Singular Inflation

Abstract

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\varphi )=A{\varphi }^n$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of 'sudden' type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.

5 pages. v2: typos corrected, references added and some sections extended. Accepted Phys. Rev. D

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Cited by in corpus (13)

• Observational Constraints on New Exact Inflationary Scalar-field Solutions
• A quantitative analysis of singular inflation with scalar-tensor and modified gravity
• Did the Universe Experienced a Pressure non-Crushing Type Cosmological Singularity in the Recent Past?
• Pre-inflationary dynamics in loop quantum cosmology: Power-law potentials
• Dissimilar Donuts in the Sky? Effects of a Pressure Singularity on the Circular Photon Orbits and Shadow of a Cosmological Black Hole
• Finite Action Principle Revisited
• Initial directional singularity in inflationary models
• On the Expanding Phase of a Singular Bounce and Intermediate Inflation: The Modified Gravity Description
• Structure Formation in Non-local Bouncing Models
• Sudden Future Singularities in Quintessence and Scalar-Tensor Quintessence Models
• New Anisotropic Sudden Singularities and Dimensional Reduction
• Singularities in inflationary cosmological models
• On the oscillation-driven cosmological expansion at the post-inflation stage