Inflation with a graceful exit in a random landscape

Abstract

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound N 10 on the number of light fields N participating during inflation from the non-observation of negative spatial curvature.

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

“…[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].…”

Initial conditions for slow-roll inflation in a random Gaussian landscape

“…The properties of string theory landscape are not well understood, and the approach adopted in much of the recent work is to substitute it by a scalar field model with a random Gaussian potential [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Slepian models for Gaussian random landscapes

“…However, depending on the restrictions imposed, it may be very difficult to obtain an example of the potential with these characteristics by producing random realizations of the scalar potential. Indeed, metastable de Sitter vacua and inflationary points compatible with observations are very rare in generic landscapes, with probabilities scaling as P ∼ exp(−N p f ), where N f is the number of scalar fields in the theory, and p > 0 is a number of order one [7][8][9][10][11][12]. To obtain realizations with the desired properties, one can of course use a Taylor expansion around the point in question and take into account the probability distribution for its coefficients [13,14].…”

“…Therefore the last contribution in (3.10) can be neglected in a neighbourhood of the extremum where |∆(φ)| U 0 |V (0)| holds. On the other hand, in the limit |u| U 0 the eigenvalue distribution of the Hessian (3.9) is approximately given by 5 11) which indicates that in this limit the magnitude of the eigenvalues is very suppressed…”