Inflation in random landscapes with two energy scales

Abstract

Abstract:We investigate inflation in a multi-dimensional landscape with a hierarchy of energy scales, motivated by the string theory, where the energy scale of Kahler moduli is usually assumed to be much lower than that of complex structure moduli and dilaton field. We argue that in such a landscape, the dynamics of slow-roll inflation is governed by the low-energy potential, while the initial condition for inflation are determined by tunneling through high-energy barriers. We then use the scale factor cutoff measure to calculate the probability distribution for the number of inflationary e-folds and the amplitude of density fluctuations Q, assuming that the low-energy landscape is described by a random Gaussian potential with a correlation length much smaller than M pl . We find that the distribution for Q has a unique shape and a preferred domain, which depends on the parameters of the low-energy landscape. We discuss some observational implications of this distribution and the constraints it imposes on the landscape parameters.

Hessian eigenvalue distribution in a random Gaussian landscape

“…It was argued in Refs. [14][15][16]18] that inflation in such regions tends to be single-field, with the inflaton field rolling in a nearly straight line along the flat direction. Other fields (corresponding to orthogonal directions) can be excited and significant deviations from a straight trajectory can occur only if some of the fields have masses smaller than the Hubble parameter during inflation, m √ U 0 in Planck units.…”

“…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].…”

Slepian models for Gaussian random landscapes

“…Inflation in random potentials has already been extensively studied [13,14,19,20,47]. More specifically, inflation around inflection points has received special attention for being capable of sustaining enough e-folds to make contact with observations, while taking place in a small region of field space with an effectively one-dimensional potential.…”

“…Let us briefly review the main results for one-dimensional inflection-point inflation (see [20,48] and references therein for more details). Let us consider a potential of the form,…”

CMB targets after the latest Planck data release

“…To explain our motivation in a more detailed way, we should note that it is possible to describe any set of the three main parameters of inflationary perturbations, A s , n s , and r, by tuning three parameters of a simple model V ¼ aϕ 2 þ bϕ 3 þ cϕ 4 [21,22]. Similarly, one can study a chaotic landscape of multifield potentials, and evaluate statistical probability of any outcome, without necessarily making sharp predictions; see, e.g., [23][24][25][26][27][28][29][30]. One can also try to find multifield models predicting controllable amount of non-Gaussianity compatible with the Planck 2018 constraints; see, e.g., [31][32][33][34][35][36] and references therein.…”