2013

Cosmological perturbation theory at three-loop order

Blas, Diego, Garny, Mathias, Konstandin, Thomas

Understand

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure.

We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series.
We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present.
Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

Built on

F. J. Dyson, “Divergence of perturbation theory in quantum electrodynamics,” Phys. Rev. 85
1952
Earlier work this paper cites.
G. A. Baker Jr. (Ed.) and J. L. Gammel (Ed.), “Pade Approximant in Theoretical Physics” (Elsevier Science , 1970)
1970
Earlier work this paper cites.
C. M. Bender and S. A. Orszag, “Advanced mathematical methods for scientists and engineers” (McGraw-Hill , 1978)
1978
Earlier work this paper cites.
P. J. E. Peebles, “The Large-Scale Structure of the Universe” (Princeton University Press, 1980)
1980
Earlier work this paper cites.
M. H. Goroff, B. Grinstein, S. J. Rey and M. B. Wise, “Coupling of Modes of Cosmological Mass Density Fluctuations,” Astrophys. J. 311
1986
Earlier work this paper cites.
J. N. Fry, “The Minimal power spectrum: Higher order contributions,” Astrophys. J. 421
1994
Earlier work this paper cites.
R. Scoccimarro and J. Frieman, “Loop corrections in nonlinear cosmological perturbation theory,” Astrophys. J. Suppl. 105
1996
Earlier work this paper cites.
D. J. Eisenstein and W. Hu, “Power spectra for cold dark matter and its variants,” Astrophys. J. 511
1997
Earlier work this paper cites.
T. Matsubara, A. Yoshisato and M. Morikawa, “Beyond Zeldovich type approximations in gravitational instability theory: Pade prescription in spheroidal collapse,” Astrophys. J. 504
1998
Earlier work this paper cites.
A. Lewis, A. Challinor and A. Lasenby, “Efficient computation of CMB anisotropies in closed FRW models,” Astrophys. J. 538
2000
Earlier work this paper cites.
G. D. Moore and K. Rummukainen, “Electroweak bubble nucleation, nonperturbatively,” Phys. Rev. D 63
2001
Earlier work this paper cites.

Similar

F. Bernardeau, S. Colombi, E. Gaztanaga and R. Scoccimarro, “Large scale structure of the universe and cosmological perturbation theory,” Phys. Rept. 367
2002
Cited alongside, same era.
P. Valageas, “Dynamics of gravitational clustering v. subleading corrections in the quasi-linear regime,” A & A, 382
Original
2002
Cited alongside, same era.
T. Hahn, “CUBA: A Library for multidimensional numerical integration,” Comput. Phys. Commun. 168
2005
Cited alongside, same era.
M. Crocce and R. Scoccimarro, “Renormalized cosmological perturbation theory,” Phys. Rev. D 73
2006
Cited alongside, same era.
M. Crocce and R. Scoccimarro, “Memory of initial conditions in gravitational clustering,” Phys. Rev. D 73
2006
Cited alongside, same era.
T. Tatekawa, “Improving of the Lagrangian perturbative solution for cosmic fluid: Applying Shanks transformation,” Phys. Rev. D 75
2007
Cited alongside, same era.
W. J. Percival, S. Cole, D. J. Eisenstein, R. C. Nichol, J. A. Peacock, A. C. Pope and A. S. Szalay, “Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS,” Mon. Not. Roy. Astron. Soc. 381
Original
2007
Cited alongside, same era.
F. Bernardeau, M. Crocce and R. Scoccimarro, “Multi-Point Propagators in Cosmological Gravitational Instability,” Phys. Rev. D 78
Original
2008
Cited alongside, same era.
J. Carlson, M. White and N. Padmanabhan, “A critical look at cosmological perturbation theory techniques,” Phys. Rev. D 80
Original
2009
Cited alongside, same era.
S. Pueblas and R. Scoccimarro, “Generation of Vorticity and Velocity Dispersion by Orbit Crossing,” Phys. Rev. D 80
Original
2009
Cited alongside, same era.
J. Kim, C. Park, G. Rossi, S. M. Lee and J. R. Gott, III, “The New Horizon Run Cosmological N-Body Simulations,” J. Korean Astron. Soc. 44
Original
2011
Cited alongside, same era.
T. Nishimichi, A. Shirata, A. Taruya, K. Yahata, S. Saito, Y. Suto, R. Takahashi and N. Yoshida et al
Original
Cited in the paper.

Then

S. Nadkarni-Ghosh and D. F. Chernoff, “Extending the domain of validity of the Lagrangian approximation,” Mon. Not. Roy. Astron. Soc. 410
Original
2011
Later among the works it cites.
T. Okamura, A. Taruya and T. Matsubara, “Next-to-leading resummation of cosmological perturbations via the Lagrangian picture: 2-loop correction in real and redshift spaces,” JCAP 1108
Original
2011
Later among the works it cites.
S. Anselmi and M. Pietroni, “Nonlinear Power Spectrum from Resummed Perturbation Theory: a Leap Beyond the BAO Scale,” JCAP 1212
Original
2012
Later among the works it cites.
A. Taruya, F. Bernardeau, T. Nishimichi and S. Codis, “RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
J. J. M. Carrasco, M. P. Hertzberg and L. Senatore, “The Effective Field Theory of Cosmological Large Scale Structures,” JHEP 1209
Original
2012
Later among the works it cites.
M. Pietroni, G. Mangano, N. Saviano and M. Viel, “Coarse-Grained Cosmological Perturbation Theory,” JCAP 1201
Original
2012
Later among the works it cites.
M. Baldi, “Dark Energy Simulations,” Phys. Dark Univ. 1
Original
2012
Later among the works it cites.
A. Kehagias and A. Riotto, “Symmetries and Consistency Relations in the Large Scale Structure of the Universe,” Nucl. Phys. B 873
Original
2013
Closest in time.
M. Peloso and M. Pietroni, “Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure,” JCAP 1305
Original
2013
Closest in time.
N. S. Sugiyama and T. Futamase, “Relation between standard perturbation theory and regularized multi-point propagator method,” Astrophys. J. 769
Original
2013
Closest in time.
L. Amendola et al
Original
2013
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…