Maximising the scientific return from cosmic non-gaussianity. Christian Byrnes (University of Bielefeld)

Transcription

1 Maximising the scientific return from cosmic non-gaussianity Christian Byrnes (University of Bielefeld)

2 Specific motivations There is a lot we don't know about inflation Perturbations may be generated during inflation: Multifield inflation, particle production during inflation Or after inflation using seed perturbations from inflation Curvaton scenario late decaying scalar field whose energy density grows with time Talk: Fonseca, Lerner, Seto Modulated (p)reheating Talk: McAllister, Shellard, Riotto This wonderful session! Huston, Mulryne, D. Battefeld Talk: Zavala More! Non-canonical kinetic term, non standard gravity, include vector perturbations, gauge issues... Talk: Fasiello, Rodriguez Garcia, Noller, Ribeiro, Dimopoulos, Urakawa, Koh Need many observables to discriminate between scenarios E.g. non-gaussianity: Scale-dependence of the polyspectra Prepare for Planck, predictions should come first! Plus lots more talks and relevant posters a hot topic

3 The bispectrum Simplest definition, motivated but not exact local model Can picture the bispectrum as a triangle, with wavenumbers k denoting the side lengths Often reduced to an amplitude times scale-independent shape function Focus on quasi-local shape Other shapes: Equilateral, folded, orthogonal Overview non-gaussianity talk: Shellard

4 Some scale dependence is expected! For any fixed triangle shape CB, Nurmi, Tasinato and Wands, '09 Analogous to the power spectrum, f NL (local) should have a mild scale dependence Also true for other bispectral shapes, e.g. equilateral Varying sound speed in DBI (equilateral form of non-gaussianity): Chen '05 Reflects evolution/dynamics during inflation (e.g. it ends) Breaks degeneracy between early universe models As well as the trispectrum Can distinguish between different non-gaussian scenarios, not just between Gaussian and non-gaussian models The amplitude of f NL can be tuned in most non-gaussian models, so a precise measurement of f NL wont do this Avoid posterior detections (hard to quantify the significance)

5 Observational prospects Planck could reach a tight constraint Predicted to reach for CMBPol (COrE) has double this sensitivity CMB: Sefusatti, Ligouri, Yadav, Jackson, Pajer; '09 Galaxy clusters should later provide tighter constraints First LSS simulations: Shandera, Dalal & Huterer '10 LSS: Becker, Huterer, Kadota '10 Error bar is inversely proportional to the fiducial value of f NL It is possible that Planck will provide the first detection of non- Gaussianity, and simultaneously detect its scale dependence! We have a separable ansatz for the bispectrum CB, Gerstenlauer, Nurmi, Tasinato & Wands; '10

6 Interacting curvaton scenario: Intro Strength of self interaction (at horizon exit, *) In the limit of s=0 recover scale invariance - because the quadratic curvaton perturbation has a linear equation of motion Energy density of the curvaton is subdominant during inflation, but it grows relative to that of radiation (from the decayed inflaton) while it oscillates about the (quadratic) minimum of its potential Energy density of curvaton at time of decay CB, Enqvist, Nurmi, Takahashi; '11

7 Scale dependence can be very large Small s regime: CB, Enqvist, Takahashi '10 Any s (self-interaction) regime: CB, Enqvist, Nurmi, Takahashi '11 Axionic curvaton potential: Huang '10 See: Riotto & Sloth '10 for a step-function like f NL Typically the scale dependence grows with the interaction strength, but there are large spikes even for s<1. However spikes tend to correspond to small values of the non-linearity parameters. No scale dependence for s=0, large s regime shown soon.

8 f NL and its scale dependence The black lines show, the regions outside of these lines are detectable with Planck at 1-sigma and CMBPol/CORE at 2-sigma. Real chance of a detection.

9 This complex model can be ruled out In spite of the many free parameters (compared to the quadratic model), observation of f NL and g NL with scale dependence can rule out the model, most regions of the plots cannot be realised for any parameter values

10 Large self-interaction limit Consider s>>1, i.e. potential is dominated by the selfinteraction term during inflation It will eventually oscillate in a quadratic minimum before decaying n=4: n=6: non-linearity parameters are small n=8: So scale dependence is an order of magnitude larger than the spectral index which makes this topic very interesting We could probe the self interactions of a field which is always subdominant

11 Single-source models Models where any single field generates the perturbations Not assumed to be the inflaton, could be the curvaton Scale dependence arises from the non-linearity of the field evolution just after horizon exit Only exception is a free test field (quadratic potential) has a linear equation of motion The assumption that f NL is scale independent is only valid in the simplest toy models! Neither the spectral index, nor its running, probe higher derivatives of the isocurvature's field potential Easy to apply our formulas, please do! See:

12 Mixed inflaton-curvaton scenario The inflaton phi has Gaussian perturbations, the curvaton field sigma (quadratic potential) is non- Gaussian phi and sigma have different spectral indices assume a small field model of inflation New consistency relation Trispectrum where

13 Conclusions Almost every non-gaussian models has a scale dependence Should include this scale-dependence (it could be significant) Powerful observable Unique probe of early universe models Probes self-interactions Probes whether a model is single or multi-source Easy to calculate using our formalism Together with the trispectrum it can break the degeneracy between the plethora of non-gaussian models CB, Nurmi, Tasinato & Wands; [astro-ph.co] CB, Gerstenlauer, Nurmi, Tasinato & Wands; [astro-ph.co] CB, Enqvist, Takahashi; [astro-ph.co] CB, Enqvist, Nurmi, Takahashi; [astro-ph.co]

14 Simple extension of local f NL The multivariate local model phi is the Gaussian inflaton field, uncorrelated sigma generates non-gaussianity quite general - applies to mixed inflaton and curvaton/modulated reheating scenarios, provided is a constant Bispectrum has the usual local shape not changed So a scale dependence of f NL is simple and natural Trispectrum

15 Two-component hybrid inflation If we choose initial conditions to maximise f NL then N is the number of e-foldings from horizon crossing till the end of inflation; Scales which exit earlier are more non-gaussian First to calculate scale dependence of local model: Byrnes, Choi & Hall '08 ii)

16 Loop corrections? With extreme parameter values, the bispectrum can be large through a loop correction The bispectrum diverges in the IR Applying a sharp IR cut-off L Boubekeur & Lyth; '05 Suyama & Takahashi; '08 Preheating: Chambers and Rajantie '08 delta N application: Byrnes et al '10 Review: Seery '10 If we take L~1/H - then on CMB scales Kumar, Leblond & Rajaraman; '09 Could be distinguishable from power law scale dependence