Stefano Gariazzo. Light sterile neutrinos with pseudoscalar interactions in cosmology. Based on [JCAP 08 (2016) 067] University and INFN, Torino

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1 Stefano Gariazzo University and INFN, Torino Light sterile neutrinos with pseudoscalar interactions in cosmology Based on [JCAP 08 (2016) 067] 5 September NOW Otranto (IT)

2 Neutrino Oscillations Analogous to CKM mixing for quarks: ν α = 3 U αk ν k (α = e, µ, τ) k=1 [Pontecorvo, 1958] [Maki, Nakagawa, Sakata, 1962] ν α flavour eigenstates, U αk PMNS mixing matrix, ν k mass eigenstates. Current knowledge of the 3 active ν mixing: [PDG - Olive et al. (2015)] m 2 ji = m 2 j m 2 i, θ ij mixing angles NO: Normal Ordering, m 1 < m 2 < m 3 IO: Inverted Ordering, m 3 < m 1 < m 2 msol 2 = (7.53 ± 0.18) 10 5 ev 2 = m21 2 matm 2 = (2.44 ± 0.06) 10 3 ev 2 (NO) = m32 2 m2 31 = (2.49 ± 0.06) 10 3 ev 2 (IO) sin 2 (2θ 12 ) = ± sin 2 (2θ 23 ) = (NO) (IO) sin 2 (2θ 13 ) = ± See various talks in next days CP violating phase δ CP still unknown. Hint: δ CP = π/2? [T2K Collaboration, 2015] S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 1/16

3 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 2/16 Short Baseline (SBL) anomaly Problem: anomalies in SBL experiments A short review: { errors in flux calculations? deviations from 3-ν description? LSND search for ν µ ν e, with L/E = m/mev. Observed a 3.8σ excess of ν e events [Aguilar et al., 2001] Reactor re-evaluation of the expected anti-neutrino flux disappearance of ν e events compared to predictions ( 3σ) with L < 100 m [Azabajan et al, 2012] Gallium calibration of GALLEX and SAGE Gallium solar neutrino experiments give a 2.7σ anomaly (disappearance of ν e ) [Giunti, Laveder, 2011] MiniBooNE (inconclusive) search for ν µ ν e and ν µ ν e, with L/E = m/mev. No ν e excess detected, but ν e excess observed at 2.8σ [MiniBooNE Collaboration, 2013] Possible explanation: Additional squared mass difference m 2 SBL 1 ev2 [SG et al., JPG 43 (2016) ] See various talks in next days

4 3+1 Neutrino Model S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 3/16 SBL anomalies m 2 SBL 1 ev2 Existence of an additional neutrino degree of freedom, mass around 1 ev, no weak interaction light, sterile neutrino (LSν) 3 active (m i 1 ev) + 1 sterile (m s 1 ev) ν scenario We must update our mixing paradigm: 3+1 ν α = U αk ν k (α = e, µ, τ, s) k=1 ν s is mainly ν 4 : m s m 4 m 2 41 m 2 SBL Active ν: mν,active 0 Sterile ν: 0.82 m 2 s /ev (3σ) [SG et al., 2016]

5 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 4/16 (Relativistic) LSν in cosmology: N eff Radiation energy density ρ r in the early Universe: [ ρ r = ( ) 4 4/3 N eff] ρ γ = [ N eff ] ρ γ 8 11 ρ γ photon energy density, 7/8 is for fermions, (4/11) 4/3 due to photon reheating after neutrino decoupling N eff all the radiation contribution not given by photons N eff 1 correspond to a single family of active neutrino, in equilibrium in the early Universe Active neutrinos: N eff = [Mangano et al., 2005] due to not instantaneous decoupling for the neutrinos + Non Standard Interactions: < N eff < [de Salas et al., 2016] additional LSν contributes with N eff = N eff 3.046: [ N eff = ρrel s 7 π 2 ] 1 1 = ρ ν 8 15 T ν 4 π 2 dp p 3 f s (p) ρ ν energy density for one active neutrino species, ρ rel s energy density of LSν when relativistic, p neutrino momentum, f s (p) momentum distribution, T ν = (4/11) 1/3 T γ [Acero et al., 2009]

6 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 4/16 (Relativistic) LSν in cosmology: N eff Radiation energy density ρ r in the early Universe: [ ρ r = ( ) 4 4/3 N eff] ρ γ = [ N eff ] ρ γ 8 11 ρ γ photon energy density, 7/8 is for fermions, (4/11) 4/3 due to photon reheating after neutrino decoupling N eff all the radiation contribution not given by photons N eff 1 correspond to a single family of active neutrino, in equilibrium in the early Universe Active neutrinos: N eff = [Mangano et al., 2005] due to not instantaneous decoupling for the neutrinos + Non Standard Interactions: < N eff < [de Salas et al., 2016] additional LSν contributes with N eff = N eff 3.046: [ N eff = ρrel s 7 π 2 ] 1 1 = ρ ν 8 15 T ν 4 π 2 dp p 3 f s (p) ρ ν energy density for one active neutrino species, ρ rel s energy density of LSν when relativistic, p neutrino momentum, f s (p) momentum distribution, T ν = (4/11) 1/3 T γ See Pastor talk [Acero et al., 2009]

7 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 4/16 (Relativistic) LSν in cosmology: N eff Radiation energy density ρ r in the early Universe: [ ρ r = ( ) 4 4/3 N eff] ρ γ = [ N eff ] ρ γ 8 11 ρ γ photon energy density, 7/8 is for fermions, (4/11) 4/3 due to photon reheating after neutrino decoupling N eff all the radiation contribution not given by photons N eff 1 correspond to a single family of active neutrino, in equilibrium in the early Universe Active neutrinos: N eff = [Mangano et al., 2005] due to not instantaneous decoupling for the neutrinos + Non Standard Interactions: < N eff < [de Salas et al., 2016] additional LSν contributes with N eff = N eff 3.046: [ N eff = ρrel s 7 π 2 ] 1 1 = ρ ν 8 15 T ν 4 π 2 dp p 3 f s (p) ρ ν energy density for one active neutrino species, ρ rel s energy density of LSν when relativistic, p neutrino momentum, f s (p) momentum distribution, T ν = (4/11) 1/3 T γ See Pastor talk [Acero et al., 2009]

8 LSν thermalization Using SBL best-fit parameters for the LSν ( m 2 41, θ s): [Hannestad et al., JCAP 1207 (2012) 025] [Mirizzi et al., PRD 86 (2012) ] (colors coding N eff ) (L: lepton asymmetry) Unless L O(10 3 ), N eff 1 See also: [Saviano et al., PRD 87 (2013) ], [Hannestad et al., JCAP 08 (2015) 019] S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 5/16

9 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 6/16 (Non-relativistic) LSν in cosmology: m eff s m s 1 ev ν s is non-relativistic today (T ν 10 4 ev) LSν density parameter today: ω s = Ω s h 2 = ρ s h 2 = h2 m s ρ c ρ c π 2 dp p 2 f s (p) ρ s energy density of non-relativistic LSν, ρ c critical density and h reduced Hubble parameter Alternatively: m eff s = 94.1 ev ω s and m s The factor (94.1 ev) is the same for the active neutrinos: ω ν,active = m ν /(94.1 ev) active If f s (p) = f active (p), m eff s m s [Acero et al., 2009] [Planck 2013 Results, XVI] Thermal production = f s (p) = 1 e p/ts + 1 = meff s = N 3/4 eff m s

10 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 6/16 (Non-relativistic) LSν in cosmology: m eff s m s 1 ev ν s is non-relativistic today (T ν 10 4 ev) LSν density parameter today: ω s = Ω s h 2 = ρ s h 2 = h2 m s ρ c ρ c π 2 dp p 2 f s (p) ρ s energy density of non-relativistic LSν, ρ c critical density and h reduced Hubble parameter Alternatively: m eff s = 94.1 ev ω s and m s The factor (94.1 ev) is the same for the active neutrinos: ω ν,active = m ν /(94.1 ev) active If f s (p) = f active (p), m eff s m s [Acero et al., 2009] [Planck 2013 Results, XVI] Thermal production = f s (p) = 1 e p/ts + 1 = meff s = N 3/4 eff m s

LSν constraints from cosmology CMB+local: [Planck Collaboration, 2015] [Archidiacono et al., JCAP 08 (2016) 067] N eff 1.0 0.8 0.6 0.4 0.

11 LSν constraints from cosmology CMB+local: [Planck Collaboration, 2015] [Archidiacono et al., JCAP 08 (2016) 067] N eff ΛCDM+N eff +m s : TT ΛCDM+N eff +m s : TT+HST ΛCDM+N eff +m s : TT+HST+BAO H0 [km/s/mpc] m s [ev] 66.4 { Neff < 3.7 < 0.52 ev m eff s (TT+lensing+BAO) [m s < 5 ev] free N dataset eff [m s < 10 ev] N eff = 1 (TT) N eff < 3.5 m s < 0.66 ev (+H 0) N eff < 3.9 m s < 0.55 ev (+BAO) N eff < 3.8 m s < 0.53 ev BBN constraints: N eff = 2.90 ± 0.22 (BBN+Y p ) [Peimbert et al., 2016] Summary: N eff = 1 from LSν incompatible with m s 1 ev! TT=Planck 2015 TT + lowteb All the constraints are at 2σ CL S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 7/16

12 Tensions on the Hubble parameter 68% CL error bars Hubble parameter today: v = H 0 d, with H 0 = H(z = 0) Local measurements: H(z = 0), local and independent on evolution (model independent, but systematics?) CMB measurements (probe z 1100): H 0 from the cosmological evolution (model dependent, well controlled systematics) Planck ΛCDM+Ω k Riess2011 Efstathiou2013 Riess2016 WMAP 9yr + ACT + SPT -- ΛCDM Planck ΛCDM Planck ΛCDM Planck ΛCDM+N eff Planck wcdm H 0 [Km s 1 Mpc 1 ] Using HST Cepheids: [Efstathiou 2013] H 0 = 72.5 ± 2.5 Km s 1 Mpc 1 [Riess et al., 2016] H 0 = ± 1.79 Km s 1 Mpc 1 (most recent) (ΛCDM model - CMB data only) [Planck 2013]: H 0 = 67.3 ± 1.2 Km s 1 Mpc 1 [Planck 2015]: H 0 = ± 0.66 Km s 1 Mpc 1 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 8/16

13 Tensions on the Hubble parameter 68% CL error bars Hubble parameter today: v = H 0 d, with H 0 = H(z = 0) Local measurements: H(z = 0), local and independent on evolution (model independent, but systematics?) CMB measurements (probe z 1100): H 0 from the cosmological evolution (model dependent, well controlled systematics) Riess2011 Efstathiou2013 Riess2016 WMAP 9yr + ACT + SPT -- ΛCDM Planck ΛCDM Planck ΛCDM Planck BAO -- ΛCDM+N eff Planck BAO -- ΛCDM+Ω k Planck BAO -- wcdm H 0 [Km s 1 Mpc 1 ] Using HST Cepheids: [Efstathiou 2013] H 0 = 72.5 ± 2.5 Km s 1 Mpc 1 [Riess et al., 2016] H 0 = ± 1.79 Km s 1 Mpc 1 (most recent) (ΛCDM model - CMB data only) [Planck 2013]: H 0 = 67.3 ± 1.2 Km s 1 Mpc 1 [Planck 2015]: H 0 = ± 0.66 Km s 1 Mpc 1 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 8/16

14 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 9/16 Tensions on the matter perturbations at small scales Assuming ΛCDM model: σ 8 : rms fluctuation in total matter (baryons + CDM + neutrinos) in 8h 1 Mpc spheres, today; Ω m: total matter density today divided by the critical density CFHTLenS weak lensing data alone [Heymans et al., 2013] (68% CL): σ 8 (Ω m /0.27) 0.46±0.02 = ± 0.04 CMB results [Planck 2013] (68% CL): σ 8 (Ω m /0.27) 0.46 = 0.89 ± 0.03 Planck SZ Cluster Counts [Planck 2013 Results XX] (68% CL): σ 8 (Ω m /0.27) 0.3 = ± Planck + WMAP pol + ACT/SPT [Planck 2013] (68% CL): σ 8 (Ω m /0.27) 0.3 = 0.87 ± 0.02 Qualitatively similar results from SPT clusters, Chandra Cluster Cosmology Project.

15 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 9/16 Tensions on the matter perturbations at small scales Assuming ΛCDM model: σ 8 : rms fluctuation in total matter (baryons + CDM + neutrinos) in 8h 1 Mpc spheres, today; Ω m: total matter density today divided by the critical density CFHTLenS weak lensing data alone [Heymans et al., 2013] (68% CL): σ 8 (Ω m /0.27) 0.46±0.02 = ± 0.04 CMB results [Planck 2013] (68% CL): 2σσ 8 (Ω discrepancy! m /0.27) 0.46 = 0.89 ± 0.03 Planck SZ Cluster Counts [Planck 2013 Results XX] (68% CL): σ 8 (Ω m /0.27) 0.3 = ± Planck + WMAP pol + ACT/SPT [Planck 2013] (68% CL): 3σσ 8 discrepancy! (Ω m /0.27) 0.3 = 0.87 ± 0.02 Qualitatively similar results from SPT clusters, Chandra Cluster Cosmology Project.

16 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 9/16 Tensions on the matter perturbations at small scales Assuming ΛCDM model: σ 8 : rms fluctuation in total matter (baryons + CDM + neutrinos) in 8h 1 Mpc spheres, today; Ω m: total matter density today divided by the critical density CFHTLenS weak lensing data alone [Heymans et al., 2013] (68% CL): σ 8 (Ω m /0.27) 0.46±0.02 = ± 0.04 CMB results [Planck 2013] (68% CL): 2σσ 8 (Ω discrepancy! m /0.27) 0.46 = 0.89 ± 0.03 Planck SZ Cluster Counts [Planck 2013 Results XX] (68% CL): σ 8 (Ω m /0.27) 0.3 = ± Planck + WMAP pol + ACT/SPT [Planck 2013] (68% CL): 3σσ 8 discrepancy! (Ω m /0.27) 0.3 = 0.87 ± 0.02 Qualitatively similar results from SPT clusters, Chandra Cluster Cosmology Project. Alert! is the nonlinear evolution well known? see e.g. [Planck 2015 Results, papers XIII and XIV] are we taking into account all the astrophysical systematics? [Joudaki et al., 2016] [Kitching et al., 2016]

17 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 10/16 Adding a new interaction Prevent LSν thermalization? new (hidden) interaction! [Archidiacono, SG et al., JCAP 08 (2016) 067] e.g.: new broken U(1) symmetry Coupling confined to sterile sector Lagrangian: L g s φ ν 4 γ 5 ν 4 pseudoscalar mediator φ ν 4 annihilation into φ at late times (to avoid mass bounds) matter effect induced by φ no ν s production until after ν a decoupling coupling g s large enough to prevent full ν s thermalization 10 6 g s 10 5 is fine [Archidiacono et al., PRD 91 (2015) ] φ must avoid mass bounds itself m φ 0.1 ev incomplete thermalization, N eff 4

18 Constraints on the pseudoscalar interaction? S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 11/16 Particle physics constraints on the pseudoscalar? IceCube constraints on secret interactions? [Ioka et al., 2014] [Cherry et al., 2014] [Ng et al.,2014] [Cherry et al., 2016] φ coupled to ν 4 + IceCube flux made of active flavor neutrinos fifth force constraints? pseudoscalar is spin coupling, but unpolarized medium don t apply very small mixing with ν 4 and interaction rate with φ [cross section g 2 s /s] don t apply SN energy loss [Farzan, 2003] g s 10 4

19 Constraints on the pseudoscalar interaction? S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 11/16 Particle physics constraints on the pseudoscalar? IceCube constraints on secret interactions? [Ioka et al., 2014] [Cherry et al., 2014] [Ng et al.,2014] [Cherry et al., 2016] φ coupled to ν 4 + IceCube flux made of active flavor neutrinos fifth force constraints? pseudoscalar is spin coupling, but unpolarized medium don t apply very small mixing with ν 4 and interaction rate with φ [cross section g 2 s /s] don t apply SN energy loss [Farzan, 2003] g s 10 4

20 Constraints on the pseudoscalar interaction? S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 11/16 Particle physics constraints on the pseudoscalar? IceCube constraints on secret interactions? [Ioka et al., 2014] [Cherry et al., 2014] [Ng et al.,2014] [Cherry et al., 2016] φ coupled to ν 4 + IceCube flux made of active flavor neutrinos fifth force constraints? pseudoscalar is spin coupling, but unpolarized medium don t apply very small mixing with ν 4 and interaction rate with φ [cross section g 2 s /s] don t apply SN energy loss [Farzan, 2003] g s 10 4

21 Constraints on the pseudoscalar interaction? S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 11/16 Particle physics constraints on the pseudoscalar? IceCube constraints on secret interactions? [Ioka et al., 2014] [Cherry et al., 2014] [Ng et al.,2014] [Cherry et al., 2016] φ coupled to ν 4 + IceCube flux made of active flavor neutrinos fifth force constraints? pseudoscalar is spin coupling, but unpolarized medium don t apply very small mixing with ν 4 and interaction rate with φ [cross section g 2 s /s] don t apply SN energy loss [Farzan, 2003] g s 10 4

22 N eff Results - I Standard LSν model: ΛCDM+N eff + m s (ΛCDM params+free N eff and m s ) ΛCDM+N eff +m s : TT ΛCDM+N eff +m s : TT+HST ΛCDM+N eff +m s : TT+HST+BAO m s [ev] H0 [km/s/mpc] [Archidiacono, SG et al., JCAP 08 (2016) 067] N fluid Pseudoscalar model (PSE): N eff = N fluid N fluid : ν s +φ contributions PSE: TT PSE: TT+HST PSE: TT+HST+BAO m s [ev] Problems with N eff = 1? solved (incomplete thermalization due to suppression of active-sterile oscillations in primordial plasma); mass bounds avoided large m s allowed and preference for m s 4 ev; high values of H 0 predicted by cosmology more compatible with local measurements. S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 12/ H0 [km/s/mpc]

23 Results - II [Archidiacono, SG et al., JCAP 08 (2016) 067] 10 1 PSE: TT ΛCDM+1ν s : TT SBL 1.0 PSE: TT ΛCDM+1ν s : TT ΛCDM+N eff +m s : TT Riess P 10-1 P/P max m s [ev] H 0 [km/s/mpc] PSE: posterior on m s wider preference for high SBL peaks? (agreement with recent results by [IceCube, 2016] and [MINOS, 2016]) PSE: very close to Riess2016 results (better than ΛCDM+N eff + m s ) ΛCDM+1ν s : even higher H 0, but from N eff = 1 and m s 0. S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 13/16

24 Results - III [Archidiacono, SG et al., JCAP 08 (2016) 067] S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 14/16 σ 8 What about the σ 8 tension (matter perturbations at small scales)? ΛCDM model: ΛCDM: Planck15 lowteb+highltt ΛCDM: Planck15 lensing only ΛCDM: CFHTLenS only (ultra conservative) Ω m H0 [km/s/mpc] σ Pseudoscalar model: Pseudoscalar: Planck15 lowteb+highltt ΛCDM: Planck15 lensing only ΛCDM: CFHTLenS only (ultra conservative) Ω m H0 [km/s/mpc] smaller Ω m today. Good? Also higher σ 8 = no improvement! The tension remains. due to higher H 0, not to reduced matter fluctuations.

25 Joint Results 10 Cosmological results as a prior in SBL analysis: SBL 1σ 2σ 3σ 10 [Archidiacono, SG et al., JCAP 08 (2016) 067] 2 m 41 2 m 41 [ev 2 ] [ev 2 ] 1 TT TT+HST TT+BAO TT+HST+BAO sin 2 2ϑ eµ 10 1 sin 2 2ϑ ee Cosmological constraints are too much permissive! Regions at m ev2 (slightly) enlarged (small) new region at m ev2 appears (3σ CL only) 1 10 sin 2 2ϑ µµ Towards [IceCube, 2016] and [MINOS, 2016] hints for m ev? S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 15/16

26 Conclusions S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 16/16 light ν s (m s 1 ev) from SBL analysis? full thermalization incompatible with cosmological measurements (given mass and mixing angles from SBL oscillations) H 0 and σ 8 problems? New interaction mediated by a pseudoscalar φ: hidden in the sterile sector, no fifth force constraints light pseudoscalar to avoid mass bounds after ν s annihilation avoid full ν s thermalization in the early Universe (10 6 g s 10 5 ) matter effect induced by φ allows N eff 4 Results: preference for large m s Towards IceCube and MINOS recent results? preference for H 0 compatible with local measurements no solution to matter fluctuations at small scales

27 Conclusions S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 16/16 light ν s (m s 1 ev) from SBL analysis? full thermalization incompatible with cosmological measurements (given mass and mixing angles from SBL oscillations) H 0 and σ 8 problems? New interaction mediated by a pseudoscalar φ: hidden in the sterile sector, no fifth force constraints light pseudoscalar to avoid mass bounds after ν s annihilation avoid full ν s thermalization in the early Universe (10 6 g s 10 5 ) matter effect induced by φ allows N eff 4 Results: preference for large m s Towards IceCube and MINOS recent results? preference for H 0 compatible with local measurements no solution to matter fluctuations at small scales

28 Conclusions S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 16/16 light ν s (m s 1 ev) from SBL analysis? full thermalization incompatible with cosmological measurements (given mass and mixing angles from SBL oscillations) H 0 and σ 8 problems? New interaction mediated by a pseudoscalar φ: hidden in the sterile sector, no fifth force constraints light pseudoscalar to avoid mass bounds after ν s annihilation avoid full ν s thermalization in the early Universe (10 6 g s 10 5 ) matter effect induced by φ allows N eff 4 Results: preference for large m s Towards IceCube and MINOS recent results? preference for H 0 compatible with local measurements no solution to matter fluctuations at small scales

29 Conclusions S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 16/16 light ν s (m s 1 ev) from SBL analysis? full thermalization incompatible with cosmological measurements (given mass and mixing angles from SBL oscillations) H 0 and σ 8 problems? New interaction mediated by a pseudoscalar φ: hidden in the sterile sector, no fifth force constraints light pseudoscalar to avoid mass bounds after ν s annihilation avoid full ν s thermalization in the early Universe (10 6 g s 10 5 ) matter effect induced by φ allows N eff 4 Results: preference for large m s Towards IceCube and MINOS recent results? preference for H 0 compatible with local measurements no solution to matter fluctuations at small scales Thank you for the attention

30 N eff and pseudoscalar interaction S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 1/4 [Archidiacono et al., PRD 91 (2015) ] δ N eff g s 10 5 obtained with sin 2 (2θ s ) = 0.05, m s = 1 ev

31 LSν annihilation S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 2/4 [Archidiacono et al., PRD 93 (2016) ] m ν,s = 0.1 ev m ν,s = 1 ev m ν,s = 10 ev ρ/ρ a ν s annihilation into pseudoscalars = energy density increased ρ 0 density of 1 active neutrino family ρ density of ν s+φ

32 LSν annihilation and matter power spectrum S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 3/4 [Archidiacono et al., PRD 93 (2016) ] ΛCDM+1ν s pseudoscalar model P(k) [(Mpc/h) 3 ] ΛCDM + 1 ν s 100 best-fit Planck 2015 m ν,s = 0.1 ev m ν,s = 1 ev m ν,s = 3 ev k [h/mpc] P(k) [(Mpc/h) 3 ] Pseudoscalar 100 best-fit Planck 2015 m ν,s = 0.1 ev m ν,s = 1 ev m ν,s = 3 ev k [h/mpc]

33 S. Gariazzo Light sterile neutrinos with pseudoscalar interactions in cosmology NOW /9/16 4/4 Divergences for small momentum transfer? ν s φ interaction = flavor measurement contribution to ν 4 thermalization. [Cherry et al., 2016]: ν s φ scattering p 2 for small p > m φ Debye screening divergence for m φ 0.1 ev? charge neutral medium in vacuum! matter effect? effective screening mass m D pion exchange: m D T more efficient than ν s φ (complexity of mesons) QED: m D et less efficient than ν s φ (potential PSE: r 3 vs QED: r 2 ) our case? complex calculation! m D T? Γ n νs g 4 s /T 2 negligible (g 4 s )! m D g s T? Can lead to additional thermalization. agnostic view Screening is just additional contribution to N eff.

Dark Radiation and Inflationary Freedom

Dark Radiation and Inflationary Freedom Based on [SG et al., JCAP 1504 (2015) 023] [Di Valentino et al., PRD 91 (2015) 123505] Stefano Gariazzo University of Torino, INFN of Torino http://personalpages.to.infn.it/~gariazzo/