Infrared divergence of pure Einstein gravity contributions to cosmological density power spectrum J....
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Transcript of Infrared divergence of pure Einstein gravity contributions to cosmological density power spectrum J....
Infrared divergence of pure Einstein gravity contributions to cosmological density power spectrum
J. Hwang, H. Noh, D. Jeong
1Phys. Rev. Lett. 103, 121301, arXiv:0902.4285
Linear order: Lifshitz (1946)/Bonnor(1957)
Second order: Peebles (1980)/Noh-Hwang(2004)
Third order: Hwang-Noh (2005)
Physical Review D, 72, 044012 (2005). Pure General Relativistic corrections
(comoving-synchronous gauge)
2
Curvature perturbation in the comoving gauge
~10-5
(K=0, comoving gauge)
General relativistic contributions to second-order power spectrum:
132211
312
22
12
321
)Re(2||||||
PPP
P
Pure General Relativistic contribution!
EinsteinNewton
EinsteinNewton
PPP ,13,1313
,3,33
Relativistic/Newtonian4
Density power spectrum to second-order:
Physical Review D, 77,123533 (2008)
Pure General Relativistic corrections P13,Einstein
Newtonian
P22 +
P13,Newton
K=0 =Λ:
5
Dashed line: negative
P13,Einstein
P22
P11
P13,Newton
PTotal
P22 + P
13,Newton
9Phys. Rev. Lett. 103, 121301, arXiv:0902.4285
P13,Einstein
Large-scale limit (k→0, r→∞):
P13,Newton
Leading orderNewton
Next-to-leading orderNewton
10
In the large scale we discover an infrared divergence in the next-to-leading-order power spectrum due to pure Einstein gravity contribution appearing in the third-order perturbation.
Despite cancellations of the leading-order and next-to-leading order terms in P
13,Newton, no such cancellations occur in
P13,Einstein
.
11
P13,Einstein
Small-scale limit (k→∞, r→0):
P13,Newton
Leading order, Einstein
Next-to-leading order, Einstein
Leading order, Newton
13
P22
In the small-scale the Einstein's gravity contribution is still negligibly small.
Due to cancellation of the leading-order and next-to-leading order terms in P
13,Einstein, despite a cancellation between P
22 in
P13,Newton
.
14