Hemispherical CMB power asymmetry: observation vs. models

Transcription

1 Helsinki May 2014 Hemispherical CMB power asymmetry: observation vs. models EnqFest May 2014 Helsinki John McDonald, Dept. of Physics, University of Lancaster

2 Outline 1. Observed Hemispherical Asymmetry 2. Phenomenological approach: Modify the inflaton perturbation power spectrum Modified inflation observables Spectral index asymmetries Hemispherical Asymmetry and BICEP2/Planck tension 3. Explaining the hemispherical asymmetry? Tachyonic growth model: Phase transition with a complex field Modulated reheating

3 1. Observed Hemispherical Asymmetry Can be modelled by a dipole [Gordon et al astro-ph/ ] Planck (SMICA): A = ± Direction (l, b) = (217.5, -20.2) ± 15 [Planck collab ] WMAP5 (ILC) : A = ± Direction (l, b) = (224, -22) ± 24 [Hoftuft et al ]

4 How is this extracted from CMB data? Need to observe the power spectrum at different points on the sky Consider patches around the point in question To extract scale-dependence, fit scale-independent C l to the CMB data over bins of multipoles. [Hansen et al astro-ph/ ] Can then define the temperature power asymmetry (A) from each bin of multipoles. Above is for l = 2 to 64. [Eriksen et al astro-ph/ ] [Hansen et al astro-ph/ ]

5 A large = ± at large angles, l = 2-64 On smaller angular scales, the asymmetry is much smaller For l = , A < (95% c.l.) [Flenders and Hotchkiss, ] A ~ at l 2000, consistent with isotropy (Planck trispectrum) [Planck collab, ] So a rather strong scale-dependence of the asymmetry is required

6 Is it real? Or could the asymmetry arise as a statistical fluctuation of isotropic Gaussian perturbations? Look at simulations of CMB power asymmetry for isotropic perturbations Less than 1 in 1000 isotropic simulations can reproduce the observed Planck asymmetry => significant at 3.3σ [Akrami et al, ] [Flenders and Hotchkiss, ] Yes, it appears to be real!

7 2. Phenomenological Approach [JMcD ] Modify the isotropic inflaton perturbation in some way (a) Add another component to the adiabatic perturbation e.g. (b) Modulate the inflaton perturbation

8 The model has a small number of parameters: Makes a number of predictions: Large and small-angle asymmetries Shifts of whole-sky (mean) CMB spectral index and running from their inflation model values Hemispherical asymmetries of the spectral index and its running More observables than parameters => Can test the consistency of a model with observations

9 Large-Angle Asymmetry from from the observed dipole

10 Small-Angle Asymmetry at large l min Fix A large = same scale-dependence => To satisfy upper bound on small-angle asymmetry A small < , need: strong scale-dependence

11 Spectral Index Shifts Power at => where Additional perturbation component => positive shift of running Modulation (suppression at low l) => negative shift of running Planck prefers negative running

12 Hemispherical asymmetry of the spectral index and its running The spectral index and running over a hemisphere are useful observables with which to characterize the CMB power asymmetry Good for comparing theory with observation Perform a CMB analysis over each hemisphere rather than over the whole sky Average power over one hemisphere Spectral index over each hemisphere

13 => Hemispherical spectral index shift Hemispherical running shift

14 We test the consistency of the power-law dipole model for by observing the hemispherical shifts: and are fixed by observed values of and These parameters in turn completely determine the hemispherical asymmetry A! Therefore by observing and A large, consistency of the input model for with observation can be tested

15 Connection between hemispherical asymmetry and BICEP2/Planck tension? [JMcD ] [If it exists Audren,Figueroa,Tram ] BICEP2: (before dust correction ) Planck: 95% c.l. no running spectral index with running n s ~ Models of inflation typically have very small n s => Need new physics to generate a negative running Planck: (no r) (with r) Planck assumes a scale-invariant running, but the likelihood is dominated by low multipoles l < 50 Could the physics responsible for the hemispherical asymmetry also produce the negative running and solve the tension?

16 For negative running, need a modulation of the inflaton perturbation which suppresses the power at low multipoles is negative Can generate both the hemispherical asymmetry and a negative running of the spectral index of the right magnitude

17 Example: Chaotic inflation By choosing model parameters appropriately, can generate the observed hemispherical asymmetry and a negative running of the right magnitude. e.g. If n σ = 0.0 then assuming A large = 0.073: ( ) (Can obtain by measuring the spectral index asymmetries.)

18 3. Explaining the hemispherical power asymmetry? So far have we have considered a phenomenological model for Still need to explain the origin of the asymmetric and scale-dependent A possible source: Tachyonic growth of a complex scalar field following phase transition [JMcD ] If N ~ 60 occurs while is still rolling to the minimum, long-wavelength fluctuations of produces a modulation of across our horizon Generates a spatially-modulated and intrinsically scale-dependent power for the phase of the complex field. Application to Modulated Reheating: [JMcD ]

19 Conclusions The hemispherical CMB power asymmetry, large at low l < 100, implies that the power spectrum from inflation must be modified. The new physics must be strongly scale-dependent => Expect shifts of the spectral index and its running from their inflation model values at low l The spectral index and its running measured over hemispheres are convenient parameters with which to characterize the CMB power asymmetry. Can directly test theoretical models of the power asymmetry. The same new physics responsible for the CMB power asymmetry may solve the tension between Planck and BICEP2 Planck favours a negative running, likelihood dominated by low multipoles, also raises the upper bound on r. Negative running at low l consistent with space-dependent modulation (suppression) of CMB power at low multipoles being the source of the power asymmetry

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21 Tachyonic Growth Model JMcD , JCAP A way to generate large superhorizon field fluctuations is the field which modulates the inflaton decay rate Field is initially at Σ = 0. At some time a phase transition occurs and field evolves in the tachyonic part of the potential from an initial Bunch-Davies vacuum on sub-horizon scales Mean field σ and change σ in a given horizon volume after N e-foldings

22 Superhorizon fluctuations after e-foldings => (a) Mean field in a horizon volume Wigner fn. semiclassical analysis Bunch-Davies initial conditions => => RMS field due to superhorizon modes:

23 Mean field in a horizon volume ~ 1-10 in cases of interest

24 (b) Mean change in field across the horizon sum over superhorizon modes c = 0.5 => Φ/Φ = 0.5 after 20 e-foldings Dominated by modes close to horizon size

25 The perturbation spectrum of the modulating field = radial direction = phase fluctuation Red spectrum for c > 0 Due to time evolution of mean radial field => Scale-dependence Intrinsic spatial variation of power spectrum Due to mean change in radial field across the horizon => Asymmetry => has the right form of perturbation to generate the CMB power asymmetry

26 Spatial variation of δσ perturbation σ 2 σ 1 Change of δσ across our horizon Other side of our horizon

27 CMB power asymmetry from Modulated Reheating JMcD Modulated reheating can produce a large CMB power asymmetry without large non-gaussianity if the inflaton decay rate is linear in the modulating field. => Modulating field perturbation must have an intrinsic asymmetry [ unlike curvaton ] Modulated reheating contribution should have a red scale-dependence to suppress the asymmetry at small scales Both properties consistent with the Tachyonic Growth Model

28 Modulated Reheating model Couple the complex from tachyonic growth to the inflaton decay process = inflaton => Modulated inflaton decay rate Adiabatic perturbation [ Ichikawa et al ] =>

29 Constraints JMcD CMB quadrupole: Non-Gaussianity: Generation of adiabatic power: All constraints can be satisfied with reasonable values,, [ f d => damping of σ after tachyonic growth ends ]

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31 CMB Power Asymmetry WMAP observed a hemispherical asymmetry in the magnitude of CMB temperature fluctuations on large angular scales > 5 o (low CMB multipoles l) Magnitude confirmed by Planck, with much smaller errors Suggests a superhorizon fluctuation of a scalar field [Other large-angle anomalies: low power, Cold Spot ]

32 Explanations? Primordial: Scalar field-based : Long-wavelength fluctuation of: Inflaton: Mean CMB temp anisotropy too large Curvaton : Probably too much non-gaussianity Modulated Reheating: Can fit all constraints JMcD: Astrophysical, phenomenological: spatial variation of the spectral index, inhomogeneous reionization optical depth, [Dai et al ]

33 Constraints A successful model must satisfy: Large angle power asymmetry: A = (Average over l < l max = 64) Suppressed small-angle asymmetry (large l): Quasar number counts => A < (95% cl) at l ~15000 Hirata => Need scale-dependent asymmetry CMB temperature homogeneity No large quadrupole a 20 < 1.9 x 10-5 Erickcek et al Planck Non-Gaussianity bound: WMAP5 Planck

34 Inflaton Erickcek, Kamionkowski, Carroll Superhorizon inflaton modulation can modulate the CMB power spectrum [simply assumed] But the inflaton fluctutation produces a large energy density fluctuation => Large fluctuation in the mean CMB temperature => too large CMB quadrupole => Modulation must come from a second scalar field

35 Curvaton Erickcek, Carroll, Kamionkowski Can modulate curvaton fluctuations via a superhorizon curvaton mode Curvaton: => => modulates To suppress CMB temperature quadrupole, need a small contribution to the energy density from the curvaton ~ 10-4 ρ total Then a sub-dominant curvaton contribution with large fluctuation δρ σ / ρ σ ~ 10-2 combined with large spatial modulation of the curvaton mean field across our horizon can account for the 10% asymmetry on large scales => O(10) % asymmetric contribution to total adiabatic perturbation But cannot account for suppression of asymmetry at quasar number count scales, since has no scale-dependence Need to suppress the curvaton contribution to the perturbation at small scales

36 Curvaton + DM isocurvature model Erickcek, Hirata, Kamionkowski To satisfy the quasar constraint, the asymmetry must be scale-dependent Subdominant curvaton decays to subdominant dark matter density => Mixture of adiabatic and DM isocurvature from curvaton decay Isocurvature component of CMB power decreases relative to the adiabatic perturbation at small scales => suppresses asymmetry C l iso / C l

37 Model can just produce sufficiently large asymmetry on large scales A = 0.072, satisfy quasar bound on small scales A < and satisfy WMAP5 bounds on the isocurvature fraction and Non-Gaussianity + CMB quadrupole bound Isocurvature Non-Gaussianity Planck constraints much stronger, especially non-gaussianity Isocurvature Non-Gaussianity Smaller f NL => smaller curvaton perturbation R = ρ curv /ρ totoal ~ 10-4 Probably cannot account for the CMB asymmetry

38 Inflaton and curvaton appear ruled out as a source of the CMB power asymmetry Non-Gaussianity is a strong constraint => Need a new source for the asymmetry which produces small non-gaussianity A complete model should also explain the superhorizon fluctuation which spatially modulates the CMB temp fluctuations A complete model that works: Scale-Dependent Modulated Reheating + Tachyonic Growth Model Modulated Reheating => CMB power asymmetry from the scalar field without large non-gaussianity JMcD Tachyonic Growth => Superhorizon scalar field perturbation Model with asymmetry and scale-dependence JMcD , JCAP

39 Summary Modulated Reheating can account for the CMB power asymmetry via a subdominant and scale-dependent adiabatic perturbation Non-Gaussianity is reduced if inflaton decay rate is linear in the modulating field Tachyonic growth of a complex field can generate modulating field perturbations of the necessary form and magnitude Existence proof for scalar field model explanation Predicts significant shifts of spectral index and running spectral index relative to common inflation models

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41 Additional Slides

42 Large-angle CMB anomalies Lack of power (low variance), Parity Asymmetry, Cold Spot, Aligned dipole,quadrupole and octupole, lack of correlation on large angles All 3-σ Planck effects No obvious explanation CMB hemispherical power asymmetry: Suggests a superhorizon fluctuation of a scalar field

43 Non-Gaussianity [ Ichikawa et al ] => => =>

44 Why inflaton decay must be dominated by a linear interaction to reduce Non-Gaussianity => => => at least 30 times larger => Too large [optimistic]

45 CMB Quadrupole Erickcek, Hirata, Kamionkowski Gravitational (Bardeen) potential perturbation: [Rad. Dom.] Tachyonic growth model => superhorizon perturbation mostly due to modes not much bigger than the horizon Model with a single superhorizon mode:

46 Expand => term responsible for the CMB quadrupole Compare with => Quadrupole Quadrupole upper bound Q => => =>

47 Condition to generate large enough adiabatic power from modulated reheating =>, => =>

48 Example: Chaotic inflation Can fix by measuring the spectral index asymmetries. This then determines in chaotic inflation as a function of ( ) e.g. If n σ = 0.0 then eg