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Register a new userInflation in multi-field random Gaussian landscapes
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We investigate slow-roll inflation in a multi-field random Gaussian landscape. The landscape is assumed to be small-field, with a correlation length much smaller than the Planck scale. Inflation then typically occurs in small patches of the landscape, localized near inflection or saddle points. We find that the inflationary track is typically close to a straight line in the field space, and the statistical properties of inflation are similar to those in a one-dimensional landscape. This picture of multi-field inflation is rather different from that suggested by the Dyson Brownian motion model; we discuss the reasons for this difference. We also discuss tunneling from inflating false vacua to the neighborhood of inflection and saddle points and show that the tunneling endpoints tend to concentrate along the flat direction in the landscape.
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We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations $n_s$ and its running $alpha_s$. These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.
It is speculated that the correct theory of fundamental physics includes a large landscape of states, which can be described as a potential which is a function of N scalar fields and some number of discrete variables. The properties of such a landscape are crucial in determining key cosmological parameters including the dark energy density, the stability of the vacuum, the naturalness of inflation and the properties of the resulting perturbations, and the likelihood of bubble nucleation events. We codify an approach to landscape cosmology based on specifications of the overall form of the landscape potential and illustrate this approach with a detailed analysis of the properties of N-dimensional Gaussian random landscapes. We clarify the correlations between the different matrix elements of the Hessian at the stationary points of the potential. We show that these potentials generically contain a large number of minima. More generally, these results elucidate how random function theory is of central importance to this approach to landscape cosmology, yielding results that differ substantially from those obtained by treating the matrix elements of the Hessian as independent random variables.
In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, $P sim 10^{-3}$.
We recapitulate multiple arguments that Eternal Inflation, and the String Landscape are actually part of the Swampland: ideas in Effective Quantum Field Theory that do not have a counterpart in genuine models of Quantum Gravity.
Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.
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