Example of equilateral non-G: modified sound speed E C=P(O, X) dtd ae ( X Px+2XPxX 2入 3k1k2k3 2(k1+k2+k3)3 好+++好+起号++号+k 内12k(+k2+k 2k1k2k3(k1+k2+k3)2 +1+周 8k1k2k3 Of order fi NL Chen, huang, Kachru, Shiu 2006
Example of equilateral non-G: modified sound speed Of order 𝑓𝑁𝐿 Chen, Huang, Kachru, Shiu 2006
Many many many similar stories 2000s-2013
Many many many similar stories 2000s – 2013
Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity Planck Collaboration P A R. Ade7, N. Aghanim6o, C. Armitage-Caplan03, M. Arnaud73, M. Ashdown70, 6, F. Atrio-Barandelai8,J. Aumont6o C. BaccigalupiB6, A. ]. Banday96,,R. B. Barreiro 67,J. G. Bartlett1,6, N. Bartolo34, E. Battaner97, K. Benabed61, 95,A. DA58AD1A25.61.951n。aA96.9MaA113751 o DiAl=96.9861pk7311pA=L68.10A Received: 22 March 2013 Accepted: 16 December 2013 The Planck nominal mission cosmic microwave background(CMB)maps yield unprecedented constraints on primordial non-Gaussianity(NG). Using three optimal bisp estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum ampli quoting as our final result f local= 2.7* 5.8, equ=-42*75, and fOrth =.25* 39(68%CL statistical). Non-Gaussianity is detected in the data; using skew-Ct sta we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-iensing bispectrum at a level expected in the ACDM scenario. The results are on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an ext suite of tests, and are confirmed by skew-Ct wavelet bispectrum and Minkowski functional estimators, Beyond estimates of individual shape amplitudes, we present r independent, three-dimensional reconstructions of the planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, inc general single-field models of inflation, excited initial states(non-Bunch-Davies vacua), and directionally-dependent vector models, We provide an initial survey of dependent feature and resonance models, These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c, 2 0.02 CL), in an effective field theory parametrization, and the curvaton decay fraction rp 20.15(95% CL). The Planck data significantly limit the viable parameter space ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model TN< 2800(95% CL). Taken together, these constraints represent the highest pr tests to date of physical mechanisms for the origin of cosmic structure. fORlocal=27±5.8, fULgur=-42±75, and fNL orth=-25±39(68% CL statistical)
Planck 2015 results XVII. Constraints on primordial non-Gaussianity Planck Collaboration P. A. R. Ade7, N. Aghanim63, M. Arnaud7, F. Arroja1,85, M. Ashdown75,6, 3. Aumont 63, C. Baccigalupi95,M Ballardini51 53 34, A. Banday109, 10, R. B. Barreiro/o,N. Bartolo33, 71,s. Basak9, E. Battaner110, 111, K. Benabed64, 108, Ronai+61 A Ransit.l av26, 64, 108 1p Bernard109,10 M Rareanlli37,52 D Rielewie,89, 10 95 11 Rock7212 A Received: 6 February 2015 Accepted: 27 January 2016 Abstract The Planck full mission cosmic microwave background(CMB)temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gauss (NG). Using three classes of optimal bispectrum estimators- separable template-fitting(KSW), binned, and modal we obtain consistent values for the primordial equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone floclNL= 2.5+ 5.7, fequN I=.16+70,, and forthoNL=34*32 CL, statistical). Combining temperature and polarization data we obtain flocaNL= 0.8* 5.0, sequin=.4+ 43, and fothoNL =-26* 21(68%CL, statistical). The resul based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, extensive suite of tests, and are consistent with estimators based on measuring the minkowski functionals of the CMB. the effect of time-domain de- glitching systemat the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch noise model in simulations and the data, Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initi modifications, models producing parity-violating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent featur resonance models, accounting for the "look elsewhere"effect in estimating the statistical significance of features, We also look for isocurvature NG, and find no signal, b obtain constraints that improve significantly with the inclusion of polarization, The primordial trispectrum amplitude in the local model is constrained to be gocanL= 7.7)X 10(68%CL statistical), and we perform an analysis of trispectrum shapes beyond the local case. The global picture that emerges is one of consistency wi premises of the ACDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations floraN=0.8±5.0,feuL=-4±43, and forthoNL=-26±21(68%CL, statistical)
WMAP 21cm COBE lyr(2003) Planck △fM~10-3 (1990s) △fM~100 (2013) △fM~0.5 △fM~20007yr(2010) △fM~5 CMB distortion △fA~20 △fML~10
COBE (1990s) ∆ 𝑓𝑁𝐿 ~2000 WMAP 1yr (2003) ∆𝑓𝑁𝐿~100 7yr (2010) ∆𝑓𝑁𝐿~20 Planck (2013) ∆𝑓𝑁𝐿~5 LSS ∆ 𝑓𝑁𝐿 ~ 0.5 21cm: ∆ 𝑓𝑁𝐿 ~ 10 − 3 CMB distortion: ∆𝑓𝑁𝐿~ 10−3