arXiv subjects

Naonori S. Sugiyama

Publications and source records attributed to Naonori S. Sugiyama.

23 records · Page 2Linked to original sources

arXiv2013

δN formalism

Precise understanding of nonlinear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale structure of the universe. The "δN formalism" is a popular and powerful technique for computing non-linear evolution of cosmological perturbations on large scales. In particular, it enables us to compute the curvature perturbation, ζ, on large scales without actually solving perturbed field equations. However, people often wonder why this is the case. In order for this approach to be valid, the perturbed Hamiltonian constraint and matter-field equations on large scales must, with a suitable choice of coordinates, take on the same forms as the corresponding unperturbed equations. We find that this is possible when (1) the unperturbed metric is given by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric; and (2) on large scales and with a suitable choice of coordinates, one can ignore the shift vector (g0i) as well as time-dependence of tensor perturbations to gij/a2(t) of the perturbed metric. While the first condition has to be assumed a priori, the second condition can be met when (3) the anisotropic stress becomes negligible on large scales. However, in order to explicitly show that the second condition follows from the third condition, one has to use gravitational field equations, and thus this statement may depend on the details of theory of gravitation. Finally, as the δN formalism uses only the Hamiltonian constraint and matter-field equations, it does not a priori respect the momentum constraint. We show that the violation of the momentum constraint only yields a decaying mode solution for ζ, and the violation vanishes when the slow-roll conditions are satisfied.

gr-qc↗

arXiv2012

Toward an accurate Dark Matter power spectrum beyond BAO scales

We propose a new approximated expression for non-linear Dark Matter power spectrum much beyond BAO scales. The proposed expression agrees with the result of N-body simulation with the accuracy better than 2 % up to k=1.0 [h/Mpc] and k=0.7 [h/Mpc] at z=3.0 and z=1.0, respectively. Even at z=0.35, the accuracy remains within 10 % up to k=0.8 [h/Mpc]. In doing so, we used an approximation for the kernel functions used in the Standard Perturbation Theory (SPT) which is also used to prove the Reg PT proposed by Bernardeau et al. (2011).

gr-qc↗

arXiv2012

An Application of Wiener Hermite Expansion to Non-linear Evolution of Dark Matter

We apply the Wiener Hermite (WH) expansion to the non-linear evolution of Large-Scale Structure, and obtain an approximate expression for the matter power spectrum in full order of the expansion. This method allows us to expand any random function in terms of an orthonormal bases in space of random functions in such a way that the first order of the expansion expresses the Gaussian distribution, and others are the deviation from the Gaussianity. It is proved that the Wiener Hermite expansion is mathematically equivalent with the $Γ$-expansion approach in the Renormalized Perturbation Theory (RPT). While an exponential behavior in the high-$k$ limit has been proved for the mass density and velocity fluctuations of Dark Matter in the RPT, we reprove the behavior in the context of the Wiener Hermite expansion using the result of Standard Perturbation Theory (SPT). We propose a new approximate expression for the matter power spectrum which interpolates the low-$k$ expression corresponding to 1-loop level in SPT and the high-$k$ expression obtained by taking a high-$k$ limit of the WH expansion. The validity of our prescription is specifically verified by comparing with the 2-loop solutions of the SPT. The proposed power spectrum agrees with the result of $N$-body simulation with the accuracy better than 1% or 2% in a range of the BAO scales, where the wave number is about $k= 0.2 \sim 0.4$ $h{\rm Mpc^{-1}}$ at $z=0.5-3.0$. This accuracy is comparable to or slightly less than the ones in the Closure Theory whose the fractional difference from N body result is within 1%. A merit of our method is that the computational time is very short because only single and double integrals are involved in our solution.

astro-ph.CO↗

arXiv2012

Consistency Relation for multifield inflation scenario with all loop contributions

The consistency relation between non-linear parameters $f_{NL}$ and $τ_{NL}$ characterizing Non-Gaussianity generated during the inflationary period have been emerged as a useful tool which have a possibility to rule out a large class of inflationary models all at once. In our previous work, we extended the Suyama-Yamaguchi inequality up to 1-loop corrections. In this paper, we derive an inequality extended up to {\it all} loop corrections which has the same expression with the original Suyama-Yamaguchi inequality, $τ_{NL} \geq (6/5f_{NL})^2$, where the equality is not satisfied in the case of single field models any more.

gr-qc↗

arXiv2011

Non-Gaussianity Consistency Relation for Multi-field Inflation

While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. We show that multi-field models described by the $δN$ formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $τ_{\rm NL}$, such that $τ_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations.

gr-qc↗