1. Infrared divergence of pure Einstein gravity contributions to cosmological density power spectrum J. Hwang, H. Noh, D. Jeong 1 Phys. Rev. Lett. 103, 121301, arXiv:0902.4285

2. 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)

3. General relativistic contributions to second-order power spectrum: Pure General Relativistic contribution! Relativistic/Newtonian 4

4. Density power spectrum to second-order: Physical Review D, 77,123533 (2008) Pure General Relativistic corrections P 13,Einstein Newtonian P 22 + P 13,Newton K=0 = Λ: 5

5. P 13,Einstein P 22 P 11 P 13,Newton 7 Phys. Rev. Lett. 103, 121301, arXiv:0902.4285

6. Dashed line: negative P 13,Einstein P 22 P 11 P 13,Newton P Total P 22 + P 13,Newton 9 Phys. Rev. Lett. 103, 121301, arXiv:0902.4285

7. P 13,Einstein Large-scale limit (k →0, r →∞ ): P 13,Newton Leading order Newton Next-to-leading order Newton 10

8. 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 P 13,Einstein. 11

9. P 13,Einstein P 13,Newton Leading order Newton Next-to-leading order Newton 12

10. P 13,Einstein Small-scale limit (k →∞, r →0 ): P 13,Newton Leading order, Einstein Next-to-leading order, Einstein Leading order, Newton 13 P 22

11. 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 P 13,Newton. 14

12. P 13,Einstein P 13,Newton Leading order Einstein Next-to-leading order Einstein 15

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