Inflationary vs. Reionization Features from Current and Future Data Cora Dvorkin Harvard University CMB-S4 workshop September 2018, Princeton 1 CMB Power Spectrum Power spectrum: predicted and measured with great precision. Planck collaboration 2 Cosmological inferences depend on the shape of the primordial power spectrum 3 Going Beyond Slow Roll Slow roll is a commonly used approximation for inflationary models where the scalar field potential is sufficiently flat and slowly varying. It leads to curvature power spectra that are featureless and nearly scale invariant. Generalized Slow-Roll approximation: allows for features in the inflationary potential. Here, the curvature power spectrum depends on a single source function (responsible for the observable features): ηmax 2 dη ln ∆ (k)=G(ln ηmin)+ W (kη)G(ln η) R η ⇧ηmin 1 ηmax dη 2 + ln 1+ X(kη)G(ln η) 2 η ⇤ ⇧ηmin ⇥ ⌅ C.Dvorkin, W.Hu, PRD (2009) 2 V,φ V,φφ G 3 2 Simple to relate to the inflaton potential: ⇥ V − V 4 ⇥ ⇥ H0 for full TT data vs. TT l<1000 d ln ∆2 • ⇤CDM : R = n 1 Georges Obied d ln k s − • SB : G0(ln s)=(1 n )+ p B (ln s) − s i i i X ⇤CDM TT vs. CDM TT l<1000 ⇤ ⇤CDM TT SB TT ⇤CDM TT SB TT is in agreement with previous (` < 1000) (` < 1000) studies: • Aghanim et al. (Planck, 2016) • Addison et al. (2016) Posterior 64 66 68 70 72 74 1 1 H0 [km s− Mpc− ] G. Obied, C. Dvorkin, et al, PRD (2017) 5 Response functions TT TE EE π 2 / ℓ C 1) + ℓ ( ℓ 2 2 Ωbh /σ Ωch /σ θMC /σ 500τ 0.3 0.2 0.1 0.0 0.1 − 0.2 − 0.3 − 2τ ln Ase− /σ ns/σ 50nrun 70nrun,run 0.8 0.6 0.4 0.2 /dp ℓ 0.0 dC 1 − ℓ 0.2 σ − 0.4 − 0.6 − 0.8 − p1 p5 p10 p15 3 2 1 0 1 − 2 6 − 101 102 103 101 102 103 101 102 103 ℓ ℓ ℓ H0 and polarization data ⇤CDM TT ⇤CDM TTEE ⇤CDM TT ⇤CDM TTEE (` < 1000) (` < 1000) Posterior 64 66 68 70 72 74 1 1 H0 [km s− Mpc− ] G. Obied, C. Dvorkin, et al, PRD (2017) 7 Functional reconstruction of Generalized tilt • 2 PCs (out of 20) deviate from zero the 99% CL. • These deviations prefer a sharp suppression in power at k=0.004 Mpc-1. Planck (2015) data G. Obied, C. Dvorkin, et al, PRD (2017) 8 Initial Curvature Power Spectrum Reconstruction with Planck data Planck (2015) data G. Obied, C. Dvorkin, et al, PRD (2017) 9 Polarization Features and Reionization History We allow arbitrary variations in the ionization history between z=6 and z=30: fid xe(z)=xe (z)+ taSa(z) a X G. Obied, C. Dvorkin, et al, PRD (2018) Planck 2015 data 10 Disentangling Inflation from Reionization ) 0.3 s n Ifn 0.2 − Ifn+Reio (1 0.1 − 0.0 0 φφ , V G δ V 0.1 2 − − 0.2 − 2 ⌘ 0.3 φ , − V V 0.4 ⇣ − 2 3 4 3 10 10 10 s [Mpc] G. Obied, C. Dvorkin, et al, PRD (2018) 11 Cosmic Variance-limited E-mode measurement G. Obied, C. Dvorkin, et al, PRD (2018) 12 Conclusions • We explored the relationship between features from inflation, reionization, and shifts in the cosmological parameters. 1/2 • Preference for high H0 and low values in from the TT data at <1000 is σ8⌦m ⇤CDM ` driven by low <40 residuals in Planck (2015) data.` • The spline parameters show 2 PCs that deviate from zero at > 95% CL. These deviations prefer a sharp suppression in power at k=0.004 Mpc-1. • We find that in the Planck 2015 data the inflation and reionization features show little interference between the two. But high redshift reionization could potentially mask the matching EE feature predicted by an inflationary explanation for the TT feature. • Polarization measurements at 10<l<40 could potentially improve by more than an order of magnitude before hitting the cosmic variance limit. With such improvements, the inflation and reionization explanations of current measurements can be more definitively tested and disentangled. 13 Extra Slides 14 H0 tension Bernal et al., JCAP (2016) 15 Amplitude of structure ⇤CDM TT ⇤CDM TT (l<1000) r⇤CDM TT r⇤CDM TT+φφ Posterior 0.35 0.40 0.45 0.50 1/2 σ8⌦m G. Obied, C. Dvorkin, et al, PRD (2017) 16 Optical Depth G. Obied, C. Dvorkin, et al, PRD (2018) 17 Reionization • Hu & Holder (2003) derived model-independent reionization observables: EE @ ln C` Tli ⌘ @x(zi) Fij = (` +1/2)TliTlj X` where xe is the free electron fraction: fid xe(z)=xe (z)+ taSa(z) a X Heinrich et al., PRD (2016) 18 On the tau prior Heinrich and Hu, PRD (2018) 19.