Planck Constraints on General Primordial Isocurvature Perturbations and Curvaton Model

Jussi Valiviita¨

Helsinki Institute of Physics, University of Helsinki

on behalf of the Planck collaboration

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 1 / 20 Astronomy & Astrophysics manuscript no. Planck˙inflation˙driver © ESO 20131 March 22, 2013 Based on Section 10 of arXiv:1303.5082 Planck 2013 results. XXII. Constraints on inflation Planck Collaboration: P. A. R. Ade86, N. Aghanim59, C. Armitage-Caplan92, M. Arnaud72, M. Ashdown69,6, F. Atrio-Barandela19, J. Aumont59, C. Baccigalupi85, A. J. Banday95,10, R. B. Barreiro66, J. G. Bartlett1,67, N. Bartolo33, E. Battaner96, K. Benabed60,94, A. Benoˆıt57, A. Benoit-Levy´ 26,60,94, J.-P. Bernard10, M. Bersanelli36,50, P. Bielewicz95,10,85, J. Bobin72, J. J. Bock67,11, A. Bonaldi68, J. R. Bond9, J. Borrill14,89, F. R. Bouchet60,94, M. Bridges69,6,63, M. Bucher1?, C. Burigana49,34, R. C. Butler49, E. Calabrese92, J.-F. Cardoso73,1,60, A. Catalano74,71, A. Challinor63,69,12, A. Chamballu72,16,59, L.-Y Chiang62, H. C. Chiang28,7, P. R. Christensen81,39, S. Church91, D. L. Clements55, S. Colombi60,94, L. P. L. Colombo25,67, F. Couchot70, A. Coulais71, B. P. Crill67,82, A. Curto6,66, F. Cuttaia49, L. Danese85, R. D. Davies68, R. J. Davis68, P. de Bernardis35, A. de Rosa49, G. de Zotti46,85, J. Delabrouille1, J.-M. Delouis60,94, F.-X. Desert´ 53, C. Dickinson68, J. M. Diego66, H. Dole59,58, S. Donzelli50, O. Dore´67,11, M. Douspis59, J. Dunkley92, X. Dupac42, G. Efstathiou63, T. A. Enßlin78, H. K. Eriksen64, F. Finelli49,51?, O. Forni95,10, M. Frailis48, E. Franceschi49, S. Galeotta48, K. Ganga1, C. Gauthier1,77, M. Giard95,10, G. Giardino43, Y. Giraud-Heraud´ 1, J. Gonzalez-Nuevo´ 66,85, K. M. Gorski´ 67,98, S. Gratton69,63, A. Gregorio37,48, A. Gruppuso49, J. Hamann93, F. K. Hansen64, D. Hanson79,67,9, D. Harrison63,69, S. Henrot-Versille´70, C. Hernandez-Monteagudo´ 13,78, D. Herranz66, S. R. Hildebrandt11, E. Hivon60,94, M. Hobson6, W. A. Holmes67, A. Hornstrup17, W. Hovest78, K. M. Huffenberger97, T. R. Jaffe95,10, A. H. Jaffe55, W. C. Jones28, M. Juvela27, E. Keihanen¨ 27, R. Keskitalo23,14, T. S. Kisner76, R. Kneissl41,8, J. Knoche78, L. Knox30, M. Kunz18,59,3, H. Kurki-Suonio27,45, G. Lagache59, A. Lahteenm¨ aki¨ 2,45, J.-M. Lamarre71, A. Lasenby6,69, R. J. Laureijs43, C. R. Lawrence67, S. Leach85, J. P. Leahy68, R. Leonardi42, J. Lesgourgues93,84, M. Liguori33, P. B. Lilje64, M. Linden-Vørnle17, M. Lopez-Caniego´ 66, P. M. Lubin31, J. F. Mac´ıas-Perez´ 74, B. Maffei68, D. Maino36,50, N. Mandolesi49,5,34, M. Maris48, D. J. Marshall72, P. G. Martin9, E. Mart´ınez-Gonzalez´ 66, S. Masi35, S. Matarrese33, F. Matthai78, P. Mazzotta38, P. R. Meinhold31, A. Melchiorri35,52, L. Mendes42, A. Mennella36,50, M. Migliaccio63,69, S. Mitra54,67, M.-A. Miville-Deschenesˆ 59,9, A. Moneti60, L. Montier95,10, G. Morgante49, D. Mortlock55, A. Moss87, D. Munshi86, P. Naselsky81,39, F. Nati35, P. Natoli34,4,49, C. B. Netterfield21, H. U. Nørgaard-Nielsen17, F. Noviello68, D. Novikov55, I. Novikov81, I. J. O’Dwyer67, S. Osborne91, C. A. Oxborrow17, F. Paci85, L. Pagano35,52, F. Pajot59, R. Paladini56, S. Pandolfi38, D. Paoletti49,51, B. Partridge44, F. Pasian48, G. Patanchon1, H. V. Peiris26, O. Perdereau70, L. Perotto74, F. Perrotta85, F. Piacentini35, M. Piat1, E. Pierpaoli25, D. Pietrobon67, S. Plaszczynski70, E. Pointecouteau95,10, G. Polenta4,47, N. Ponthieu59,53, L. Popa61, T. Poutanen45,27,2, G. W. Pratt72, G. Prezeau´ 11,67, S. Prunet60,94, J.-L. Puget59, J. P. Rachen22,78, R. Rebolo65,15,40, M. Reinecke78, M. Remazeilles59,1, C. Renault74, S. Ricciardi49, T. Riller78, I. Ristorcelli95,10, G. Rocha67,11, C. Rosset1, G. Roudier1,71,67, M. Rowan-Robinson55, J. A. Rubino-Mart˜ ´ın65,40, B. Rusholme56, M. Sandri49, D. Santos74, M. Savelainen27,45, G. Savini83, D. Scott24, M. D. Seiffert67,11, E. P. S. Shellard12, L. D. Spencer86, J.-L. Starck72, V. Stolyarov6,69,90, R. Stompor1, R. Sudiwala86, R. Sunyaev78,88, F. Sureau72, D. Sutton63,69, A.-S. Suur-Uski27,45, J.-F. Sygnet60, J. A. Tauber43, D. Tavagnacco48,37, L. Terenzi49, L. Toffolatti20,66, M. Tomasi50, M. Tristram70, M. Tucci18,70, J. Tuovinen80, L. Valenziano49, J. Valiviita45,27,64, B. Van Tent75, J. Varis80, P. Vielva66, F. Villa49, N. Vittorio38, L. A. Wade67, B. D. Wandelt60,94,32, M. White29, A. Wilkinson68, D. Yvon16, A. Zacchei48, and A. Zonca31 (Affiliations can be found after the references)

Preprint online version: March 22, 2013

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints onABSTRACT isocurvature and curvaton ESTEC 4 April 2013 2 / 20 We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to ns = 0.9603 0.0073, ruling out exact scale invariance at over 5. Planck establishes an upper bound on the tensor-to-scalar ratio at r < 0.11 (95% CL). The Planck± data shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns/d ln k = 0.0134 0.0090. We verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter± estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We investigate whether the primordial power spectrum contains any features. A penalized likelihood approach suggests a feature

arXiv:1303.5082v1 [astro-ph.CO] 20 Mar 2013 near the highest wavenumbers probed by Planck at an estimated significance of 3 after correction for the “look elsewhere” effect. We find that models with a parameterized oscillatory feature improve the fit by 2 10⇠ ; however, Bayesian evidence does not prefer these models. e↵ ⇡ We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation of non-decaying isocurvature fluctuations. The fractional primordial contributions of CDM isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component 2 can improve the e↵ by 4 due to a moderate tension between l < 40 and higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions. ⇠ Key words. Cosmology: theory – early Universe – inflation 2. In other Planck papers pure adiabatic initial conditions are assumed. So, it is important to check the robustness of this assumption.

2 3. The determination of the “standard” ΛCDM model parameters, Ωbh , 2 Ωch , τ, θ, As, ns,(H0, ΩΛ) could be signiﬁcantly affected by an undetected isocurvature contribution. Need to check how allowing for general initial conditions for perturbations affects the basic results.

Motivation: Why to study isocurvature in the Planck Inﬂation paper?

1. An important test of inflationary models. Single field inflation (with one degree of freedom) can produce only the primordial curvature perturbation, i.e., adiabatic primordial perturbations, since exciting isocurvature perturbations requires additional degrees of freedom. Therefore a detection of primordial isocurvature perturbations would point to more complicated models of inflation, such as multi-field inflationary scenarios which can produce a (possibly correlated) mixture of curvature and isocurvature perturbations.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 3 / 20 2 3. The determination of the “standard” ΛCDM model parameters, Ωbh , 2 Ωch , τ, θ, As, ns,(H0, ΩΛ) could be signiﬁcantly affected by an undetected isocurvature contribution. Need to check how allowing for general initial conditions for perturbations affects the basic results.

Motivation: Why to study isocurvature in the Planck Inﬂation paper?

2. In other Planck papers pure adiabatic initial conditions are assumed. So, it is important to check the robustness of this assumption.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 3 / 20 Motivation: Why to study isocurvature in the Planck Inﬂation paper?

2. In other Planck papers pure adiabatic initial conditions are assumed. So, it is important to check the robustness of this assumption.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 3 / 20 In the general models we have: 2 2 4 background params (as in the adiabatic ΛCDM model): Ωbh , Ωch , τ, θ. 2 adiabatic perturbation parameters describing the power law spectrum PRR(k). In addition, 4 extra perturbation parameters: 2 describing the isocurvature power law spectrum PII (k), and 2 for the correlation spectrum PRI (k) = PIR(k).

Theoretically motivated special cases with only 1 extra param Curvaton, axion.

General phenomenological models studied Flat ΛCDM model with power law primordial spectra for the adiabatic mode, for one isocurvature mode at a time, and for their correlation,

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 4 / 20 In addition, 4 extra perturbation parameters: 2 describing the isocurvature power law spectrum PII (k), and 2 for the correlation spectrum PRI (k) = PIR(k).

Theoretically motivated special cases with only 1 extra param Curvaton, axion.

General phenomenological models studied Flat ΛCDM model with power law primordial spectra for the adiabatic mode, for one isocurvature mode at a time, and for their correlation,

P (k) P (k) P(k) = RR RI , PIR(k) PII (k) where I can be any of the non-singular, i.e., non-decaying isocurvature modes: CDI (cold dark mater density isocurvature mode). NDI (neutrino density isocurvature mode). NVI (neutrino velocity isocurvature mode). BDI (There can be also baryon density isocurvature mode, which is indistinguishable from CDI by the CMB observations. effective Above, the CDI mode can be regarded to include also baryons as: = + (Ω /Ωc) ) ICDI ICDI b IBDI In the general models we have: 2 2 4 background params (as in the adiabatic ΛCDM model): Ωbh , Ωch , τ, θ. 2 adiabatic perturbation parameters describing the power law spectrum PRR(k).

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 4 / 20 Theoretically motivated special cases with only 1 extra param Curvaton, axion.

General phenomenological models studied Flat ΛCDM model with power law primordial spectra for the adiabatic mode, for one isocurvature mode at a time, and for their correlation,

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 4 / 20 General phenomenological models studied Flat ΛCDM model with power law primordial spectra for the adiabatic mode, for one isocurvature mode at a time, and for their correlation,

Theoretically motivated special cases with only 1 extra param Curvaton, axion.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 4 / 20 k = 0.002 k = 0.100 1 2 For each spectrum specify P(k ) 2 parameters: 1 – amplitude at scale k , (k ) P(k ) 1 1 2 P log(P) – amplitude at scale k , (k ) 2 P 2 −3 −2 −1 10 10 10 From these the spectral index n −1 and amplitude (k0) can be calculated k [Mpc ] as derived parameters.P Idea presented in 2004 in H. Kurki-Suonio, V. Muhonen, and J. Valiviita, Phys. Rev. D 71, 063005, and used ever since in most of isocurvature studies.

How to parametrize power law primordial spectra?

k = 0.050 0 For each spectrum specify 2 parameters: slope = n−1 P(k ) – amplitude at the pivot scale k0, (k0) 0 P

log(P) – spectral index n = dln / dlnk + 1 P −3 −2 −1 10 10 10 ALARM! Cannot be used in MCMC, k [Mpc−1] if niso or ncor (or nt) are free.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 5 / 20 How to parametrize power law primordial spectra?

k = 0.050 0 For each spectrum specify 2 parameters: slope = n−1 P(k ) – amplitude at the pivot scale k0, (k0) 0 P

log(P) – spectral index n = dln / dlnk + 1 P −3 −2 −1 10 10 10 ALARM! Cannot be used in MCMC, k [Mpc−1] if niso or ncor (or nt) are free.

k = 0.002 k = 0.100 1 2 For each spectrum specify P(k ) 2 parameters: 1 – amplitude at scale k , (k ) P(k ) 1 1 2 P log(P) – amplitude at scale k , (k ) 2 P 2 −3 −2 −1 10 10 10 From these the spectral index n −1 and amplitude (k0) can be calculated k [Mpc ] as derived parameters.P Idea presented in 2004 in H. Kurki-Suonio, V. Muhonen, and J. Valiviita, Phys. Rev. D 71, 063005, and used ever since in most of isocurvature studies.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 5 / 20 68% & 95% C.L. constraints on primord. powers at two scales For perturbations, our primary MCMC parameters with uniform priors are the powers at −1 (1) (1) (1) k1 = 0.002 Mpc , i.e., PRR, PII , PRI and at −1 (2) (2) (2) k2 = 0.100 Mpc , i.e., PRR, PII , |PRI |. 3.0 4.0 2.8 3.5 NVI 2.6 3.0 NDI (2) II (2) RR 2.4 2.5 P P

9 CDI 9 2.2 2.0 10

10 1.5 2.0 1.0 1.8 0.5 1.6 0.0 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 109 (1) 109 (1) PRR PII 1.4 4.0 1.2 3.5 1.0 3.0 (1) (2) II II 2.5

P 0.8 P

9 9 2.0 0.6 10 10 1.5 0.4 1.0 0.2 0.5 0.0 0.0 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 109 (1) 109 (2) 0.5 PRR PRR 0.5

0.0 | 0.4 (1) (2) RI RI P

0.5 |P

9 0.3 − 9 10

19 0.2 1.0 − 0.1 1.5 0.0 − 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 109 (1) 109 (2) PII PII Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 6 / 20 C` from scale-invariant spectra with equal primordial amplitude

104 ] 2 103 K µ )[ π 2

(2 10 / TT

C 1 · 10

Adiabatic + 1)

` 0 CDI

( 10 ` NDI NVI 1 10− 101 102 103 ` −2 −2 Note the (k/keq) , i.e., ` damping of CDI compared to the other modes, in particular compared to the adiabatic mode. TT With CMB C` , the CDI spectral index can never be constrained to much less⇒ than n n + 2 3, if the data are almost “adiabatic”. iso ' ad ' Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 7 / 20 n nII = d(ln II ) / d(lnk) + 1 iso ≡ P

0 0.2 0.4 0.6 0 2 4 β (k = 0.050 Mpc−1) n iso iso

Primordial isocurvature fraction and spectral index

β (k) = II (k) / [ RR(k) + II (k)] iso P P P

CDI NDI NVI

0 0.1 0.2 0.3 0.4 0 0.2 0.4 0.6 0.8 β (k = 0.002 Mpc−1) β (k = 0.100 Mpc−1) iso iso

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 8 / 20 Primordial isocurvature fraction and spectral index

β (k) = II (k) / [ RR(k) + II (k)] iso P P P

CDI NDI NVI

0 0.1 0.2 0.3 0.4 0 0.2 0.4 0.6 0.8 β (k = 0.002 Mpc−1) β (k = 0.100 Mpc−1) iso iso

n nII = d(ln II ) / d(lnk) + 1 iso ≡ P

0 0.2 0.4 0.6 0 2 4 β (k = 0.050 Mpc−1) n iso iso

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 8 / 20 Primordial correlation fraction

RI (k) cos∆ (k) = p P RR(k) II (k) P P

< 0 C.L. > 0 C.L. 67% 33% 95% 5% 98% 2%

−1 −0.5 0 0.5 1 cos∆ (k = 0.100 Mpc−1)

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 9 / 20 Non-adiabaticity of the CMB temperature ﬂuctuations

The non-adiabaticity fraction in today’s CMB (δT )2

2 (δTnon−ad) α − = h i non ad (δT )2 h total i P2500(2` + 1)(CTT + CTT ) = `=2 II,` RI,` P2500 TT `=2 (2` + 1)Ctot,`

CDI NDI NVI

−0.1 −0.05 α 0 0.05 0.1 non−ad

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 10 / 20 Constraints on the general isocurvature cases

95% C.L. constraints and ∆χ2 = χ2 χ2 eff eff,ISO,best − eff,adiabatic,best Primordial isoc. fraction Isoc. frac. in CMB ) ) 2 ∗ ∗∗ βiso αnon−ad ∆χeff low- high- (k=0.002 0.050 0.100) ` TT ` TT CDI <0.08 <0.39 <0.60 -7% . . . +2% -4.6 -4.7 -0.2 NDI <0.27 <0.27 <0.32 -9% . . . +1% -4.2 -3.8 -0.8 NVI <0.18 <0.14 <0.17 -5% . . . +4% -2.5 -2.2 +0.1

These models have 4 extra parameters compared to the pure adiabatic model.

∗) Low-` TT = Planck TT likelihood at ` = 2 — 49 (commander v4.1 lm49.clik)

∗∗) High-` TT = Planck TT likelihood at ` = 50 — 2500 (CAMspec v6.2TN 2013 02 26.clik)

∗∗∗) The rest (NOT IN THE TABLE) = WMAP-9 TE and EE (lowlike v222.clik)

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 11 / 20 Temperature C` spectra of the best-ﬁt models

1.02

ad 0.99 TT ` 0.96 /C CDI iso 0.93 NDI TT `

C 0.90 NVI

101 102 103 1600 ] 2 1200 CDI K µ [ 800 NDI l

D NVI 400 ΛCDM 0 10 20 30 40 50 60 70 `

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 12 / 20 Effect on the estimation of “standard” parameters

State-of-art in 2009 (with WMAP5 and ACBAR)

ad CDI

0.022 0.024 0.026 0.08 0.09 0.1 0.11 0.12 Ω h2 Ω h2 b c

1.03 1.04 1.05 1.06 70 80 90 H 100θ 0

0.65 0.7 0.75 0.8 0.85 0.95 1 1.05 Ω n Λ ad From: Jussi Valiviita and Tommaso Giannantonio, Phys. Rev. D 80, 123516 (2009) [arXiv:0909.5190 [astro-ph.CO]].

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 13 / 20 Effect on the estimation of background parameters

In March 2013 with Planck+WP data

ad CDI NDI NVI

0.021 0.022 0.023 0.024 0.11 0.115 0.12 0.125 0.13 Ω h2 Ω h2 b c

0.05 0.1 0.15 1.035 1.04 1.045 τ 100θ

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 14 / 20 d(lnP ) n nRR = RR + 1 ad ≡ d(lnk)

2 2.2 2.4 −1 2.6 0.95 1 1.05 P (k = 0.05 Mpc ) −9 n RR x 10 ad

..effect on the derived bg params & adiabatic spectrum

Larger values of H0 and ΩΛ are acceptable than in the pure adiabatic model

ad CDI NDI NVI

65 70 75 0.65 0.7 0.75 H Ω 0 Λ

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 15 / 20 ..effect on the derived bg params & adiabatic spectrum

Larger values of H0 and ΩΛ are acceptable than in the pure adiabatic model

ad CDI NDI NVI

65 70 75 0.65 0.7 0.75 H Ω 0 Λ

d(lnP ) n nRR = RR + 1 ad ≡ d(lnk)

2 2.2 2.4 −1 2.6 0.95 1 1.05 P (k = 0.05 Mpc ) −9 n RR x 10 ad Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 15 / 20 A theoretically motivated special case: curvaton

The Planck collaboration studied the curvaton scenario with assumptions:

(1) The average curvaton field value, χ∗, is sufficiently below the Planck mass at the time when cosmologically interesting scales exit the horizon during inflation. (2) The curvature perturbation from inflaton is negligible compared to the curvaton perturbation at horizon exit during inflation. (3) The same is true for any inflaton decay products after reheating. This means that after reheating the Universe is homogeneous, except for the spatially varying entropy (i.e., isocurvature perturbation) due to the curvaton field perturbations. (4) Later, CDM is created from the curvaton decay.

This curvaton scenario leads to fully correlated primordial curvature and isocurvature perturbations with the same shape of their power spectra: p RI = + RR II , n = n . P P P iso ad Hence only one extra parameter compared to the adiabatic model.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 16 / 20 With Planck+WP data we ﬁnd βiso < 0.0025 at 95% C.L. 5 times tighter than the WMAP9 constraint, 3 times tighter than WMAP9+ACT+SPT! This corresponds to 0.98 < r < 1 and 1.25 < f local < 1.21. D − NL − Fits within 1σ Planck constraint f local = 2.7 5.8. NL ±

... curvaton

The isocurvature fraction in this curvaton model will be 9(1 r )2 3ρ β = − D , where r = curvaton , iso r2 + 9(1 r )2 D 3ρ + 4ρ D − D curvaton radiation and the non-linearity parameter (assuming sudden decay of curvaton and quadratic potential) will be local 5 5 5rD fNL = . 4rD − 3 − 6 If the curvaton totally dominates the energy density at curvaton’s decay time, local then rD = 1, fNL = 5/4, and the curvaton perturbations are converted to pure adiabatic ones with− no residual isocurvature.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 17 / 20 ... curvaton

With Planck+WP data we ﬁnd βiso < 0.0025 at 95% C.L. 5 times tighter than the WMAP9 constraint, 3 times tighter than WMAP9+ACT+SPT! This corresponds to 0.98 < r < 1 and 1.25 < f local < 1.21. D − NL − Fits within 1σ Planck constraint f local = 2.7 5.8. NL ±

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 17 / 20 Summary on the general & special isoc. cases

95% C.L. constraints and ∆χ2 = χ2 χ2 eff eff,ISO,best − eff,adiabatic,best Primordial isoc. fraction Isoc. frac. in CMB 2 βiso αnon−ad ∆χeff (k=0.002 0.050 0.100) CDI <0.08 <0.39 <0.60 -7% . . . +2% -4.6 NDI <0.27 <0.27 <0.32 -9% . . . +1% -4.2 NVI <0.18 <0.14 <0.17 -5% . . . +4% -2.5 Special CDI cases “axion” <0.0360 <0.0390 <0.0400 <2% 0 “curvaton” <0.0025 <0.0025 <0.0025 0% . . . +3% 0 anti-corr. <0.0087 <0.0087 <0.0087 -6% . . . 0% -1.3

The general cases IN COLOR have 4 extra parameters. The special cases have 1 extra parameter compared to the adiabatic model.

“axion” = no correlation (PRI = 0), niso√= 1. “curvaton” = +100% correlation (PRI = +√PRRPII ), niso = nad. anti-corr. = -100% correlation (PRI = − PRRPII ), niso = nad.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 18 / 20 In addition, the Planck collaboration studied theoretically motivated models: Both curvaton and axion models worsen the fit to the Planck data, since they increase the power at low-`. This leads to the stringent constraints on these models: primord. isoc. frac. βiso < 0.25% (curvaton) and βiso < 3.9% (axion). A model similar to curvaton, but with 100% anticorrelation improves the fit moderately (∆χ2 1.3), and leads to β < 8.7%. eff ≈ − iso

Conclusions (NOTE: Next year the polarization data may shed light to these questions.)

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 19 / 20 Conclusions (NOTE: Next year the polarization data may shed light to these questions.)

The Planck collaboration studied in a general phenomenological set-up all non-singular primordial isocurvature modes, CDI (and BDI), NDI, NVI, one at a time, possibly correlated with adiabatic perturbations: Acoustic peak structure in the Planck data is “adiabatic” to high precision. The power of Planck low-` spectrum is about 10% below the prediction of the best-fit adiabatic ΛCDM model. A negatively correlated isocurvature component improves the fit to low-` 2 data (∆χeff ≈ −4.5), without affecting too much the high-` spectrum. This ` ∼ 10...30 “anomaly” leads to relatively large isocurvature fractions (-5% — -9%) to be allowed in the CMB temperature variance. Determination of standard cosmological parameters is only mildly affected by allowing for an isocurvature contribution! A great improvement over WMAP. In addition, the Planck collaboration studied theoretically motivated models: Both curvaton and axion models worsen the fit to the Planck data, since they increase the power at low-`. This leads to the stringent constraints on these models: primord. isoc. frac. βiso < 0.25% (curvaton) and βiso < 3.9% (axion). A model similar to curvaton, but with 100% anticorrelation improves the fit moderately (∆χ2 1.3), and leads to β < 8.7%. eff ≈ − iso Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 19 / 20 The scientific results that we present today are a product of the Planck Collaboration, including individuals from more than 100 scientific institutes in Europe, the USA and Canada

Planck is a project of the European Space Agency, with instruments provided by two scientific Consortia funded by ESA member states (in particular the lead countries: France and Italy) with contributions from NASA (USA), and telescope CITA – ICAT reflectors provided in a

UNIVERSITÀ DEGLI STUDI collaboration DI MILANO between ESA and ABabcdfghiejkl a scientific Consortium led and funded by Denmark.

Planck collab. (Jussi Valiviita,¨ Uni. Helsinki) Planck constraints on isocurvature and curvaton ESTEC 4 April 2013 20 / 20