arXiv subjects

Marcello Musso

Publications and source records attributed to Marcello Musso.

25 records · Page 2Linked to original sources

arXiv2011

The (not so) squeezed limit of the primordial 3-point function

We prove that, in a generic single-field model, the consistency relation for the 3-point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as (k_L/k_S)^2. This implies that a detection of a bispectrum signal going as 1/k_L^2 in the squeezed limit, that is suppressed only by one power of k_L compared with the local shape, would rule out all single-field models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale dependence of the bias, for scales much larger than the size of the haloes, would disprove all single-field models. We comment on the regime of squeezing that can be probed by realistic surveys.

astro-ph.CO↗

arXiv2011

Non-Gaussian halo abundances in the excursion set approach with correlated steps

We study the effects of primordial non-Gaussianity on the large scale structure in the excursion set approach, accounting for correlations between steps of the random walks in the smoothed initial density field. These correlations are induced by realistic smoothing filters (as opposed to a filter that is sharp in k-space), but have been ignored by many analyses to date. We present analytical arguments -- building on existing results for Gaussian initial conditions -- which suggest that the effect of the filter at large smoothing scales is remarkably simple, and is in fact identical to what happens in the Gaussian case: the non-Gaussian walks behave as if they were smooth and deterministic, or "completely correlated". As a result, the first crossing distribution (which determines, e.g., halo abundances) follows from the single-scale statistics of the non-Gaussian density field -- the so-called "cloud-in-cloud" problem does not exist for completely correlated walks. Also, the answer from single-scale statistics is simply one half that for sharp-k walks. We explicitly test these arguments using Monte Carlo simulations of non-Gaussian walks, showing that the resulting first crossing distributions, and in particular the factor 1/2 argument, are remarkably insensitive to variations in the power spectrum and the defining non-Gaussian process. We also use our Monte Carlo walks to test some of the existing prescriptions for the non-Gaussian first crossing distribution. Since the factor 1/2 holds for both Gaussian and non-Gaussian initial conditions, it provides a theoretical motivation (the first, to our knowledge) for the common practice of analytically prescribing a ratio of non-Gaussian to Gaussian halo abundances.

astro-ph.CO↗

arXiv2011

An Improved Calculation of the Non-Gaussian Halo Mass Function

The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has been calculated by several authors in different ways, typically by exploiting the smallness of certain parameters which naturally appear in the calculation, to set up a perturbative expansion. We improve upon the existing results for the mass function by combining path integral methods and saddle point techniques (which have been separately applied in previous approaches). Additionally, we carefully account for the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity for large mass scales and at high redshifts, and must therefore be treated non-perturbatively. Our approach allows us to do this, and to also account for multi-scale density correlations which appear in the calculation. We thus derive an accurate expression for the mass function which is based on approximations that are valid over a larger range of mass scales and redshifts than those of other authors. By tracking the terms ignored in the analysis, we estimate theoretical errors for our result and also for the results of others. We also discuss the complications introduced by the choice of smoothing filter function, which we take to be a top-hat in real space, and which leads to the dominant errors in our expression. Finally, we present a detailed comparison between the various expressions for the mass functions, exploring the accuracy and range of validity of each.

astro-ph.CO↗

arXiv2011

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $δ_c$, the void excursion set problem involves two barriers $δ_v$ and $δ_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.

astro-ph.CO↗

arXiv2011

Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic non-Gaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.

hep-th↗

arXiv2005

On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation

A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naively suspected and, in general, only breaks down at the very end of inflation.

hep-th↗

arXiv2005

Solving Stochastic Inflation for Arbitrary Potentials

A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models namely large field, small field, hybrid and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.

hep-th↗