Constraints on primordial abundances and neutron life-time from CMB PhD Astronomy, Astrophysics and Space Science University of Sapienza and Tor Vergata Advisor: Alessandro Melchiorri
Introduction Comparison of different methods to estimate primordial abundances of light elements produced during the Big Bang Nucleosynthesis: direct astrophysical observations, values inferred from Cosmic Microwave Background. Results: new results from Planck 2015 description of low-multipoles likelihood constrain nuclear quantities from Cosmic Microwave Background neutron life-time. 1
Big Bang Nucleosynthesis Big Bang Nucleosynthesis (BBN): formation of light nuclei in the first minutes after the Big Bang. Before BBN: neutrinos decoupling 2.0 MeV<E<3.5 MeV e ± annihilation, photons reheating n departure from equilibrium for n. n p,id =3 7 8 4/3 4 11 neutrinos energy density, Instantaneous Decoupling n n (mn m p )c 2 =exp n p KT N e 3,ID neutrinos energy density, Non Instantaneous Decoupling Relativistic degrees of freedom N e =3.046 r = " 1+ 7 8 4/3 4 N e # 11 Steigmann, Annu. Rev. Nucl. Part. Sci. 2007.57:463-491 Total energy density of radiation Lesgourgues et al., New J. Phys.16 (2014) 065002 2
Big Bang Nucleosynthesis Initial conditions, t ' 2s, E 10 2 kev : neutrinos fully decoupled from other particles baryons and photons strictly coupled n n ' 0.2 n p 2-body reactions: nuclear reactions between protons and neutrons strong interactions high cross sections and rapid reaction rates BBN is a fast process. Final conditions, t ' 1000 s, E < 30 kev : 75% H 25% He traces of other elements ( D, He 3, Li 7, Be 7 ) 3
Big Bang Nucleosynthesis BBN: good check for the Standard Model of Cosmology. cosmological parameters Evaluate primordial abundances: observe regions with low astrophysical evolution estimate post-bbn trends of light elements D: monotonically decreasing trend He 3, He 4, Li 7 : trends depend on models of stellar and galactic evolution. We concentrate on D and He 4 abundances: Y BBN p = 4n He n b He abundance as mass fraction. y DP = 10 5 n D n b D abundance as mass fraction. Y BBN p =0.2465 ± 0.0097 (68 % c.l.) Aver et al. (2013) y DP =2.53 ± 0.04 (68 % c.l.) Cooke et al. (2014) y DP =2.87 ± 0.22 (68 % c.l.) Iocco et al. (2009) 4
Cosmic Microwave Background Cosmic Microwave Background (CMB): radiation coming from Last Scattering Surface. Fixsen et al. 1996 Apj 473 576. At first approximation: homogeneous and isotropic black-body spectrum. ht i =2.7255 K Planck 2013 results. XVI. 2014 A&A 571, A16 Temperature fluctuations v + u 2 t* T 10 5 T Planck 2013 results. XVI. 2014 A&A 571, A16 Planck 2015 results. I. arxiv:1502.01582 5
Cosmic Microwave Background After BBN: Universe is completely opaque. baryonic matter completely ionized Coulomb interactions free electrons Scattering Thomson photons thermal equilibrium: photon-baryonic fluid CMB formation Recombination Decoupling Last Scattering Surface (LSS) Baryon content from ionized to neutral. z = 1370 T = 3740 K Photons-electrons interaction rate slower than the expansion rate of the Universe. z = 1100 T = 3000 K Last scattering of photon with electron. Later: photon free streaming. z = 1100 T = 3000 K The Universe becomes transparent. 6
Cosmic Microwave Background Main observable: temperature anisotropies. T (n) = T (n) ht i ht i Hypothesis of gaussian fluctuations. C( ) =h T (n) T (n 0 )i Angular correlation function Spherical harmonic expansion 1X `X T (n) = `=0 m= ` a`m Y`m (n) C( ) = 1 4 1X C`(2` + 1)P`(cos ) `=0 Angular power spectrum Legendre transform of angular correlation function credit: http://lambda.gsfc.nasa.gov 7
Cosmic Microwave Background Planck TT spectrum Acoustic peaks: froze-in of photon-baryonic fluid oscillations. increase of! b = b h 2 higher amplitude of odd peaks Damping tail : related to the thickness of LSS. Damping of anisotropies on scales smaller than this thickness. Planck 2015 results. XIII. arxiv:1502.01589 Helium recombination : it affects free electrons fraction. Effects can be seen on the damping tail: increase of the diffusion damping. increase of Y p higher suppression at high ` 8
BBN and CMB BBN CMB astrophysical measurements of primordial abundances acoustic peaks:! b = b h 2! b = b h 2 primordial abundances 10 = 10 10 n 3 b n = 273.78 TCMB b h 2 2.7255 K Ishida et al., Phys. Rev. D 90 (2014) 8, 083519 Standard BBN (BBN): primordial abundances from CMB only as functions of! b = b h 2 and N e. negligible lepton asymmetry and neutrinos chemical potential. 9
BBN and CMB Primordial abundances from CMB: PArthENoPe code (Pisanti et al. 2008) fixing the neutron decay-time to n = (880.3 ± 1.1) [s] (Particle Data Group 2014, Olive et al. 2014) Few remarks: main uncertainty on helium fraction is obtained propagating the error on (Y BBN p )=0.0003 main uncertainty on D is due to the one on the rate of the interaction (y DP )=0.06 n d(p, )He 3 (Adelberger et al. 2011) 10
BBN and CMB Results from Planck 2015 Planck 2015 results. XIII. arxiv:1502.01589 Planck 2015 results. XIII. arxiv:1502.01589 N e =3.046 Planck TT + lowp CDM =)! b Relaxing N e He + Planck TT + lowp agreement between BBN and CMB! b =0.02222 +0.00045 0.00043 Y BBN P =0.24665 +(0.00020)0.00063 (0.00019)0.00063 N e =3.11 +0.59 0.57 D + Planck TT + lowp (95% c.l.) y DP =2.620 +(0.083)0.15 (0.085)0.15 (95% c.l.) N e =2.95 +0.52 0.52 (95% c.l.) uncertainty coming from baryon density theoretical uncertainty on BBN predictions 11
Planck 2015 results. XIII. arxiv:1502.01589 BBN and CMB Results from Planck 2015 Planck 2015 results. XIII. arxiv:1502.01589 Measuring Y p directly from CMB. Relaxing N e Planck TT + lowp Y p =0.253 +0.041 0.042 (95% c.l.) N e in agreement with the standard value. No evidence for extra relativistic degrees of freedom. Planck TT + lowp Y p =0.252 +0.058 0.065 (95% c.l.) 12
BBN and CMB How to improve estimate of primordial abundances: main uncertainties are due to particle-nuclear physics. Deuterium y DP =2.620 +(0.083)0.15 (0.085)0.15 Planck 2015 results. XIII. arxiv:1502.01589 SMALL TENSION y DP,C =2.53 ± 0.04 Cooke et al. arxiv:1308.3240 uncertainty on the rate of the reaction d(p, )He 3 S(E) exp <S(E) th of about 5 10% PArthENoPE code 30 kev <E BBN < 300 kev present CMB data: provide information on nuclear physics R 2 (T )=A 2 R exp 2 (T ) Di Valentino et al., Phys. Rev. D 90 (2014) 2, 023543 Considering Deuterium observations A 2 =1.106 ± 0.071 Planck 2015 results. XIII. arxiv:1502.01589 Higher reaction rate: more deuterium is destroyed better agreement between Planck and direct astrophysical measurements. 13
BBN and CMB Neutron life-time (Salvati et al., in preparation) Helium 4 Main uncertainty on helium abundance is due to the one on the neutron life-time. n From Particle Data Group Combining 5 most recent measurements with bottle method. bottle n = (879.6 ± 0.8) [s] Combining 2 most recent measurements with beam method. Value of neutron life-time quoted from the Particle Data Group. PDG n = (880.3 ± 1.1) [s] Olive et al., (PDG), Chin. Phys. C, 38, 090001 (2014). beam n = (888.0 ± 2.1) [s] Pignol, arxiv:1503.03317. 14
Neutron life-time (Salvati et al., in preparation) CMB:! b,y p + BBN: Y p (! b,n e, n ) constraints on n Variation on damping tail. n affects mainly the CMB itself is insensitive to the neutron life-time BUT the input value of is dependent on. Y p n affects the damping tail. assuming SBBN. 15
We consider CDM model + n. Neutron life-time Planck and current cosmological data (Salvati et al., in preparation) For the analysis: Monte Carlo Markov Chain (MCMC) package cosmomc (publicly available). Each step in MCMC: evaluate Y p using a fitting formula from PArthENoPE BBN code, evaluate neutron life-time. Y BBN p (! b, N e, n )= n 880.3 0.728 h 0.2311 + 0.9502! b 11.27! 2 b + + N e (0.01356 + 0.008581! b 0.1810! b 2 )+ i + Ne 2 ( 0.0009795 0.001370! b +0.01746! b 2 ) N e = N e 3.046 Precision check (given! b and Y p ) errors are negligible with n = 20 [s]! =0.1[s] respect to the statistical one (inferred from CMB). n = 60 [s]! =1.3[s] n = 100 [s]! =3.0[s] Fitting formula is still valid. 16
Neutron life-time Planck and current cosmological data (Salvati et al., in preparation) Future cosmological constraints CMB sensitivity to n small scale region of power spectrum tigther constraints from next-generation CMB missions in this regime Simulated datasets, in combination with Planck 2015 if necessary. Cosmic Variance Limited: most accurate precision reached from CMB experiments. 17
Neutron life-time CMB + astrophysical measurements (Salvati et al., in preparation) CMB measurements + direct astrophysical measurements of Y p new constraints on n For the analysis: select eight primordial He measurements (latest ten years) combine these with Planck data: gaussian prior on the input He abundance run the MCMC code as before. 18
Neutron life-time CMB + astrophysical measurements (Salvati et al., in preparation) experimental prior recovered He mass fraction Forecast future He astrophysical observations: to reach PDG accuracy =) Yp =0.0002 CMB + He measurements: tighter constraints on n 19
Planck Likelihood in collaboration with Cosmology group at University of Ferrara, P. Natoli and M. Lattanzi Planck 2015 results. XI. to be submitted. Planck Likelihood: statistical description of 2-points correlation function for temperature and polarization all uncertainties, instrumental and astrophysical. Low-multipole likelihood: `<30 standard joint pixel-based likelihood nearly independent component for temperature and polarization. m = {T,Q,U} m = s + n M=S[C`( )] + N Stokes parameters maps Component separation signal CMB + FG noise Full data covariance Full likelihood L(C`) =P (m C`) = 1 1 exp 2 M 1/2 2 mt M 1 m 20
Planck Likelihood in collaboration with Cosmology group at University of Ferrara, P. Natoli and M. Lattanzi Low-multipole Likelihood - Polarization Planck 2015 results. XI. to be submitted. Subset of the full Planck polarization data. 70 GHz channel S2 S4 Foreground cleaning: template fitting procedure for Q, U maps. 30 GHz: synchrotron 353 GHz: polarized dust. m {Q, U} m = 1 1 (m 70 m 30 m 353 ) scaling coefficients Find coefficients best-fit minimizing the quantity: 2 =(1 ) 2 m t [S(C`)+N 70 ] 1 m Select mask for cosmological analysis: f sky = 46 % 21
Planck Likelihood in collaboration with Cosmology group at University of Ferrara, P. Natoli and M. Lattanzi Planck 2015 results. XI. to be submitted. Low-multipole Likelihood - Polarization Monte Carlo validation 1000 signal simulations + 1000 noise simulations (TQU) FFP8 simulated maps For each simulation: foreground cleaning parameters estimation we consider, log[10 10 A s ] fixing the others to Planck best-fit. Empirical distributions: centered around the input values. template fitting is a good procedure: no introduction of bias error on parameters lower then 10% Validate both foreground cleaning and Likelihood 22
Conclusions We have seen: consistency between astrophysical observations and CMB for primordial abundances Planck 2015 results Planck likelihood uncertainties dominated from errors in determination of nuclear quantities. Constrain neutron life-time with CMB+BBN independent estimation 23
Thank you for your attention Published papers: Blue gravity waves from BICEP2? M. Gerbino, A. Marchini, L. Pagano, L. Salvati, E. Di Valentino, A. Melchiorri Phys.Rev. D90 (2014) 4, 047301 Is Planck data consistent with primordial deuterium measurements? L.Salvati, N. Said, A. Melchiorri Phys.Rev. D90 (2014) 10, 103514 Submitted papers: Planck 2015 results. I. arxiv: 1502.01582 Planck 2015 results. XIII. arxiv: 1502.01589 Papers in preparation: Planck 2015 results. XI. Cosmological constraints on the neutron lifetime L. Salvati, L. Pagano, A. Melchiorri Ongoing work: Li 7 problem ISW from CMB
Particle Data Group To average data: standard weighted least-squares procedure, increasing the errors with a scale factor. PDG, Chinese Physics C Vol. 38, No 9 (2014) 090001 x ± x = w i = 1 ( x i ) 2 P P i w ix i i w i ± X i w i! 1/2 assuming that measurements are uncorrelated 2 = X w i ( x x i ) 2 i 2 N 1 > 1 S = s 2 N 1 scale factor x fin = S x credit: http://pdg8.lbl.gov 25
Forecasts (Salvati et al., in preparation) We produce a CMB dataset: experimental dataset evaluate noise. We assume: Planck 2015 as fiducial model foreground-removal uncertainties smaller than statical errors negligible beam uncertainties white noise. Lewis, Phys. Rev. D 71 (2005) 083008. Euclid mission: follow experimental specification in Fisher matrix formalism Martinelli et al., Phys. Rev. D 83 (2011) 023012. Amendola et al., JCAP 0804 (2008) 013. sum Euclid Fisher matrix with CMB inverse covariance matrix assuming gaussian probability distribution fro cosmological parameters. 26