A n' s dn s /d ln k. HarrisonZel' dovich


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1 4 3 4 Vol 43 No Journal of Shanghai Normal University Natural Sciences Astrophysics Aug DOI /J 1SSN O A B  BICEP2 1 B  B  BICEP r = % CL 7 0σ r = 0 BICEP2 Planck 2 Planck + WP + highl n s = ± r < % CL n' s dn s /d ln k n s = ± r < 0 26 n' s = % CL n' s B  V chaotic inflation V ~ n6 natural inflation V ~ V 0 cos /f HarrisonZel' dovich n s  1 ~ CG ZR shnu edu cn shnu edu cn
2 O 102 n' s ~ O efolding N N 20 ~ M  2 pl = 8πG = V V = λ a n 2n λ = M2 pl 2 V' ( V ) 1 2 V η = M 2 pl V ξ = V'V ' M4 pl 2 V 2 n s n' s n s  1 2η n s ' 16 η ξ 4 ξ η ξ = α + β  α η α β 1 5 n 2 a n a n = 1 Σn1 4n 2n  1 n  1 k = 1 a nk 2β  3α k 2 + αn + α  β k a k  4 k + 1 n  k 2n  2k  1 n  k  1 a k a 1 λ a 1 = 1 β = 0 a n n 2 = 0 V ~ 2 V ~ e V ~ Σ n /n Taylor Taylor α β λ SUGRA K hler V = e K K i j D i W D W W  3 W 2 D i W = i W + i K W 5 7 K = g 1 φ + φ φ + φ 2 + X 2  c X X shift φ 槡 2Imφ X
3 4 393 W = XΣ h n n + W α α β 1 V V ~ = b n 2n η = 2 c n 2n ξ = 2 d n 2n b 0 = 4 c 0 = 2 d 0 = 2βn 1 b n c n d n Σ n k = 1 b n = 4 n + 1 a n+1 + Σ n k = 1 [ ] 10 4 k + 1 n  k + 1 a k +1 a nk +1  Σ k +1 a m a k +2 m b 11 nk c n = 2 n + 1 2n + 1 a n+1  Σ n k = 1 d n = 8 n + 2 2n + 3 n + 1 a n+2 + m = 1 a k +1 c nk [ ] 12 8 k + 1 n  k + 2 2n  2k + 3 n  k + 1 a k +1 a nk +2  Σ k +1 a m a k +2 m d 13 nk 3 efolding f 0 = 1 t end end V N = Hdt =  t V' f n = a n+1  Σ n k = 1 d = 2 4 Σ k = 0 f n n + 1 2n m = 1 k + 1 a k +1 f nk n 12n end end b n 2n end end end ~ M pl
4 ( ) k P s = A s k * n s 1 +n s 'ln k /k * /2 17 A s n s 3 n s ' = dn s /d ln k n s ' = 16 η α  2 β  α η 18 r r α 2 n' s ~ O ~ O 102 r r n s n' s n s r = Planck WMAP Planck + WP highl Planck BAO ± Planck + WP ± Planck + WP + lensing ± Planck + WP + highl ± Planck + WP + BAO n' s = ± Planck + WP n' s = ± Planck + WP + lensing n' s = Planck + WP + highl n' s = Planck + WP + BAO 19 Background Imaging of Cosmic Extragalactic Polarization B2 Planck WP r = Supernova Legacy Survey SNLS r = Planck Union BAO BICEP2 r = BAO r = B α β 3 /M pl O 10 Planck A s k = Mpc  1 = λ n ( ) λ 3π2 2 a n 2 α β 21 r A s
5 α β 1σ 2σ α β r 0 2 n' s O 102 n s a n b n c n d n f n a n 6 V 5 26 a k x k b k x k k = 0 k = 0 = k = 0 c k x k c n = Σ n k = 0 a k b nk 6 11 ~ 13 a n b n c n d n 2n 2na n 2n = 2n 2n  1 a n 2n = 2n 4n n + 1 2n + 1 a n+1 2n = c n 2n b n 2n 21 α 2 α  β α b n  2 α  β c n  2 d n 2n = d n 2n 2n 2α n + 2 α  β a n  8n n + 1 2n + 1 a n+1 2n  8 α  β n 2 a n 2n a n αb n  2 α  β c n  2 d ~ a 1 λ a 1 = 1 5
6 a 1 = a 2 a 3 = β = β 5β  3α 2880 a 4 = β ( 10α2 223αβ + 15β ) a 5 = β (  210α α 2 β  330αβ β ) b 0 = 4 31 b 1 = β 3 32 b 2 = β 5β  4α 240 b 3 = β ( 18α αβ + 13β ) b 4 =  β ( 20α336α 2 β + 5αβ β ) b 5 =  β (  42α4 + 43α 3 β + 120α 2 β 2175αβ β ) c 0 = 2 37 c 1 c 2 = 5β = β 15β  14α 480 c 3 = β ( 162α αβ + 47β ) c 4 = β (  110α3 + 81α 2 β + 110αβ β ) c 5 = β ( 1092α α 3 β α 2 β αβ β ) d 0 = 2β 43 d 1 = β 5β  3α 12 44
7 4 397 d 2 = β ( 10α2 224αβ + 15β ) 480 d 3 = β (  126α α 2 β  234αβ β ) d 4 =  β (  90α α 3 β + 34α 2 β 2180αβ β ) d 5 =  β ( 924α5 + 74α 4 β α 3 β α 2 β αβ β ) f 0 = 1 49 f 1 =  β f 2 = β f 3 = β (  30α2 229αβ + 25β ) f 4 = β ( 42α α 2 β  111αβ 2 34β ) f 5 =  β ( 630α α 3 β α 2 β αβ β ) ADE P A R AIKIN R W BARKATS D et al BICEP2 Collaboration BICEP2 I Detection of Bmode polarization at degree angular scales J /OL arxiv astro  ph CO 2ADE P A R AGHANIM N ARMITAGECAPLAN C et al Planck Collaboration Planck 2013 results XXII Constraints on inflation J /OL arxiv astro  ph CO 3GUTH A H The inflationary universe A possible solution to the horizon and flatness problems J Phys Rev D LINDE A D A new inflationary universe scenario A possible solution of the horizon flatness homogeneity isotropy and primordial monopole problems J Phys Lett B ALBRECHT A STEINHARDT P J Cosmology for grand unified theories with radiatively induced symmetry breaking J Phys Rev Lett LINDE A D Chaotic inflation J Phys Lett B FRESSE K FRIEMAN J A OLINTO A V Natural inflation with pseudonambugoldstone bosonsj Phys Rev Lett GONG Y The challenge for single field inflation with BICEP2 result J /OL arxiv gr  qc 9CHUNG D J H SHIU G TRODDEN M Running of the scalar spectral index from inflationary models J Phys Rev D EASTHER R PEIRIS H Implications of a running spectral index for slow roll inflation J JCAP ~ 8
8 astro  ph / FENG B LI M Z ZHANG R J et al An inflation model with large variations in spectral index Phys Rev D astro  ph / KOBAYASHI T TAKAHASHI F Running spectral index from inflation with modulations J JCAP ~ J J MA Y Z WANG Y Reconstructing the local potential of inflation with BICEP2 data J /OL arxiv astro  ph CO 16CHOUDHURY S MAZUMDAR A Reconstructing inflationary potential from BICEP2 and running of tensor modesj / OL arxiv hep  th 17NAKAYAMA K TAKAHASHI F YANAGIDA T T Polynomial chaotic inflation in supergravity J Journal of Cosmology and Astroparticle Physics ~ 18 18KOBAYASHI T SETO O Polynomial inflation models after BICEP2 J /OL arxiv astro  ph CO 19CHENG C HUANG Q G Constraints on the cosmological parameters from BICEP2 Planck and WMAP J /OL arxiv astro  ph CO 20CHENG C HUANG Q G Constraint on inflation model from BICEP2 and WMAP 9year data J /OL arxiv astro  ph CO 21LI H XIA J Q ZHANG X Global fitting analysis on cosmological models after BICEP2 J /OL arxiv astro  ph CO 22WU F LI Y LU Y et al Cosmological parameter fittings with the BICEP2 data J /OL arxiv astro  ph CO 23LIZARRAGA J URRESTILLA J DAVERIO D et al Can topological defects mimic the BICEP2 Bmode signal J /OL arxiv astro  ph CO 24HO C M HSU S D Does the BICEP2 observation of cosmological tensor modes imply an era of nearly planckian energy densities J /OL arxiv hep  ph 25ADE P A R AGHANIM N ARMITAGECAPLAN C et alplanck Collaboration Planck 2013 results XVI Cosmological parameters J /OL arxiv astro  ph CO 26GRADSHTEYN I S RYZHIK I M JEFFREY A et al Table of integrals series and productsm 7th edition USA Elsevier Academic Press 2007 Power series inflation and primordial gravitational waves FENG ChaojunLI Xinzhou Shanghai United Center for Astrophysics SUCA Shanghai Normal UniversityShanghai China Abstract The tensortoscalar ratio can be measured by observing the polarization of photos in the cosmic microwave background It shows very strong power on constraining inflation models However for a single field inflation model it can not predict both a large tensortoscalar ratio and a large running of the scalar power spectral index To solve this problem the authors propose an inflation model with power series potential It is found that this model is consistent with latest observations Key words tensortoscalar ratio spectral index running of spectral index power series inflation
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