Loop Quantum Cosmology, Non-Gaussianity, and the CMB Ivan Agullo Louisiana State University

Transcription

1 Loop Quantum Cosmology Non-Gaussianity and CMB ILQGS Oct

2 Motivation 2

3 Motivation Standard Model of Cosmology Dark energy domination era 13.0 billion years after Big Bang Matter domination era t x Formation of CMB years after Big Bang Radiation domination era (opaque Universe) Generation of primordial density perturbations (QFT in C-ST) Quantum gravity era??? Many proposals: Inflation Bounce Ekpyrotic etc. 3

4 Motivation Way to test: Observations (CMB and LSS) CMB: info encoded in statistics of temperature anisotropies Two point function in real space: h T (ˆn) T (ˆn 0 )i c = X` ( T (ˆn) T (ˆn) T ) 4 2` +1 C` P`(cos ) (for an isotropic distribution) classical statistical average C` angular Power Spectrum Equivalently in angular Fourier space: ha`m a?`0m i 0 c = ``0 mm 0 C` where T (ˆn) = X`m a`m Y`m (ˆn) 4

5 Motivation Inflation: quantum fields (curvature perturbations) in inflationary geometry Given V ( ) one can compute: ha`m a?`0m 0 i q = ``0 mm 0 C infl ` Observations (Planck 2015) `(` + 1) C`/2 Inflation Observations Spectacular agreement Some deviations for `. 30 Deviations from ory Note change to log scale here 5

6 Motivation duction S. Plaszczynski73 E. Pointecouteau100 9 G. Polenta4 46 L. Popa63 G. W. Pratt75 G. Prézeau11 69 S. Prunet Agullo J.-L. Puget60 J. P. Rachen23 82 R. Rebolo M. Reinecke82 M. Remazeilles C. Renault77 Ivan A. Renzi I. Ristorcelli100 9 Astronomy G. Rocha C. Rosset M. Rossetti A. Rotti G. Roudier J. A. Rubiño-Martín c & Astrophysics manuscript no. planck_2015_iands ESO June B. Rusholme M. Sandri D. Santos M. Savelainen G. Savini D. Scott M. D. Seiffert E. P. S. Shellard T. Souradeep L. D. Spencer V. Stolyarov R. Stompor R. Sudiwala R. Sunyaev D. Sutton64 72 A.-S. Suur-Uski28 44 J.-F. Sygnet61 J. A. Tauber40 L. Terenzi41 48 L. Toffolatti M. Tomasi35 49 M. Tristram73 Planck 2015 results. XVI. Isotropy and statistics of CMB T. Trombetti48 M. Tucci18 J. Tuovinen10 L. Valenziano48 J. Valiviita28 44 B. Van Tent78 P. Vielva67 F. Villa L. A. Wade69 B. D.Collaboration: Wandelt I. K. Wehus Akrami D. Yvon A.Aluri Zacchei 88J.75 P. A. Zonca30 Planck P. A. R. Ade N. Aghanim Y. P. K. M. Arnaud M. Zibin Ashdown72 6and ú J. Aumont C. Baccigalupi A. J. Banday R. B. Barreiro N. Bartolo S. Basak E. Battaner K. Benabed61 99 A. Benoît58 A. Benoit-Lévy J.-P. Bernard100 9 M. Bersanelli35 49 P. Bielewicz J. J. Bock69 11 A. Bonaldi70 L. Bonavera67 J. R. Bond8 J. Borrill14 94 F. R. Bouchet61 92 F. Boulanger60 M. Bucher1 C. Burigana (Affiliations can be found after 67 R. C. Butler48 E. Calabrese J.-F. Cardoso B. Casaponsa A. references) Catalano77 74 A. Challinor planck_2015_iands A&A proofs: manuscript no. A. Chamballu H. C. Chiang P. R. Christensen S. Church D. L. Clements56 S. Colombi61 99 L. P. L. Colombo25 69 C. Combet77 D. Contreras24 F. Couchot73 A. Coulais74 B. P. Crill69 11 M. Cruz21 A. Curto June 5Bernardis A. de Rosa48 G. de Zotti45 88 J. Delabrouille1 70 Cuttaia48 L. Danese88 R. D. Davies70 R. J. Davis P. de A&A proofs:f. manuscript no. planck_2015_iands 67 F.-X. Désert54 J. M. Diego H. Dole60 59 S. Donzelli49 O. Doré69 11 M. Douspis60 A. Ducout61 56 X. Dupac39 G. Efstathiou64 F. Elsner T. A. Enßlin82 H. K. Eriksen65 Y. Fantaye37 J. Fergusson12 R. Fernandez-Cobos67 F. Finelli48 50 O. Forni100 9 M. Frailis47 A. A. Fraisse29 E. Franceschi48 A. Frejsel86 A. Frolov91 S. Galeotta47 S. Galli71 ABSTRACT K. Ganga1 C. Gauthier1 81 T. Ghosh60 M. Giard Y. Giraud-Héraud1 E. Gjerløw65 J. González-Nuevo20 67 K. M. Górski S. Gratton72 64 A. Gregorio A. Gruppuso48 J. E. Gudmundsson29 F. K. Hansen D. Hanson83and D.Gaussianity L. Harrison64 72 of S. Henrot-Versillé Hernández-Monteagudo D. Herranz We test statisticals.isotropy cosmic C.microwave background (CMB) anisotropies using obr. Hildebrandt69 11 E. Hivon61 99 M. Hobson6 W. A. Holmes69 A. Hornstrup17 W. Hovest82 Z. Huang8 27 satellite full Planck servations made K. bym. Planck results are100based Huffenberger G. Hurier60 A.Our H. Jaffe T. R. Jaffe W. C.mainly Jones29 M.on Juvela E. Keihänen28 R. mission Keskitalo14 for temperature J. Kim T. S. Kisner J. Knoche M. Kunz H. Kurki-Suonio G. Lagache A. Lähteenmäki maps derived from but also include some polarization measurements. In particular CMB anisotropy we consider J.-M. Lamarre A. Lasenby M. Lattanzi C. R. Lawrence R. Leonardi J. Lesgourgues F. Levrier data by65several component-separation For multi-frequency Planck methods. anisotropies we find M. Liguori P. B. Lilje M. Linden-Vørnle17 H. Liu86 38 M. López-Caniego P. M. Lubin temperature J. F. Macías-Pérez G. Maggio D. Maino N. Mandolesi A. Mangilli D. Marinucci M. Maris P. G. Martin excellent agreement between results based on se sky maps over both a very large fraction of sky and a broad E. Martínez-González67 S. Masi34 S. Matarrese P. McGehee57 P. R. Meinhold30 A. Melchiorri34 51 L. Mendes affect our 61 range of angulara.scales establishing potential residuals do not studies. of skewness Mennella35 M. Migliacciothat K. Mikkelsen65 foreground S. Mitra55 69 M.-A. Miville-Deschênes D. Molinari67 48 A. MonetiTests L. Montier G. Morgante D. Mortlock A. Moss D. Munshi J. A. Murphy P. Naselsky F. Nati kurtosis multi-normality N -point functions and Minkowski functionals indicate consistency with Gaussianity while P. Natoli C. B. Netterfield22 H. U. Nørgaard-Nielsen17 F. Noviello70 D. Novikov80 I. Novikov86 80 C. A. Oxborrow is manifested example low a power deficit at large angular scales several ways for map variance. The results of a F. Paci L. Pagano F. Pajot60 N. Pant55 in D. Paoletti F. Pasian G. Patanchon1 T. J. Pearson O. Perdereau L. Perotto with F. Perrotta V. Pettorino F. Piacentini M. Piat E. Pierpaoli D.The Pietrobon peak statistics analysis are consistent expectations of a Gaussian random field. Cold Spot is detected S. Plaszczynski73 E. Pointecouteau100 9 G. Polenta4 46 L. Popa63 G. W. Pratt75 G. Prézeau11 69 S. Prunet statistics with several methods peak temperature profile. We37 52 thoroughly probe J.-L.including Puget60 J. P.map Rachenkurtosis R. Rebolo M. Reineckeand M.mean Remazeilles C. Renault A. Renzi I. Ristorcelli G. Rocha C. Rosset M. Rossetti A. Rotti G. Roudier J. A. Rubiño-Martín large-scale dipolarb. power asymmetry detecting it with several independent tests and address subject of a posterusholme57 M. Sandri48 D. Santos77 M. Savelainen28 44 G. Savini87 D. Scott24 M. D. Seiffert69 11 E. P. S. Shellard large to riori correction. Tests directionality suggest 6presence of angular clustering from scales but at a T. of Souradeep L. D. Spencer V. Stolyarov R. Stompor R. Sudiwala R. Sunyaev D. Sutton64 72small Suur-Uski on J.-F. Sygnet J. A. Tauber L. Terenzi We L. Toffolatti M. Tomasi M. Tristramof polarization data significance that isa.-s. dependent details of approach. perform first examination T. Trombetti48 M. Tucci18 J. Tuovinen10 L. Valenziano48 J. Valiviita28 44 B. Van Tent78 P. Vielva67 F. Villa finding morphologyl.of stacked peaks to be31 consistent with of24 statistically A. Wade B. D. Wandelt I. K. Wehus69 D. Yvon16 A. expectations Zacchei47 J. P. Zibin and A. Zonca30 isotropic simulations. Well-understood physical processes due to integrated Sachs-Wolfe (ISW) effect (Planck Collaboration oduction Well-understood physical processes due to gravitainteper one of a set associated with 2015 release XVII 2014; Planck Collaboration XXI 2015) and 1 Sachs-Wolfe effect (Planck Collaboration from Planck mission (Planck Collaboration I grated tional lensing (Planck(ISW) Collaboration XIX 2014; Planck Colaper one of a set associated with 2015 release XVII 2014; Planck Collaboration XXI 2015) and gravitaescribes a set of 1studies undertaken to determine laboration XV 2015) lead to secondary anisotropies that from Planck mission (Planck Collaboration I lensing (Planck Collaboration XIX 2014; Planck Colstical properties of both temperature and po- tional exhibit marked deviation from Gaussianity. In addition describes a setofof studies undertaken determine laboration XV 2015) lead to secondary anisotropies that n anisotropies cosmic microwavetobackground Doppler boosting due to our motion with respect to tistical properties of both temperature and po- exhibit marked deviation from Gaussianity. In addition CMB rest frame induces both a dipolar modulation of on anisotropies of cosmic microwave background Doppler boosting due to our motion with respect to temperature anisotropies and an aberration that cor.standard cosmological model is described well by CMB rest frame induces both a dipolar modulation of responds to a change in apparent arrival directions of dmann-lemaître-robertson-walker solution of temperature anisotropies and an aberration that corstandard cosmological model is described well by CMB photons (Challinor & van Leeuwen 2002). Both field equations. This model is characterized by a edmann-lemaître-robertson-walker solution of responds to a change in apparent arrival directions of of se effects are aligned with CMB dipole and were neous isotropic background and a scale n fieldand equations. This model is metric characterized by a CMB photons (Challinor & van Leeuwen 2002). Both detected at a statistically level dipole on small angular expanding Universe. It is hyposized that of se effects are aligned significant with CMB and were neous and isotropic background metric and a scale scales in Planck Collaboration XXVII (2014). Beyond se early times Universe went through a period of expanding Universe. It is hyposized that detected at a statistically significant level on small angular PlanckinCollaboration XXIII (2014 PCIS13) esrated so-called infla- scales Planck Collaboration XXVII hereafter (2014). Beyond se early expansion times Universe went cosmological through a period tablished that with Planck 2013 data set showed eviriven a hypotical scalar inflaton. Where field y overlap se results are consistent XXIII Planck 2013 analysis based onlittle nominal mission data and Planck Collaboration (2014 hereafter PCIS13) eseratedbyexpansion so-called cosmological infla(affiliations can be found after references) provideapproximately our most thorough of for statistics of CMB fluctuations to date. dence non-gaussianity with data exception of little a number nflation Universe behaves as view a tablished that Planck 2013 set showed evidriven by a hypotical scalar field inflaton. A&A proofs: manuscript June of CMB temperature anisotropy anomalies on large angur inflation space providing conditions by which some of for non-gaussianity with exception of a number Universe behaves approximately as a dence Key words. cosmology: observations cosmic background radiation polarization methods: data analysis methods: larcmb scalestemperature that confirmed earlier anomalies claims based on WMAP properties can be realized and statistical anisotropy on large anguerntspace providing conditions by specifically which somereof of ABSTRACT data. Moreover given 1. that claims broaderbased frequency coverhe of initial In particular Introduction scales that confirmed earlier on WMAP entproblem properties can beconditions. realized and specifically re- lar We test statistical isotropy and Gaussianity of cosmic microwave background (CMB) anisotropies using obage ofmoreover Planck instruments improved at gave rise to present large-scale matter distriservations made by Planck satellite. Our given results arethat based mainly on full Planck mission for compotemperature data. allowed broader frequency cover problem of initial conditions. In particular but also include some polarization measurements. In particular we consider CMB anisotropy maps derived from nent separation methods to be applied in derivation of ia gravitational instability originatedmatter as quantum This paper of a set associated with 2015 release age ofdata Planck instruments allowed improved compohat gave rise to present large-scale distrimulti-frequency Planck by several component-separation methods. For one temperature anisotropies we find 1 excellent agreement between results based on se sky maps over both a very large fraction of sky and a broad foreground-cleaned CMB maps it was generally considered ons gravitational of inflaton about itsoriginated vacuum state. These nent separation methods be applied in derivation of (Planck Collaboration I of to data from Planck mission via instability as quantum range of angular scales establishing that potential foreground residuals do not affect our studies. Tests of skewness that N case forand anomalous features had been kurtosis multi-normality -point functions Minkowski functionals consistency withconsidered Gaussianity while undertaken to determine ons inof density perturforeground-cleaned CMB maps itindicate wasingenerally tions inflaton inflatonproduce about itsenergy vacuum state. These 2015) describes a CMB set of studies a power deficit at large angular scales is manifested in several ways for example low map variance. The results of a Article number page 1 ofand 61 postrengned. Hence such have considthat are distributed as a statistically homogeneous that casewith for features in attracted CMB tions in inflaton produce energy density perturpeak statistics analysis are consistent anomalous expectations of anomalies astatistical Gaussian random field. The Cold had Spot isbeen detected properties of both temperature with several methods including map kurtosis peak statistics and mean temperature We could thoroughly probe erable attention in community since y be ropic Gaussian random Linear ory relates strengned. Hence such anomalies haveprofile. attracted considthat are distributed as afield. statistically homogeneous large-scale dipolar power asymmetry detecting it with several independentanisotropies tests and address of subject of cosmic a postelarization microwave background riori correction. Tests of directionality presence of angular clustering from large tocould smalloccurring scales visible tracessuggest of in fundamental physical processes erable attention community since y be but at a erturbations to temperature andory polarization tropic Gaussian random field. Linear relates significance that is dependent on details of approach. We perform first examination of polarization data (CMB). in early Universe. visible traces of physicalofprocesses occurring pies of CMB a distribution for erturbations to implying temperature and polarization finding morphology of stacked peaks to befundamental consistent with expectations statistically isotropic simulations. Where y overlap se results are consistent with Planck 2013 analysis based on nominal mission data and The standard cosmological model is described well by in early Universe. opies of CMB implying a distribution for pies very close to that of a statistically isotropic However literature also supports an ongoing debate provide our most thorough view of statistics of CMB fluctuations to date. Friedmann-Lemaître-Robertson-Walker solution of opies very field. close to that of a statistically isotropic However background literature also supports anthe ongoing debate n random about significance of se anomalies. central issue Key words. cosmology: observations cosmic radiation polarization methods: data analysis methods: statistical an random significance ofeinstein se anomalies. The issue in this discussion is connected with role central of a This posterifield equations. model is characterized by a aim of thisfield. paper is to use full mission Planck about discussion is connected with role of posteriori this choices wher interesting features in a data bias homogeneous and isotropic background metric and a scale aim of this paper is to useisotropy full of mission Planck test Gaussianity and CMB as in ori choices wher interesting features in data bias tests of or if arbitrary choices in It is hyposized that Gaussianity and of capacity CMB as choice of statisticalfactor expanding Universe. dtest in both intensity and in aisotropy more limited choice of statistical tests or if arbitrary choices in feaed in both intensity and in a more limited capacity subsequent data analysis enhance significance of Loops 15 Erlangen 2015 no. planc Well grated XVII 20 tional le laborati exhibit Doppler CMB re tem respond CM of se detected 6

7 Motivation To summarize Inflation nice but open issues of two kinds: Theory: Big bang Trans-Planckian issues How inflation begins Initial conditions for inflation Where is and V ( ) coming from? Reheating Observations: CBM anomalies at large angles: dipole modulation (hence anisotropies) and power suppression Goal of program: use LQC to answer se questions 7

8 Motivation Previous talks (I.A. Ashtekar Nelson Gupt ) Precise answers to ory questions: - Big bounce (Ashtekar-Pawlowski-Singh) - Naturalness of inflation in LQC (Ashtekar-Sloan Corichi-Karami) - QFT in Q-ST (Ashtekar-Kaminski-Lewandowski; I.A.-Ashtekar-Nelson) Many more contributions: Ashtekar Barrau Bojowald Brizuela Calcagni Campiglia Corichi Dapor Garay Grain Lewandowsky Linsefors Martin Martin-Benito Mena-Marugan Milczarek Olmedo Pawlowski Putchta Singh Taveras Tsujikawa Vandersloot Vidoto Wilson-Ewing... This talk: Argue that LQC provides a mechanism ( bounce) for: Generating a dipole modulation in CMB for large angles Accounting for power suppression at large angles Predicting similar anomalies for CMB polarization correlated with anomalies in temperature anisotropies The mechanisms is based on Non-Gaussian correlations with super-hubble modes 8

9 LQC and Power Spectrum (at leading order) 9

10 LQC and Power Spectrum Strategy: 1) Perturbations start in vacuum at early times 2) Evolution across bounce amplifies curvature perturbations for long wavelengths (compared to space-time curvature scale) 3) Then standard slow-roll inflation begins but perturbations reach onset of inflation in an excited state rar than Bunch-Davies vacuum Remark: I ll use V ( )= 1 potential but or choice are certainly possible and 2 m2 2 results have been shown to be robust (Bonga-Gupt 2015) 10

11 LQC and Power Spectrum Why perturbations are affected by bounce? Wave equation of a (e.g. massless) particle: [@ 2 t In an expanding universe: (2) (1) 2 t + 3ȧ(t) t ~r 2 ~x ] (~x t) =0 e i(wt ± ~ k ~x) 1 a(t) 2 ~ r 2 ~x (~x t) =0 Independent solutions: e i(wt ± ~ k ~x) positive frequency waves negative frequency waves positive and negative frequency waves are not solutions anymore!! 11

12 LQC and Power Spectrum 12

13 LQC and Power Spectrum 13

14 LQC and Power Spectrum Why perturbations are affected by bounce? Qualitative discussion to gain intuition: Tensor modes in Fourier space (same conclusions for scalars) T 00 k ( )+2 a0 ( ) a( ) T 0 k( )+k 2 T k ( ) =0 Factorize 1/a( ) : T k ( ) = 1 a( ) k( ) 00 k k( )+a 2 2 ( ) a 2 ( ) 6 R( ) Ricci scalar k( ) =0 Therefore: (k/a) 2 R( ) curvature unimportant Minkowski spacetime-like evolution (k/a) 2. R( ) curvature affects evolution amplification ( particle creation ) 14

15 LQC and Power Spectrum Evolution of curvature in LQC: t radius of curvature 1 < LQC crosses curvature radius only during inflation t inflation LQC < 2 < I crosses curvature radius before and during inflation 2 > I doesn t cross curvature radius t bounce 1 LQC 2 I 2 Length Therefore: we expect LQC pre-inflationary evolution to affect LQC < < I Fourier modes in range k LQC >k>k I will reach onset of inflation in an excited state which we can compute and study its observational consequences 15

16 LQC and Power Spectrum Results of numerical evolution (I.A.-Ashtekar-Nelson I.A.-Morris 2015) Scalar Power Spectrum Tensor Power Spectrum B =1.22 m = and vacuum initial condition at bounce Grey point: numerical result for individual k s Black line: average of grey points k? /a 0 =0.002 Mpc 1 As expected pre-inflationary evolution modifies power for lowest k-values (longest wavelengths) we can observe and for even longer wavelengths (super-hubble modes) 16

17 LQC and Power Spectrum In angular space: Agreement with inflationary results for ` > 30 agreement with observational constraints LQC effects for ` < 30. Most important: reduction of tensor-to-scalar ratio (slightly alleviates constrains on quadratic potential) modification of consistency relation r< 8 n t effects on spectral indices and runnings Most of LQC-effects are swept away to super-hubble scales! Furrmore: we obtain enhancement of power at large angles 17

18 LQC and Power Spectrum The power spectra and its relation with observations have been analyzed in great detail (I.A.-Ashtekar-Nelson I.A.-Morris 2015) Robustness tests: Conclusions robust against initial conditions (I.A.-Ashtekar-Nelson 2013 I.A.-Morris 2015) Conclusions robust against change in potential (Bonga-Gutp 2015) Conclusions robust against quantum fluctuation of FLRW geometry (I.A.-Ashtekat-Gutp 2015) Or approaches for perturbations (within LQC) produce quite similar results (French group Madrid Group) many interesting results have been obtained on way but We need to be more ambitious 18

19 Non-Gaussianity and Power Spectrum 19

20 Non-Gaussianity and Power Spectrum Is re any way super-hubble modes can affect observable ones??? The Observable Universe obs SH The Universe Super-Hubble mode The answer is yes if modes SH and obs are correlated: Non-Gaussianity (Adhikari Brahma Bartolo Bramante Byrnes Carrol Dai Dimastrogiovanni Erickcen Hui Jeong Kamionkowski LoVerde Matarrese Mota Nelson Nurmi Peloso Pullen Ricciardone Shandera Schmidt Tasinato Thorsrud Urban...) 20

21 Non-Gaussianity and Power Spectrum The statement: If we only observe a small patch within a larger universe correlations with super- Hubble modes will generically modify observed power spectrum (change in power anisotropies etc.) Anor way of saying same: ( scalar curvature perturbations) Q ~k If hq ~kobs Q ~k 0 obs Q ~ksh i large and we cannot observe ~ ksh correlations between ~ kobs ~ k 0 and obs non-diagonal contribution to hq ~kobs Q ~k 0 obs i hq(~x)q(~x + ~x)i will depend on ~x and direction of ~x inhomogeneities and anisotropies in observable patch of universe 21

22 Non-Gaussianity and Power Spectrum Come back to LQC: Does LQC have a mechanism to correlate observable and super-hubble modes? (in standard inflation y are not correlated) I.A.-Parker 2010: if perturbations are in an excited state at onset of inflation. non-gaussianity of type we need (squeezed configurations) will be generated during inflation But recall evolution across bounce excites perturbations: we expect correlations Therefore: LQC creates excitations and Inflation correlates m 22

23 Non-Gaussianity and Power Spectrum Three point function: I.A hq ~k1 Q ~k2 Q ~k3 i =(2 ) 3 ( ~ k 1 + ~ k 2 + ~ k 3 ) B Q (k 1 k 2 k 3 ) Ratio (inflation+lqc)/inflation Bispectrum: k 2 /k? B R /B BD Q R Q modes in observable range k 3 /k? k 1 =0.22k? k? /a 0 =0.002 Mpc 1 The plot tells us: Observable modes are not correlated among mselves: ok with observations But longest wavelengths we can observe are strongly correlated with super- Hubble modes (as expected) will modify power spectrum 23

24 Modulated Power Spectrum in LQC 24

25 Modulated Power Spectrum in LQC two point function acquires non- As mentioned before in presence of diagonal terms: ~ ksh Hui Schmidt Adhikari Brahma Dai Erickcen Jeong Kamionkowski Nelson Shandera...) hq ~kobs Q ~k 0 i = P Q (k) h(2 ) 3 ( ~ k obs + ~ k 0 obs obs)+g( ~ k obs ~ i k SH ) Q ~ksh where G( ~ k obs ~ k SH )= B Q( ~ k obs ~ k 0 obs ~ k SH ) P Q (k obs )P Q (k SH ) and ~ kobs + ~ k 0 obs + ~ k SH =0 In angular space: Wigner 3j-symbols ha`m a?`0m 0 i = ``0 mm 0 C` + X LM A LM G``0L mm0 M (C` + C`0) The modulating amplitude A LM can be computed from bispectrum I.A

26 Modulated Power Spectrum in LQC 4 Questions: 1) Are re values of free parameters in our model ( B and m) for which dipole asymmetry is in quantitative agreement with observations? Answer: Yes A ha L=1 i { B =1.22 m = and vacuum initial condition before bounce Observations: A obs L=1 =0.07 ± 0.02 when averaged for ` < 64 A scale dependent dipole modulation arises naturally from bounce 26

27 Modulated Power Spectrum in LQC 2) Ok. But what about higher multipoles? Answer: also compatible with observations A A ha L=2 i ha L=3 i { { Observations: A obs L compatible with zero for L>1 27

28 Modulated Power Spectrum in LQC 3) Can you explain something different with same values of free parameters? E.g what about observed power suppression? Answer: Pay attention to L=0 (monopole) A ha L=0 i { ` This modulation can both increase and decrease Power Spectrum at low ` Monte Carlo simulations: 34% of simulated spectra show a suppression of at least 10% for ` < 30 In standard inflation: a few per mil! (of course this is why people call it anomaly ) Remark: see (Ashtekar-Gupt to appear) for anor way of obtaining suppression 28

29 Modulated Power Spectrum in LQC Plot for typical shape of suppression: `(` + 1) C`/ Inflation Inflation+LQC and no modulation Inflation+LQC + NG-modulation ` I.A

30 Modulated Power Spectrum in LQC 4) Can you predict something that hasn t been observed yet? Recall: Answer: Yes If hq ~kobs Q ~k 0 obs Q ~ksh i large modulation in hq ~kobs Q ~k 0 obs i For same reason: If ht ~kobs T ~k 0 obs Q ~ksh i large modulation in ht ~kobs T ~k 0 obs i Since both correlations are generated by same Q ~ksh y are correlated I ve computed ht ~kobs T ~k 0 Q ~ksh i obs and results are very similar to hq ~kobs Q ~k 0 Q ~ksh i obs Values for ha L=0 i ha L=1 i ha L=2 i ha L=3 i almost identical ` Prediction: if low s features are originated from a bounce must also show anomalies tensor perturbations 30

31 Conclussions 31

32 Conclussions LQC has matured significantly in last 4 years regarding connexion with observations: Solid mamatical framework Agreement with current observational constraints New mechanisms to account for new features in CMB New predictions More work needed: Connexion full ory Convergence of different approaches Inflation field and its potential More about Non-Gaussianity LQC is best chance we have to make solid contact with observations 32