TY - JOUR

T1 - Perturbation theory of large scale structure in the ΛcDM Universe

T2 - Exact time evolution and the two-loop power spectrum

AU - Fasiello, Matteo

AU - Fujita, Tomohiro

AU - Vlah, Zvonimir

N1 - Funding Information:
M. F. would like to acknowledge support from the “Atracción de Talento” Grant No. 2019-T1/TIC15784; his work is partially supported by the Spanish Research Agency (Agencia Estatal de Investigación) through the Grant IFT Centro de Excelencia Severo Ochoa No. CEX2020-001007-S, funded by Grant No. MCIN/AEI/10.13039/501100011033. T. F. acknowledges the support by the Grant-in-Aid for Scientific Research Fund of the JSPS Grants No. 18K13537 and No. 20H05854. Z. V. acknowledges the support of the Kavli Foundation.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/12/15

Y1 - 2022/12/15

N2 - We derive exact analytic solutions for density and velocity fields to all orders in Eulerian standard perturbation theory for ΛCDM cosmology. In particular, we show that density- and velocity-field kernels can be written in a separable form in time and momenta at each perturbative order. The kernel solutions are built from an analytic basis of momentum operators and their time-dependent coefficients, which solve a set of recursive differential equations. We also provide an exact closed perturbative solution for such coefficients, expanding around the (quasi-)Einstein-de Sitter (EdS) approximation. We find that the perturbative solution rapidly converges towards the numerically obtained solutions and its leading-order result suffices for any practical requirements. To illustrate our findings, we compute the exact two-loop dark matter density- and velocity power spectra in ΛCDM cosmology. We show that the difference between the exact ΛCDM and the (quasi-)EdS approximated result can reach the level of several percent (at redshift zero, for wave numbers k<1 h/Mpc). This deviation can be partially mitigated by exploiting the degeneracy with the effective field theory counterterms. As an additional benefit of our algorithm for the solutions of time-dependent coefficients, the computational complexity of power-spectra loops in ΛCDM is comparable to the EdS case. In performing the two-loop computation, we devise an explicit method to implement the so-called IR cancellations, as well as the cancellations arising as a consequence of mass and momentum conservation.

AB - We derive exact analytic solutions for density and velocity fields to all orders in Eulerian standard perturbation theory for ΛCDM cosmology. In particular, we show that density- and velocity-field kernels can be written in a separable form in time and momenta at each perturbative order. The kernel solutions are built from an analytic basis of momentum operators and their time-dependent coefficients, which solve a set of recursive differential equations. We also provide an exact closed perturbative solution for such coefficients, expanding around the (quasi-)Einstein-de Sitter (EdS) approximation. We find that the perturbative solution rapidly converges towards the numerically obtained solutions and its leading-order result suffices for any practical requirements. To illustrate our findings, we compute the exact two-loop dark matter density- and velocity power spectra in ΛCDM cosmology. We show that the difference between the exact ΛCDM and the (quasi-)EdS approximated result can reach the level of several percent (at redshift zero, for wave numbers k<1 h/Mpc). This deviation can be partially mitigated by exploiting the degeneracy with the effective field theory counterterms. As an additional benefit of our algorithm for the solutions of time-dependent coefficients, the computational complexity of power-spectra loops in ΛCDM is comparable to the EdS case. In performing the two-loop computation, we devise an explicit method to implement the so-called IR cancellations, as well as the cancellations arising as a consequence of mass and momentum conservation.

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U2 - 10.1103/PhysRevD.106.123504

DO - 10.1103/PhysRevD.106.123504

M3 - Article

AN - SCOPUS:85144117231

VL - 106

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 12

M1 - 123504

ER -