${c}_{s}$ is the speed of sound. By computing the magnitude of field fluctuations, we determine the coefficients of Fokker-Planck equations describing the probability distribution of the spatially averaged field $ensuremath{phi}$. The field fluctuations are generally large in the inflationary attractor regime; hence, eternal self-reproduction is a generic feature of $k$-inflation. This is established more formally by demonstrating the existence of stationary solutions of the relevant Fokker-Planck equations. We also show that there exists a (model-dependent) range ${ensuremath{phi}}_{R}<ensuremath{phi}<{ensuremath{phi}}_{mathrm{max}}$ within which large fluctuations are likely to drive the field towards the upper boundary $ensuremath{phi}={ensuremath{phi}}_{mathrm{max}}$, where the semiclassical consideration breaks down. An exit from inflation into reheating without reaching ${ensuremath{phi}}_{mathrm{max}}$ will occur almost surely (with probability 1) only if the initial value of $ensuremath{phi}$ is below ${ensuremath{phi}}_{R}$. In this way, strong self-reproduction effects constrain models of $k$-inflation." @default.
• W1984127945 created "2016-06-24" @default.
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• W1984127945 date "2006-09-29" @default.
• W1984127945 modified "2023-09-23" @default.
• W1984127945 title "Self-reproduction in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>k</mml:mi></mml:math>-inflation" @default.
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• W1984127945 doi "https://doi.org/10.1103/physrevd.74.063528" @default.
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