1,720,969 research outputs found
Random functions via Dyson Brownian Motion: progress and problems
No full textWe develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C-2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also off er an ad hoc modification of DBM that suppresses this growth to some degree
Vacuum selection on axionic landscapes
No full textWe compute the distribution of minima that are reached dynamically on multi field axionic landscapes, both numerically and analytically. Such landscapes are well suited for inflationary model building due to the presence of shift symmetries and possible alignment effects (the KNP mechanism). The resulting distribution of dynamically reached minima differs considerably from the naive expectation based on counting all vacua. These differences are more pronounced in the presence of many fields due to dynamical selection effects: while low lying minima are preferred as fields roll down the potential, trajectories are also more likely to get trapped by one of the many nearby minima. We show that common analytic arguments based on random matrix theory in the large D-limit to estimate the distribution of minima are insufficient for quantitative arguments pertaining to the dynamically reached ones. This discrepancy is not restricted to axionic potentials. We provide an empirical expression for the expectation value of such dynamically reached minimas' height and argue that the cosmological constant problem is not alleviated in the absence of anthropic arguments. We further comment on the likelihood of inflation on axionic landscapes in the large D-limit.SCOAP
A smooth landscape: ending saddle point inflation requires features to be shallow
No full textWe consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and find a negative, potentially large, local non-linearity parameter. To be consistent with current observational bounds, the hole needs to be shallow, i.e. considerably wider than deep in natural units. To avoid singling out our vacuum as special (i.e. more special than a positive cosmological constant entails), we deduce that all features on field space should be similarly shallow, severely limiting the type of landscapes one may use for inflationary model building. We justify the use of a truncated Fourier series with random coefficients, which are suppressed the higher the frequency, to model such a smooth landscape by a random potential, as is often done in the literature without a good a priory reason
A universal bound on excitations of heavy fields during inflation
No full textWe discuss a universal bound on any excitation of heavy fields during inflation: the ratio of the heavy field's energy density to the one driving inflation must be less than the maximally allowed relative amplitude of oscillations in the power-spectrum (rho(h)/rho(I) less than or similar to 0.01 according to PLANCK). This bound can be traced back to the sudden change of the equation of state parameter across the excitation event. We employ a sudden transition approximation at the perturbed level, which has been used before in different settings; we check its validity by comparison to the full multi-field result in a concrete case study involving a sudden mass change of an inflaton.CAPES (Brazil); CNPq (Brazil); DAAD (Germany
On the unlikeliness of multi-field inflation: bounded random potentials and our vacuum
No full textBased on random matrix theory, we compute the likelihood of saddles and minima in a class of random potentials that are softly bounded from above and below, as required for the validity of low energy effective theories. Imposing this bound leads to a random mass matrix with non-zero mean of its entries. If the dimensionality of field-space is large, inflation is rare, taking place near a saddle point (if at all), since saddles are more likely than minima or maxima for common values of the potential. Due to the boundedness of the potential, the latter become more ubiquitous for rare low/large values respectively. Based on the observation of a positive cosmological constant, we conclude that the dimensionality of field-space after (and most likely during) inflation has to be low if no anthropic arguments are invoked, since the alternative, encountering a metastable deSitter vacuum by chance, is extremely unlikely
Particle production during inflation in light of Planck data
No full textWe consider trapped inflation in a higher dimensional field space: particle production at a dense distribution of extra species points leads to a terminal velocity at which inflation can be driven in steep potentials. We compute an additional, nearly scale invariant contribution to the power spectrum, caused by backscattering of the continuously produced particles. Since this contribution has a blue tilt, it has to be subdominant, leading to an upper bound on the coupling constant between the inflatons and the extra species particles. The remaining allowed parameter space is narrow
Anatomy of bispectra in general single-field inflation — Modal expansions
No full textWe discuss bispectra of single-field inflationary models described by general Lorentz invariant Lagrangians that are at most first order in field derivatives, including the fast-roll models investigated by Noller and Magueijo. Based on a factor analysis, we identify the least correlated basic contributions to the general shape and show quantitatively which templates provide a good approximation. We compute how relative contributions of basic shapes to the total bispectrum scale as slow roll is relaxed. To enable future comparison with CMB observations, we provide a modal expansion of these non-separable bispectra in Fourier space, employing the formalism by Fergusson et al. Convergence is rapid, usually better than ninety-five percent with less than thirty modes, due to the smoothness of these primordial shapes. Truncated polynomial modal expansions have restrictions, which we highlight using an example with slow convergence. The particular shape originates from particle production during inflation ( common in trapped inflation) and entails both localized and oscillatory features. We show that this shape can be recovered efficiently using a Fourier basis and outline the prospect of future model parameter extraction and N-body simulations based on modal techniques
Local random potentials of high differentiability to model the Landscape
No full textWe generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class C-k, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes (k >= 2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k = 2 for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D similar to 100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications
Enhanced preheating after multi-field inflation: on the importance of being special
No full textWe discuss preheating after multi-field inflation in the presence of several preheat matter fields that become light in the vicinity of (but not at) the inflatons' VEV, at distinct extra-species-points (ESP); this setup is motivated by inflationary models that include particle production during inflation, e. g. trapped inflation, grazing ESP encounters or modulated trapping, among others. While de-phasing of inflatons tends to suppress parametric resonance, we find two new effects leading to efficient preheating: particle production during the first in-fall (efficient if many preheat matter fields are present) and a subsequent (narrow) resonance phase (efficient if an ESP happens to be at one of several distinct distances from the inflatons' VEV). Particles produced during the first in-fall are comprised of many species with low occupation number, while the latter are made up of a few species with high occupation number. We provide analytic descriptions of both phases in the absence of back-reaction, which we test numerically. We further perform lattice simulations to investigate the effects of back-reaction. We find resonances to be robust and the most likely cause of inflaton decay in multi-field trapped inflation if ESP distributions are dense
Probing two-field open inflation by resonant signals in correlation functions
No full textWe derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of detecting these tell-tale signs in current experiments, which is challenging, but not impossible. At the technical level, we pay special attention to the applicability conditions for truncating fluctuations to the light (inflaton) field and derive upper limits on the oscillation amplitude of the heavy field. A violation of these bounds requires a multi-field analysis at the perturbed level.NSF [1066293
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