Inflation in multi-field random Gaussian landscapes

Masoumi, Ali; Vilenkin, Alexander; Yamada, Masaki

doi:10.1088/1475-7516/2017/12/035

Cited by 18 publications

(56 citation statements)

References 57 publications

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“…[6] for a review and refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] for recent works.) 2 Thermal inflation is another possible solution to the cosmological moduli problem, where the moduli density is diluted by a mini-inflation around the TeV scale [23][24][25][26].…”

Section: Jhep01(2018)053mentioning

confidence: 99%

Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles

Kawasaki

Takahashi

Yamada

2018

J. High Energ. Phys.

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Abstract:The string theory predicts many light fields called moduli and axions, which cause a cosmological problem due to the overproduction of their coherent oscillation after inflation. One of the prominent solutions is an adiabatic suppression mechanism, which, however, is non-trivial to achieve in the case of axions because it necessitates a large effective mass term which decreases as a function of time. The purpose of this paper is twofold. First, we provide an analytic method to calculate the cosmological abundance of coherent oscillation in a general situation under the adiabatic suppression mechanism. Secondly, we apply our method to some concrete examples, including the one where a string axion acquires a large effective mass due to the Witten effect in the presence of hidden monopoles.

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Section: Jhep01(2018)053mentioning

confidence: 99%

Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles

Kawasaki

Takahashi

Yamada

2018

J. High Energ. Phys.

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“…To illustrate the main point of our method, it is convenient to initially absorb the hyperparameters h and of equation (1.2) into f and x. The covariance function is then given by, 8) and the covariances of the first few derivatives of f at x are:…”

Section: Motivational Examplementioning

confidence: 99%

Local, algebraic simplifications of Gaussian random fields

Bjorkmo

Marsh

2018

J. Cosmol. Astropart. Phys.

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Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we show how that problem can be completely circumvented for the local Taylor coefficients of a Gaussian random field with a Gaussian (or 'square exponential') covariance function. Our results hold for any dimension of the field and to any order in the Taylor expansion. We present two applications. First, we show that this method can be used to explicitly generate non-trivial potential energy landscapes with many fields. This application is particularly useful when one is concerned with the field locally around special points (e.g. maxima or minima), as we exemplify by the problem of cosmic 'manyfield' inflation in the early universe. Second, we show that this method has applications in machine learning, and greatly simplifies the regression problem of determining the hyperparameters of the covariance function given a training data set consisting of local Taylor coefficients at single point. An accompanying Mathematica notebook is available at https://doi.

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“…The details of the high-energy vacuum landscape are not well understood, and it is often modeled as a random Gaussian field. The statistics of vacuum energy densities and of slow-roll inflation in such a landscape have been extensively studied in the literature [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Another well studied model is the axionic landscape, which can also be approximated by a random Gaussian field in a certain limit [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Hessian eigenvalue distribution in a random Gaussian landscape

Yamada

Vilenkin

2018

J. High Energ. Phys.

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The energy landscape of multiverse cosmology is often modeled by a multidimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.

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Inflation in multi-field random Gaussian landscapes

Cited by 18 publications

References 57 publications

Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles

Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles

Local, algebraic simplifications of Gaussian random fields

Hessian eigenvalue distribution in a random Gaussian landscape

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