agullo uruguay 2017 -...

Ivan Agullo

Punta del Este, March 30, 2017

Louisiana State University

The phenomenology of the LQC-bounce preceding inflation

Quantum Gravity in the Southern Cone VII

1. Motivation

LQC, Non-Gaussianity and CMB anomalies

Ivan Agullo

Loops 15, Erlangen, 2015

Louisiana State UniversityIvan Agullo

Inflation

ds

2 = �dt

2 + a(t)2d~x2(Within our observable patch) FLRW metric:

a(t) ⇠ e�Ht

a(t) ⇠pt

Rad domination

Inflation

???

ton

tend

t

length

RH = H�1

º!

�~x

0`P ` ⇠ 105`P `

⇢ ⇠ 10�11⇢P `

teq


Ivan Agullo



1. Inflation occurs: most popular models assume existence of potential dominated

3. Scalar perturbations were in the vacuum state at the onset of inflation

Assumptions may seem ad-hoc, but what one gets is far more than what one puts in

Summary of main assumptions:

2. Cosmic Inhomogeneities during inflation are well approximated by first order perturbations propagating on a classical FLRW universe

�(~x, t)

5


Ivan Agullo



Why the vacuum if we ignore the pre-inflationary evolution of the universe???

Extended point of view: the huge inflationary expansion will dilute any quanta initially present, washing away deviations from the vacuum.

t

wxy

z

space as the hyperboloid of Fig. 28.7. At this point, it is worth mentioninganother model, called anti-de Sitter space, which is a Lorentzian 4-spherein a pseudo-Minkowskian 5-space of signature þþ""" (Fig. 28.8).[28.4]

Note that anti-de Sitter space is not a very sensible spacetime, physically,because it possesses (causality violating) closed timelike curves (e.g. thecircle in the plane spanning the t and w axes); see §17.9 and Fig. 17.18.Sometimes the term ‘anti-de Sitter space’ refers to an ‘unwrapped’ version inwhich each circle in a constant-(x, y, z) plane has been unwrapped into aline, and the whole space becomes simply-connected (§12.1). I have drawna strict conformal diagram for de Sitter space in Fig. 28.9a, for the portionof it that represents the steady-state model in Fig. 28.9b (the dotted

Fig. 28.6 One of the underlying mo-tivations of inflation is that an expo-nential expansion scale of perhaps 1050

(say between times 10"35 s and 10"32 s)might serve to ‘iron out’ a generic initialstate, so as to provide an essentiallyuniform, spatially flat, post-inflationuniverse.

Fig. 28.7 The de Sitter spacetime (pictured as ahyperboloid, with two spatial dimensions sup-pressed) is a Lorentzian ‘4-sphere’ (of imaginaryradius, giving intrinsic metric signatureþ " "") in Minkowski 5-space M5 (whosemetric is ds2 ¼ dt2 " dw2" dx2 " dy2 " dz2).To get the steady-state model, we ‘cut’ thehyperboloid into half, along t ¼ w; constanttime being given by constant positive t" w.

[28.4] Write down explicitly the equations for the de Sitter and anti-de Sitter 4-spaces in the

background 5-space, using the coordinates t, w, x, y, z indicated in Figs. 28.8 and 28.9. Findcoordinates within ‘half’ of de Sitter space, so that its intrinsic metric takes the ‘steady-state’ form

given later in this section.

748

§28.4 CHAPTER 28

Picture from Road to Reality, R. Penrose

3. Scalar perturbations were in the vacuum state at the onset of inflation


Ivan Agullo



Intuition certainly true for classical perturbations. But evolution of quantum excitation is more subtle:

The stimulated creation process compensates for the dilution of the quanta initially present, keeping their number density constant during inflation

Spontaneous particle creation from the vacuum comes together with Stimulated creation

Quantum correlation functions keep memory of the initial state.

There is (finite) red-shift, but not dilution

I.A., L. Parker 2010:

Non-Gaussianity (3-point correlation function) a quite sensitive observable

7


Ivan Agullo



Opportunity: observational window to the pre-inflationary universe!

a(t) ⇠ e�Ht

a(t) ⇠pt

Rad domination

Inflation

???

ton

tend

t

length

RH = H�1

º!

�~x

0`P ` ⇠ 105`P `

⇢ ⇠ 10�11⇢P `

⇢ ⇠ 10�115⇢P `teq


Ivan Agullo



To summarize:

Don’t know how inflation started and what happen before. But predictions are sensitive to those details.

Look for extensions of the inflationary scenario. Very likely Quantum Gravity must be involved.

Question: is there any motivation from observation to look for physics beyond inflation? Yes!


Ivan Agullo



Astronomy & Astrophysics manuscript no. planck_2015_iands c•ESO 2015June 5, 2015

Planck 2015 results. XVI. Isotropy and statistics of the CMB

Planck Collaboration: P. A. R. Ade89, N. Aghanim60, Y. Akrami65, 103, P. K. Aluri55, M. Arnaud75, M. Ashdown72, 6,J. Aumont60, C. Baccigalupi88, A. J. Banday100, 9 ú, R. B. Barreiro67, N. Bartolo32, 68, S. Basak88, E. Battaner101, 102,

K. Benabed61, 99, A. Benoît58, A. Benoit-Lévy26, 61, 99, J.-P. Bernard100, 9, M. Bersanelli35, 49, P. Bielewicz85, 9, 88, J. J. Bock69, 11,A. Bonaldi70, L. Bonavera67, J. R. Bond8, J. Borrill14, 94, F. R. Bouchet61, 92, F. Boulanger60, M. Bucher1, C. Burigana48, 33, 50,

R. C. Butler48, E. Calabrese97, J.-F. Cardoso76, 1, 61, B. Casaponsa67, A. Catalano77, 74, A. Challinor64, 72, 12,A. Chamballu75, 16, 60, H. C. Chiang29, 7, P. R. Christensen86, 38, S. Church96, 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. Curto67, 6, 72,F. Cuttaia48, L. Danese88, R. D. Davies70, R. J. Davis70, P. de Bernardis34, A. de Rosa48, G. de Zotti45, 88, J. Delabrouille1,

F.-X. Désert54, J. M. Diego67, H. Dole60, 59, S. Donzelli49, O. Doré69, 11, M. Douspis60, A. Ducout61, 56, X. Dupac39,G. Efstathiou64, F. Elsner26, 61, 99, 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,K. Ganga1, C. Gauthier1, 81, T. Ghosh60, M. Giard100, 9, Y. Giraud-Héraud1, E. Gjerløw65, J. González-Nuevo20, 67,

K. M. Górski69, 104, S. Gratton72, 64, A. Gregorio36, 47, 53, A. Gruppuso48, J. E. Gudmundsson29, F. K. Hansen65,D. Hanson83, 69, 8, D. L. Harrison64, 72, S. Henrot-Versillé73, C. Hernández-Monteagudo13, 82, D. Herranz67,

S. R. Hildebrandt69, 11, E. Hivon61, 99, M. Hobson6, W. A. Holmes69, A. Hornstrup17, W. Hovest82, Z. Huang8,K. M. Hu�enberger27, G. Hurier60, A. H. Ja�e56, T. R. Ja�e100, 9, W. C. Jones29, M. Juvela28, E. Keihänen28, R. Keskitalo14,

J. Kim82, T. S. Kisner79, J. Knoche82, M. Kunz18, 60, 3, H. Kurki-Suonio28, 44, G. Lagache5, 60, A. Lähteenmäki2, 44,J.-M. Lamarre74, A. Lasenby6, 72, M. Lattanzi33, C. R. Lawrence69, R. Leonardi39, J. Lesgourgues62, 98, F. Levrier74,

M. Liguori32, 68, P. B. Lilje65, M. Linden-Vørnle17, H. Liu86, 38, M. López-Caniego39, 67, P. M. Lubin30, J. F. Macías-Pérez77,G. Maggio47, D. Maino35, 49, N. Mandolesi48, 33, A. Mangilli60, 73, D. Marinucci37, M. Maris47, P. G. Martin8,

E. Martínez-González67, S. Masi34, S. Matarrese32, 68, 42, P. McGehee57, P. R. Meinhold30, A. Melchiorri34, 51, L. Mendes39,A. Mennella35, 49, M. Migliaccio64, 72, K. Mikkelsen65, S. Mitra55, 69, M.-A. Miville-Deschênes60, 8, D. Molinari67, 48, A. Moneti61,

L. Montier100, 9, G. Morgante48, D. Mortlock56, A. Moss90, D. Munshi89, J. A. Murphy84, P. Naselsky86, 38, F. Nati29,P. Natoli33, 4, 48, C. B. Netterfield22, H. U. Nørgaard-Nielsen17, F. Noviello70, D. Novikov80, I. Novikov86, 80, C. A. Oxborrow17,

F. Paci88, L. Pagano34, 51, F. Pajot60, N. Pant55, D. Paoletti48, 50, F. Pasian47, G. Patanchon1, T. J. Pearson11, 57,O. Perdereau73, L. Perotto77, F. Perrotta88, V. Pettorino43, F. Piacentini34, M. Piat1, E. Pierpaoli25, D. Pietrobon69,S. Plaszczynski73, E. Pointecouteau100, 9, G. Polenta4, 46, L. Popa63, G. W. Pratt75, G. Prézeau11, 69, S. Prunet61, 99,

J.-L. Puget60, J. P. Rachen23, 82, R. Rebolo66, 15, 19, M. Reinecke82, M. Remazeilles70, 60, 1, C. Renault77, A. Renzi37, 52,I. Ristorcelli100, 9, G. Rocha69, 11, C. Rosset1, M. Rossetti35, 49, A. Rotti55, G. Roudier1, 74, 69, J. A. Rubiño-Martín66, 19,

B. Rusholme57, M. Sandri48, D. Santos77, M. Savelainen28, 44, G. Savini87, D. Scott24, M. D. Sei�ert69, 11, E. P. S. Shellard12,T. Souradeep55, L. D. Spencer89, V. Stolyarov6, 72, 95, R. Stompor1, R. Sudiwala89, R. Sunyaev82, 93, D. Sutton64, 72,

A.-S. Suur-Uski28, 44, J.-F. Sygnet61, J. A. Tauber40, L. Terenzi41, 48, L. To�olatti20, 67, 48, M. Tomasi35, 49, M. Tristram73,T. Trombetti48, M. Tucci18, J. Tuovinen10, L. Valenziano48, J. Valiviita28, 44, B. Van Tent78, P. Vielva67, F. Villa48,

L. A. Wade69, B. D. Wandelt61, 99, 31, I. K. Wehus69, D. Yvon16, A. Zacchei47, J. P. Zibin24, and A. Zonca30

(A�liations can be found after the references)

June 5, 2015

ABSTRACT

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using ob-servations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature,but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived fromthe multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we findexcellent agreement between results based on these sky maps over both a very large fraction of the sky and a broadrange of angular scales, establishing that potential foreground residuals do not a�ect our studies. Tests of skewness,kurtosis, multi-normality, N -point functions, and Minkowski functionals indicate consistency with Gaussianity, whilea power deficit at large angular scales is manifested in several ways, for example low map variance. The results of apeak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detectedwith several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe thelarge-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a poste-riori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at asignificance that is dependent on the details of the approach. We perform the first examination of polarization data,finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations.Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data andprovide our most thorough view of the statistics of the CMB fluctuations to date.

Key words. cosmology: observations – cosmic background radiation – polarization – methods: data analysis – methods:statistical

Article number, page 1 of 61

Astronomy & Astrophysics manuscript no. planck_2015_iands c•ESO 2015June 5, 2015

Planck 2015 results. XVI. Isotropy and statistics of the CMB

Planck Collaboration: P. A. R. Ade89, N. Aghanim60, Y. Akrami65, 103, P. K. Aluri55, M. Arnaud75, M. Ashdown72, 6,J. Aumont60, C. Baccigalupi88, A. J. Banday100, 9 ú, R. B. Barreiro67, N. Bartolo32, 68, S. Basak88, E. Battaner101, 102,

K. Benabed61, 99, A. Benoît58, A. Benoit-Lévy26, 61, 99, J.-P. Bernard100, 9, M. Bersanelli35, 49, P. Bielewicz85, 9, 88, J. J. Bock69, 11,A. Bonaldi70, L. Bonavera67, J. R. Bond8, J. Borrill14, 94, F. R. Bouchet61, 92, F. Boulanger60, M. Bucher1, C. Burigana48, 33, 50,

R. C. Butler48, E. Calabrese97, J.-F. Cardoso76, 1, 61, B. Casaponsa67, A. Catalano77, 74, A. Challinor64, 72, 12,A. Chamballu75, 16, 60, H. C. Chiang29, 7, P. R. Christensen86, 38, S. Church96, 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. Curto67, 6, 72,F. Cuttaia48, L. Danese88, R. D. Davies70, R. J. Davis70, P. de Bernardis34, A. de Rosa48, G. de Zotti45, 88, J. Delabrouille1,

F.-X. Désert54, J. M. Diego67, H. Dole60, 59, S. Donzelli49, O. Doré69, 11, M. Douspis60, A. Ducout61, 56, X. Dupac39,G. Efstathiou64, F. Elsner26, 61, 99, 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,K. Ganga1, C. Gauthier1, 81, T. Ghosh60, M. Giard100, 9, Y. Giraud-Héraud1, E. Gjerløw65, J. González-Nuevo20, 67,

K. M. Górski69, 104, S. Gratton72, 64, A. Gregorio36, 47, 53, A. Gruppuso48, J. E. Gudmundsson29, F. K. Hansen65,D. Hanson83, 69, 8, D. L. Harrison64, 72, S. Henrot-Versillé73, C. Hernández-Monteagudo13, 82, D. Herranz67,

S. R. Hildebrandt69, 11, E. Hivon61, 99, M. Hobson6, W. A. Holmes69, A. Hornstrup17, W. Hovest82, Z. Huang8,K. M. Hu�enberger27, G. Hurier60, A. H. Ja�e56, T. R. Ja�e100, 9, W. C. Jones29, M. Juvela28, E. Keihänen28, R. Keskitalo14,

J. Kim82, T. S. Kisner79, J. Knoche82, M. Kunz18, 60, 3, H. Kurki-Suonio28, 44, G. Lagache5, 60, A. Lähteenmäki2, 44,J.-M. Lamarre74, A. Lasenby6, 72, M. Lattanzi33, C. R. Lawrence69, R. Leonardi39, J. Lesgourgues62, 98, F. Levrier74,

M. Liguori32, 68, P. B. Lilje65, M. Linden-Vørnle17, H. Liu86, 38, M. López-Caniego39, 67, P. M. Lubin30, J. F. Macías-Pérez77,G. Maggio47, D. Maino35, 49, N. Mandolesi48, 33, A. Mangilli60, 73, D. Marinucci37, M. Maris47, P. G. Martin8,

E. Martínez-González67, S. Masi34, S. Matarrese32, 68, 42, P. McGehee57, P. R. Meinhold30, A. Melchiorri34, 51, L. Mendes39,A. Mennella35, 49, M. Migliaccio64, 72, K. Mikkelsen65, S. Mitra55, 69, M.-A. Miville-Deschênes60, 8, D. Molinari67, 48, A. Moneti61,

L. Montier100, 9, G. Morgante48, D. Mortlock56, A. Moss90, D. Munshi89, J. A. Murphy84, P. Naselsky86, 38, F. Nati29,P. Natoli33, 4, 48, C. B. Netterfield22, H. U. Nørgaard-Nielsen17, F. Noviello70, D. Novikov80, I. Novikov86, 80, C. A. Oxborrow17,

F. Paci88, L. Pagano34, 51, F. Pajot60, N. Pant55, D. Paoletti48, 50, F. Pasian47, G. Patanchon1, T. J. Pearson11, 57,O. Perdereau73, L. Perotto77, F. Perrotta88, V. Pettorino43, F. Piacentini34, M. Piat1, E. Pierpaoli25, D. Pietrobon69,S. Plaszczynski73, E. Pointecouteau100, 9, G. Polenta4, 46, L. Popa63, G. W. Pratt75, G. Prézeau11, 69, S. Prunet61, 99,

J.-L. Puget60, J. P. Rachen23, 82, R. Rebolo66, 15, 19, M. Reinecke82, M. Remazeilles70, 60, 1, C. Renault77, A. Renzi37, 52,I. Ristorcelli100, 9, G. Rocha69, 11, C. Rosset1, M. Rossetti35, 49, A. Rotti55, G. Roudier1, 74, 69, J. A. Rubiño-Martín66, 19,

B. Rusholme57, M. Sandri48, D. Santos77, M. Savelainen28, 44, G. Savini87, D. Scott24, M. D. Sei�ert69, 11, E. P. S. Shellard12,T. Souradeep55, L. D. Spencer89, V. Stolyarov6, 72, 95, R. Stompor1, R. Sudiwala89, R. Sunyaev82, 93, D. Sutton64, 72,

A.-S. Suur-Uski28, 44, J.-F. Sygnet61, J. A. Tauber40, L. Terenzi41, 48, L. To�olatti20, 67, 48, M. Tomasi35, 49, M. Tristram73,T. Trombetti48, M. Tucci18, J. Tuovinen10, L. Valenziano48, J. Valiviita28, 44, B. Van Tent78, P. Vielva67, F. Villa48,

L. A. Wade69, B. D. Wandelt61, 99, 31, I. K. Wehus69, D. Yvon16, A. Zacchei47, J. P. Zibin24, and A. Zonca30

(A�liations can be found after the references)

June 5, 2015

ABSTRACT

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using ob-servations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature,but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived fromthe multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we findexcellent agreement between results based on these sky maps over both a very large fraction of the sky and a broadrange of angular scales, establishing that potential foreground residuals do not a�ect our studies. Tests of skewness,kurtosis, multi-normality, N -point functions, and Minkowski functionals indicate consistency with Gaussianity, whilea power deficit at large angular scales is manifested in several ways, for example low map variance. The results of apeak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detectedwith several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe thelarge-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a poste-riori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at asignificance that is dependent on the details of the approach. We perform the first examination of polarization data,finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations.Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data andprovide our most thorough view of the statistics of the CMB fluctuations to date.

Key words. cosmology: observations – cosmic background radiation – polarization – methods: data analysis – methods:statistical


A&A proofs: manuscript no. planck_2015_iands

1. Introduction

This paper, one of a set associated with the 2015 releaseof data from the Planck

1 mission (Planck Collaboration I2015), describes a set of studies undertaken to determinethe statistical properties of both the temperature and po-larization anisotropies of the cosmic microwave background(CMB).

The standard cosmological model is described well bythe Friedmann-Lemaître-Robertson-Walker solution of theEinstein field equations. This model is characterized by ahomogeneous and isotropic background metric and a scalefactor of the expanding Universe. It is hypothesized thatat very early times the Universe went through a periodof accelerated expansion, the so-called “cosmological infla-tion,” driven by a hypothetical scalar field, the “inflaton.”During inflation the Universe behaves approximately as ade Sitter space, providing the conditions by which some ofits present properties can be realized and specifically re-laxing the problem of initial conditions. In particular, theseeds that gave rise to the present large-scale matter distri-bution via gravitational instability originated as quantumfluctuations of the inflaton about its vacuum state. Thesefluctuations in the inflaton produce energy density pertur-bations that are distributed as a statistically homogeneousand isotropic Gaussian random field. Linear theory relatesthose perturbations to the temperature and polarizationanisotropies of the CMB, implying a distribution for theanisotropies very close to that of a statistically isotropicGaussian random field.

The aim of this paper is to use the full mission Planck

data to test the Gaussianity and isotropy of the CMB asmeasured in both intensity and, in a more limited capacity,polarization. Testing these fundamental properties is cru-cial for the validation of the standard cosmological scenario,and has profound implications for our understanding of thephysical nature of the Universe and the initial conditionsof structure formation. Moreover, the confirmation of thestatistically isotropic and Gaussian nature of the CMB isessential for justifying the corresponding assumptions usu-ally made when estimating the CMB power spectra andother quantities to be obtained from the Planck data. In-deed, the isotropy and Gaussianity of the CMB anisotropiesare implicitly assumed in critical science papers from the2015 release, in particular those describing the likelihoodand the derivation of cosmological parameter constraints(Planck Collaboration XI 2015; Planck Collaboration XIII2015). Conversely, if the detection of significant deviationsfrom these assumptions cannot be traced to known system-atic e�ects or foreground residuals, the presence of whichshould be diagnosed by the statistical tests set forth inthis paper, this would necessitate a major revision of thecurrent methodological approaches adopted in deriving themission’s many science results.

ú Corresponding author: A. J. Banday [email protected]

Planck (http://www.esa.int/Planck) is a project of the Eu-ropean Space Agency (ESA) with instruments provided by twoscientific consortia funded by ESA member states and led byPrincipal Investigators from France and Italy, telescope reflec-tors provided through a collaboration between ESA and a sci-entific consortium led and funded by Denmark, and additionalcontributions from NASA (USA).

Well-understood physical processes due to the inte-grated Sachs-Wolfe (ISW) e�ect (Planck CollaborationXVII 2014; Planck Collaboration XXI 2015) and gravita-tional lensing (Planck Collaboration XIX 2014; Planck Col-laboration XV 2015) lead to secondary anisotropies thatexhibit marked deviation from Gaussianity. In addition,Doppler boosting, due to our motion with respect to theCMB rest frame, induces both a dipolar modulation ofthe temperature anisotropies and an aberration that cor-responds to a change in the apparent arrival directions ofthe CMB photons (Challinor & van Leeuwen 2002). Bothof these e�ects are aligned with the CMB dipole, and weredetected at a statistically significant level on small angularscales in Planck Collaboration XXVII (2014). Beyond these,Planck Collaboration XXIII (2014, hereafter PCIS13) es-tablished that the Planck 2013 data set showed little evi-dence for non-Gaussianity, with the exception of a numberof CMB temperature anisotropy anomalies on large angu-lar scales that confirmed earlier claims based on WMAPdata. Moreover, given that the broader frequency cover-age of the Planck instruments allowed improved compo-nent separation methods to be applied in the derivation offoreground-cleaned CMB maps, it was generally consideredthat the case for anomalous features in the CMB had beenstrengthened. Hence, such anomalies have attracted consid-erable attention in the community, since they could be thevisible traces of fundamental physical processes occurringin the early Universe.

However, the literature also supports an ongoing debateabout the significance of these anomalies. The central issuein this discussion is connected with the role of a posteri-ori choices — whether interesting features in the data biasthe choice of statistical tests, or if arbitrary choices in thesubsequent data analysis enhance the significance of the fea-tures. Indeed, the WMAP team (Bennett et al. 2011) basetheir rejection of the presence of anomalies in the CMB onsuch arguments. Of course, one should attempt to correctfor any choices that were made in the process of detect-ing an anomaly. However, in the absence of an alternativemodel for comparison to the standard Gaussian, statisti-cally isotropic one adopted to quantify significance, this isoften simply not possible. In this work, whilst it is recog-nized that care must be taken in the assessment of signif-icance, we proceed on the basis that allowing a posteriorireasoning permits us to challenge the limits of our existingknowledge (Pontzen & Peiris 2010). That is, by focusingon specific properties of the observed data that are shownto be empirically interesting, we may open up new pathsto a better theoretical understanding of the Universe. Wewill clearly describe the methodology applied to the data,and attempt to study possible links among the anomaliesin order to search for a physical interpretation.

The analysis of polarization data introduces a new op-portunity to explore the statistical properties of the CMBsky, including the possibility of improvement of the sig-nificance of detection of large-scale anomalies. However,this cannot be fully included in the current data assess-ment, since the component-separation products in polar-ization are high-pass filtered to remove large angular scales(Planck Collaboration IX 2015), owing to the persistence ofsignificant systematic artefacts originating in the High Fre-quency Instrument (HFI) data (Planck Collaboration VII2015; Planck Collaboration VIII 2015). In addition, limi-tations of the simulations with which the data are to be



1. Introduction













1. Introduction












9

2. The Model


Ivan Agullo



Idea: use Loop Quantum Cosmology to extend the inflationary scenario

Cf. Abhay’s talk

12


Ivan Agullo



4/10/15, 5:29 PMThe Beginning of Everything: A New Paradigm Shift for the Infant Universe — Eberly College of Science

Page 1 of 4http://science.psu.edu/news-and-events/2012-news/Ashtekar11-2012

The Beginning of Everything: A New ParadigmShift for the Infant Universe

Diagram showing evolution of the Universe according to the new paradigm of Loop Quantum Origins, developedby scientists at Penn State University and published on 11 December 2012 as an "Editor's Suggestion" paper in thescientific journal Physical Review Letters. Image source: P. Singh Physics 5, 142 (2012). Image credit: Alan Stonebraker.For re-use requests, contact APS.

28 November 2012 — A new paradigm for understanding the earliest eras in the history of the universe has beendeveloped by scientists at Penn State University. Using techniques from an area of modern physics called loopquantum cosmology, developed at Penn State, the scientists now have extended analyses that include quantumphysics farther back in time than ever before -- all the way to the beginning. The new paradigm of loop quantumorigins shows, for the first time, that the large-scale structures we now see in the universe evolved from fundamentalfluctuations in the essential quantum nature of "space-time," which existed even at the very beginning of the universeover 14 billion years ago. The achievement also provides new opportunities for testing competing theories of moderncosmology against breakthrough observations expected from next-generation telescopes. The research will bepublished on 11 December 2012 as an "Editor's Suggestion" paper in the scientific journal Physical Review Letters.

"We humans always have yearned to understand more about the origin and evolution of our universe," said AbhayAshtekar, the senior author of the paper. "So it is an exciting time in our group right now, as we begin using ournew paradigm to understand, in more detail, the dynamics that matter and geometry experienced during the earliesteras of the universe, including at the very beginning." Ashtekar is the Holder of the Eberly Family Chair in Physics atPenn State and the director of the university's Institute for Gravitation and the Cosmos. Coauthors of the paper,


Ivan Agullo



Idea: use Loop Quantum Cosmology to extend the inflationary scenario

Cf. Abhay’s talk







FLRW spacetime arises from quantum corrected Friedman eqns.

H2 =8⇡G

3⇢

✓1� ⇢

⇢sup

◆

Curvature perturbations described as quantum field on this spacetime

Scenario derived from first principles

Goal: look for phenomenological implications

⇢sup ⇡ ⇢P `;


Ivan Agullo









Strategy:

1) Perturbations start in the vacuum at early times

2) Evolution across the bounce amplifies curvature perturbations

3) Then standard slow-roll inflation begins, but perturbations reach the onset of inflation in an excited and non-Gaussian state, rather than the vacuum

4) These excitations impact observables quantities

3. Some details

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Ivan Agullo



Initial conditions for perturbations

Initial data for �B (= amount of expansion between bounce and onset inflation)

Inflation potential

� e.g. at the bounce time:

To do concrete calculations there are some choices to be made

I’ll use the potential, but other choice are certainly possible and results have been shown to be robust (Bonga-Gupt 2015)

V (�) =1

2m2�2

�

V (�)

I’ll show plots for Adiabatic vacuum in the past (compare with Abhay’s)

Results of numerical evolution

Scalar Power Spectrum Tensor Power Spectrum

(I.A.-Ashtekar-Nelson 2012-13, I.A.-Morris 2015)

m = 1.1⇥ 10�6�B = 1.22 k?/a0 = 0.002Mpc�1In these plots: , ,


Ivan Agullo



Results of numerical evolution

Scalar Power Spectrum

(I.A.-Ashtekar-Nelson 2012-13, I.A.-Morris 2015, Bonga-Gupt 2016, Martin de Blas-Olmedo 2016)


Ivan Agullo



The pre-inflationary evolution modifies the power for low k-values (long wavelengths)

For large values of predictions are indistinguishable from standard inflation

Most important:

reduction of tensor-to-scalar ratio (slightly alleviates constrains on quadratic potential)

modification of consistency relation r<� 8 nt

effects on spectral indices and runnings

�B

QG extension of the inflationary scenario

For smaller , QG corrections at large angles in CMB. In particular:�B


Ivan Agullo



Conclusions robust against initial conditions (I.A.-Ashtekar-Nelson 2013, I.A.-Morris 2015)

Conclusions robust against change in the potential (Bonga-Gutp 2015-16)

Conclusions robust against choice of the quantum of FLRW geometry (I.A., Ashtekat, Gutp 2016)

Other approaches for perturbations (within LQC) produce quite similar results

Robustness tests:

Extension to anisotropic bounces (I.A., Olmedo, Vijayakumar)


Ivan Agullo



Conclusions robust under inclusion of Back-reaction (I.A., Gupt, Mato, in progress)

(Mena-Marugan, Martin de Blas, Martin-Benito, Olmedo)

4. Beyond the Power Spectrum

Hemispherical anomaly Quadrupole-octopole alignment Low power @ large scales (more prominent in angular space) Parity anomaly ...

Significance . 3�

Observed anomalies at large angular scales (WMAP, PLANCK)


Ivan Agullo



Warning:

But observed in different ways and by different teams (WMAP, PALNCK, etc)

could be just a statistical fluke

Hemispherical anomaly Quadrupole-octopole alignment Low power @ large scales (more prominent in angular space) Parity anomaly ...

Significance . 3�

Observed anomalies at large angular scales (WMAP, PLANCK)


Ivan Agullo



Warning:

But observed in different ways and by different teams (WMAP, PALNCK, etc)

�T (n̂) =X

`m

a`m Y`m(n̂)

Message: all these anomalies have a common feature. They seem to require correlations between different modes:

non-diagonal terms

anisotropies

ha`ma`0m0i = �``0�mm0 C`+?

Additionally, effects only appears at large angles (low ’s): we may need a scale-dependent non-diagonal (anisotropic) terms!

`

could be just a statistical fluke

Recent discussions: we do not need anisotropic physics to modify the statistics in our observable universe. Large correlations between modes can do the job(Adhikari, Brahma, Bartolo, Bramante, Byrnes, Carrol, Dai, Deutsch, Dimastrogiovanni, Erickcen, Hui, Jeong, Kamionkowski, LoVerde, Matarrese, Mota, Nelson, Nurmi, Peloso, Pullen, Ricciardone, Shandera, Schmidt, Tasinato, Thorsrud, Urban,...)

Non-Gaussian modulation of the power spectrum

A typical realization shows larger anisotropies if the distribution is non-Gaussian


Ivan Agullo



In angular space:

Wigner 3j-symbols

Non-Gaussian modulation of the power spectrum caused by a long wave length mode

In k-space: Non-Gaussianity


Ivan Agullo



~kL

off-diagonal = anisotropies

hR~k1R?

~k2i = PR(k1)

h(2⇡)3�(~k1 � ~k2) + fNL(~k1,~k2,~kL)R~kL

i

ha`ma?`0m0i = �``0�mm0 C` +X

L,M

AL(`, `0)G``0L

�mm0M (C` + C`0)

25


Ivan Agullo



25


Ivan Agullo



But there are strong limits on non-Gaussianity for the CMB (PLANCK)

|fNL| . 10 ` & 1000for

We need a mechanism to produce strongly scale dependent non-Gaussianity

25


Ivan Agullo



But there are strong limits on non-Gaussianity for the CMB (PLANCK)

|fNL| . 10 ` & 1000for

We need a mechanism to produce strongly scale dependent non-Gaussianity

kLQC

Goal: Compute the modulating amplitude using the bounce+inflation

Proposal: bounce preceding inflation

New scale: spacetime curvature at the bounce (denoted previously by )

AL(`)

5. Non-Gaussianity from the bounce

I.A., Bolliet, Vijayakumar: In Progress…

Hint(��, �P�) =

Zd3~x

n 9P 3�

4 a4 ⇡a��3 � 3P�

2 a4 ⇡a�P 2

� �� +3P 2

�

a⇡a��2@2�

� 3 a2 P�

2⇡a�� @i�� @i�� + �P� @i�� @i� +

3 a2 P�

2⇡a�� @2�@2�

� 3 a2 P�

2⇡a�� @i@j�@i@j� � 3 a2 P� V��

2⇡a��3 +

a3 V��

6��3

o

@2� =�p2�2⇡2

a

d

dt

✓��p�

⇡a��

◆


Ivan Agullo



Challenging computation:

1. No slow-roll approximation available

Work in flat slicing gauge: ��(~x)

Where

2. Challenging numerical integrals


Ivan Agullo



A sample of the result:

10�3 10�2 10�1 100 101

k/k?

10�3

10�2

10�1

100

101

102

103

104

|fN

L(k

)|

|f SL

NL(k)|

10�2 10�1 100 101

k/k?

10�11

10�10

10�9

10�8

10�7

10�6

P s(k

)

Ps(k)

Non-Gaussianity significantly more sensitive to the bounce!

Exponential growing ⇠ e�(k1+k2+k3)/kLQC

analytically understood. k = k1 ⇡ k2 = 100 k3

Oscillatory

We can choose in such a way that non-Gaussianity large only on large scales: OK with observe. constraints.

29


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The shape: peaked in squeezed (but not too squeezed) configurations

30


Ivan Agullo



31


Ivan Agullo



A sample of results for the modulation amplitudes:

10 20 30 40 50 60 70{

0.1

0.2

0.3

0.4

A 0

hA0i

`10 20 30 40 50 60 70

{

0.02

0.04

0.06

0.08

0.10

0.12

A 1

hA1i

10 20 30 40 50 60 70{

0.001

0.002

0.003

0.004

0.005

0.006

0.007A 2

hA2i

`

`


Ivan Agullo



The monopole is able to produce suppression ` < 30

A scale dependent dipole modulation of the right size

There is a choice of the parameters (i.e. ) for which:

Much smaller quadrupole, octopole, etc

In summary: the LQC bounce preceding inflation is a good candidate to account for the CMB large scale anomalies

Prediction: tensor perturbations must also show similar anomalies

Conclussions


Ivan Agullo



�B

7. Summary

BR/BBDR

k2/k?

k3/k?

Friday, June 5, 15

20 40 60 80l

0.0005

0.0010

0.0015

A3

20 40 60 80l

0.0005

0.0010

0.0015

A3

20 40 60 80l

0.0005

0.0010

0.0015

A3

20 40 60 80{

0.040.060.080.100.120.140.16A1

20 40 60 80{

0.002

0.004

0.006

0.008

0.010

0.012A2

20 40 60 80{

0.0005

0.0010

0.0015

A3

hA1ihA1i

hA1i hA2i hA3i

Friday, June 5, 15







LQC and FRW space-timeLQC and the Spectrum of primordial perturbations

LQC and the spectrum of Non-Gaussianity LQC and CMB anomalies

10�2 10�1 100 101

k/k?

10�3

10�2

10�1

100

101

102

103

104

105

|fN

L(k

)|

|fEL

NL(k)|

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