Extended inflation with an exponential potential

Susperregi, Mikel; Mazumdar, Anupam

doi:10.1103/physrevd.58.083512

Cited by 15 publications

(12 citation statements)

References 28 publications

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“…To derive the conditions for eternal inflation, we first note that a stochastic differential equation has the general form dX = a(X, t)dt + b(X, t)dW, (30) where a(X, t) is known as the drift coefficient which effects the deterministic evolution of the system, while b(X, t) is known as the dispersion coefficient which introduces random/stochastic fluctuations into the system. Using Eq.…”

Section: The Conditions For Eternal Inflationmentioning

confidence: 99%

“…Linde and Linde [29] investigated the global structure of an inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early universe. Susperregi and Mazumdar [30] considered an exponential inflation potential and showed that this theory predicts a uniform distribution for the Planck mass at the end of inflation, for the entire ensemble of universes that undergo stochastic inflation. Vanchurin, Vilenkin, and Winitzki [31] investigated methods of inflationary cosmology based on the Fokker-Planck equation of stochastic inflation and direct simulation of inflationary spacetime.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic eternal inflation in a Bianchi type I universe

Kohli

Haslam

2016

Phys. Rev. D

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The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi Type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for eternal inflation. It is shown that for eternal inflation to occur, the amount of anisotropy must be small. In fact, it is shown that eternal inflation will only take place if the shear anisotropy variables take on values within a small region of the interior of the Kasner circle. We then calculate the probability of eternal inflation occurring based on techniques from stochastic calculus.

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Section: The Conditions For Eternal Inflationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic eternal inflation in a Bianchi type I universe

Kohli

Haslam

2016

Phys. Rev. D

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“…(6 and 12-13) while the conservation equations are defined by Eqs (20)(21). The solution behaves as (22), therefore we have obtained the following solution a 1 = a 2 = a 3 = 1, q = 0, ∀m ∈ (−1, 1) \ {0} , so the metric collapses to Eq. (48), i.e.…”

Section: Non-interacting Scalar and Matter Fields With G-varmentioning

confidence: 90%

“…(6 and 12-13) and the corresponding conservation equations given by Eqs (20)(21). The solution behaves as (22), therefore we have obtained the following solution…”

Section: Non-interacting Scalar and Matter Fields With G-varmentioning

confidence: 98%

(An)Isotropic models in scalar and scalar-tensor cosmologies

Belinchón¹

2011

Astrophys Space Sci

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We study how the constants $G$ and $\Lambda$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $\Lambda$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive to the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function

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“…Linde and Linde [LL94] investigated the global structure of an inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early universe. Susperregi and Mazumdar [SM98] considered an exponential inflation potential and showed that this theory predicts a uniform distribution for the Planck mass at the end of inflation, for the entire ensemble of universes that undergo stochastic inflation. Vanchurin, Vilenkin, and Winitzki [VVW00] investigated methods of inflationary cosmology based on the Fokker-Planck equation of stochastic inflation and direct simulation of inflationary spacetime.…”

Section: Introductionmentioning

confidence: 99%

Mathematical issues in eternal inflation

Kohli

Haslam

2015

Class. Quantum Grav.

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Abstract. In this paper, we consider the problem of existence and uniqueness of solutions to the Einstein field equations for a spatially flat FLRW universe in the context of stochastic eternal inflation where the stochastic mechanism is modelled by adding a stochastic forcing term representing Gaussian white noise to the Klein-Gordon equation. We show that under these considerations, the KleinGordon equation actually becomes a stochastic differential equation. Therefore, the existence and uniqueness of solutions to Einstein's equations depend on whether the coefficients of this stochastic differential equation obey Lipschitz continuity conditions. We show that for any choice of V (φ), the Einstein field equations are not globally well-posed, hence, any solution found to these equations is not guaranteed to be unique. Instead, the coefficients are at best locally Lipschitz continuous in the physical state space of the dynamical variables, which only exist up to a finite explosion time. We further perform Feller's explosion test for an arbitrary power-law inflaton potential and prove that all solutions to the EFE explode in a finite time with probability one. This implies that the mechanism of stochastic inflation thus considered cannot be described to be eternal, since the very concept of eternal inflation implies that the process continues indefinitely. We therefore argue that stochastic inflation based on a stochastic forcing term would not produce an infinite number of universes in some multiverse ensemble. In general, since the Einstein field equations in both situations are not well-posed, we further conclude that the existence of a multiverse via the stochastic eternal inflation mechanism considered in this paper is still very much an open question that will require much deeper investigation.

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Extended inflation with an exponential potential

Cited by 15 publications

References 28 publications

Stochastic eternal inflation in a Bianchi type I universe

Stochastic eternal inflation in a Bianchi type I universe

(An)Isotropic models in scalar and scalar-tensor cosmologies

Mathematical issues in eternal inflation

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