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/ gariazzo@to.infn.it TAUP 2015, Torino - September 7, 2015

1 Inflationary Freedom The Inflationary Paradigm Beyond Power-Law Primordial Power Spectrum 2 Constraints on Light Sterile Neutrino Properties Light Sterile Neutrino Constraints 3 Constraints on Thermal Axion Properties Thermal Axion Model Constraints 4 Constraints on the Primordial Power Spectrum and Conclusions

Primordial Power Spectrum from Inflation Slow roll inflation [Linde, 1982]: inflation occurred by a scalar field (Inflaton) rolling down a potential energy hill. End of inflation depends on the shape of the inflaton potential V (φ); the spatially variating perturbation of the inflaton field δφ(t, x). Fluctuations in the inflaton modulate the end of inflation: in different regions, inflation ends at different times. δφ(t, x) converted into energy density fluctuations δρ after inflation. small scale dependence of the Primordial Power Spectrum (PPS) of scalar perturbations: (n s 1) d ln P s(k) = 2 V ( ) V 2 d ln k V 3, V more general than P s (k) = A s (k/k ) ns 1. Is n s constant? Can the PPS deviate from a Power-Law (PL)? S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 2

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 3 Beyond Power-Law PPS: Theory [Sagnotti et al, 2014] [Planck Collaboration, 2015] [Romano et al., 2014] Given an inflationary model one gets one Primordial Power Spectrum (PPS), more or less complicated Much more models were developed: see e.g. [ Encyclopædia Inflationaris, Martin et al., 2014]

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 4 Planck 2015 results Planck 2015 temperature auto-correlation power spectrum: [Planck Collaboration, 2015]

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 5 Beyond Power-Law PPS: Reconstructions [Hunt et al., 2014] (WMAP data) [Hazra et al, 2014] (Planck 2013 data) [de Putter et al, 2014] (Planck 2013) [Planck Collaboration, 2015]

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 6 PCHIP Parametrization Fix the Primordial Power Spectrum (PPS) form leads to possible bias: analysis with free, non-parametric form for the PPS. [SG et al., JCAP 1504 (2015) 023] Proposal: fix a series of nodes k 1,..., k 12 and use an interpolating function among them, P s(k) = P 0 f (k; P s,1,..., P s,12) with P 0 = 2.2 10 9, P s,j = P s(k j) In our case we use: PCHIP [Fritsch et al., 1980] piecewise cubic Hermite interpolating polynomial f (k; P s,1,..., P s,12) = PCHIP(k; P s,1,..., P s,12) Advantage over natural cubic splines: no spurious oscillations. f(k) 1.4 1.2 1 0.8 0.6 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 10 k [Mpc -1 ] PCHIP natural spline nodes Interpolate piecewise a series of nodes P s,j = P s(k j) with j [1, 12]: continue and derivable; preserve monotonicity of the nodes: 1 st derivative in the node fixed using the secants between consequent nodes; if the monotonicity changes, the node is a local extremum; 2 nd derivative not continue in the nodes.

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 7 Motivations for a Light Sterile Neutrino neutrino oscillations see e.g. [PDG - Olive et al. (2014)] ν α = 3 U αk ν k (α = e, µ, τ) k=1 Parameters: msol 2, m2 ATM sin 2 (2θ 12 ), sin 2 (2θ 23 ), sin 2 (2θ 13 ) CP violating phase δ + Short BaseLine (SBL) anomalies LSND [Aguilar et al., 2001] MiniBooNE [MiniBooNE, 2013] Reactors [Azabajan et al, 2012] Gallium anomaly [Giunti, Laveder, 2011] 3+1 ν α = U αk ν k (α = e, µ, τ, s) k=1 with mν,active 0 ( m s ) m s msbl 2 1 ev More details: recent review [SG et al., 2015], dedicated talks in next days ν α flavour eigenstates, U αk PMNS mixing matrix, ν k mass eigenstates, m 2 ji = m 2 j m 2 i, θ ij mixing angles

Parameterization in Cosmology Light (m s 1 ev) sterile (no weak interactions) neutrino Relativistic in the early Universe Non-relativistic in the late Universe ρ r = [1 + 0.2271N eff ] ρ γ and ν s contributes with N eff = N eff 3.046 ρ m = ρ c + ρ b + ρ ν + ρ s and ν s contributes with ρ s m s ( N eff ) 3/4 N eff = 3.046 from active neutrinos [Mangano et al., 2005] We consider a thermalized sterile neutrino: T s = N 1/4 eff Tν ρ i energy density, for the fluid i: m (matter), γ (photons), r (radiation), c (cold dark matter), b (baryons), s (sterile neutrino),... S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 8

[SG et al., JCAP 1504 (2015) 023] Light Sterile Neutrino Results - I PPS free form: nodes Ps,1,..., Ps,12, Standard: Power-Law (PL) interpolate with PCHIP function versus ΛCDM(PL PPS) + νs model ΛCDM(PCHIP PPS) + νs model Ps (k) = As (k/kpivot )ns 1 Ps (k) = P0 f (k; Ps,1,..., Ps,12 ) Results for the Thermal sterile neutrino, mass ms, no SBL prior on ms : 1.0 1.0 COSMO (PL) higher Neff admitted; COSMO (PCHIP) 0.6 0.6 change on ms constraints due to Neff change; Neff 0.8 Neff 0.8 0.4 0.4 0.2 0.2 0.0 0.0 0.5 1.0 1.5 ms [ev] 2.0 2.5 3.0 0.0 0.0 0.5 1.0 1.5 ms [ev] 2.0 2.5 3.0 fully thermalized sterile neutrino preferred. COSMO = CMB(Planck13+WMAP Polarization+ACT/SPT)+LSS(WiggleZ)+HST(Riess2011)+CFHTLenS+PlanckSZ S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 9

[SG et al., JCAP 1504 (2015) 023] Light Sterile Neutrino Results - II PPS free form: nodes Ps,1,..., Ps,12, Standard: Power-Law (PL) interpolate with PCHIP function versus ΛCDM(PL PPS) + νs model ΛCDM(PCHIP PPS) + νs model Ps (k) = As (k/kpivot )ns 1 Ps (k) = P0 f (k; Ps,1,..., Ps,12 ) Results for the Thermal sterile neutrino, mass ms, with SBL prior on ms : 1.0 1.0 COSMO+SBL (PL) COSMO+SBL (PCHIP) 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.8 1.0 1.2 ms [ev] 1.4 1.6 0.0 0.8 higher Neff admitted; no change on ms constraints; Neff 0.8 Neff 0.8 1.0 1.2 ms [ev] 1.4 1.6 fully thermalized sterile neutrino admitted (inside 2σ region). COSMO = CMB(Planck13+WMAP Polarization+ACT/SPT)+LSS(WiggleZ)+HST(Riess2011)+CFHTLenS+PlanckSZ S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 10

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 11 Motivations Strong CP problem Axions pseudo-nambu-golstone bosons for a global U(1) PQ (Peccei-Quinn) symmetry spontaneously broken at the axion scale f a Nonthermal production by misalignment mechanism Thermal production π + π π + a can be only hot DM not hot, but cold DM (total fraction of DM?) not explored here! effects similar to the massive neutrinos explored here

Parameterization thermal process π + π π + a + U(1) PQ breaking at f a axion mass m a = fπmπ R f a 1+R = 0.6 ev 107 GeV f a decoupling T D (f a ) from Γ(T D ) = H(T D ) (numerically) d.o.f. at decoupling g S (T D ) density parameter ω a m a n a m a /g S (T D ) axion number density n a (f a ) = g S(T 0 ) g S (T D ) nγ 2 N eff = 4 7 ( 3na 2n ν ) 4/3 More details: Rosenberg talk tomorrow T 0 CMB temperature today n γ (ν) number density of photons (neutrinos) f π=93 MeV pion decay constant R = 0.553 ± 0.043 up-to-down quark masses ratio S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 12

Thermal Axion Results Standard: Power-Law (PL) ΛCDM(PL PPS) + m a model ns 1 P s(k) = A s(k/k pivot) P PPS versus [Di Valentino et al., PRD 91 (2015) 123505] free form: nodes P s,1,..., P s,12, interpolate with PCHIP function ΛCDM(PCHIP PPS) + m a model s(k) = P 0 f (k; P s,1,..., P s,12) σ 8 0.95 0.90 0.85 0.80 0.75 0.70 0.65 ΛCDM+m a (PL) - CMB ΛCDM+m a (PL) - CMB+BAO+HST ΛCDM+m a (PL) - CMB+BAO+HST+PSZ ΛCDM+m a (PL) - CMB+BAO+HST+PSZ(fixed bias) 0.5 1.0 1.5 2.0 2.5 3.0 m a [ev] σ 8 0.95 0.90 0.85 0.80 0.75 0.70 0.65 ΛCDM+m a (PCHIP) - CMB ΛCDM+m a (PCHIP) - CMB+BAO+HST ΛCDM+m a (PCHIP) - CMB+BAO+HST+PSZ ΛCDM+m a (PCHIP) - CMB+BAO+HST+PSZ(fixed bias) 0.5 1.0 1.5 2.0 2.5 3.0 m a [ev] inflationary freedom relaxed bounds on m a ; cluster counts give m a > 0 (free-streaming lowers σ 8 ), more evident with non-standard PPS. CMB=Planck13+WMAP Polarization+ACT/SPT BAO=BOSS DR11+WiggleZ+6dF+SDSS-II HST=Efstathiou2013 PSZ=PlanckSZ: prior σ 8 (Ω m/0.27) 0.3 = 0.764 ± 0.025 (0.78 ± 0.01 with fixed bias) S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 13

PPS Results ΛCDM(PCHIP PPS) + νs ΛCDM(PCHIP PPS) + ma CMB(Planck13+WMAP Polarization+ACT/SPT)+ LSS(WiggleZ)+HST(Riess2011)+CFHTLenS+PlanckSZ CMB(Planck13+WMAP Polarization+ACT/SPT) ΛCDM+ma (PCHIP) - CMB COSMO (PCHIP) k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12 100 10-1 101 109 x PS (k) 109 x PS (k) 101 10-5 10-4 10-3 10-2 10-1 100 k [Mpc 1 ] [SG et al., JCAP 1504 (2015) 023] 101 k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12 100 10-1 10-5 10-4 10-3 10-2 10-1 100 101 k [Mpc 1 ] [Di Valentino et al., PRD 91 (2015) 123505] Different cosmological models, similar results: CMB constraints for 1 10 4 Mpc 1 (` = 2) k 0.3 Mpc 1 (` ' 2500); power-law is a good approximation in the range 7 10 3 Mpc 1 k 0.2 Mpc 1 ; feature at k = 2 10 3 Mpc 1 correspond to dip ` ' 22 in CMB spectrum; feature at k = 3.5 10 3 Mpc 1 correspond to small bump ` ' 40. S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 14

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 15 Conclusions Theoretical and experimental reasons to study features in the Primordial Power Spectrum for scalar perturbations: features if inflation cannot be described by the simplest model; observed features in low-l CMB spectrum from Planck, WMAP; only statistical fluctuations or a signals for new physics? Non-standard spectrum from inflation have an impact on extensions of the ΛCDM model! Main degeneracy with N eff : wider range allowed for the thermal axion mass; light sterile neutrino fully compatible with cosmology. update with Planck 2015 data: work in progress! Inflationary freedom can bias also other constraints: e.g. degeneracies with primordial non-gaussianities in future probes, see [SG et al., arxiv:1506.05251, accepted by PRD].

S. Gariazzo Dark Radiation and Inflationary Freedom TAUP 2015, Torino, 07/09/2015 16 Conclusions Theoretical and experimental reasons to study features in the Primordial Power Spectrum for scalar perturbations: features if inflation cannot be described by the simplest model; observed features in low-l CMB spectrum from Planck, WMAP; only statistical fluctuations or a signals for new physics? Non-standard spectrum from inflation have an impact on extensions of the ΛCDM model! Main degeneracy with N eff : wider range allowed for the thermal axion mass; light sterile neutrino fully compatible with cosmology. update with Planck 2015 data: work in progress! Inflationary freedom can bias also other constraints: e.g. degeneracies with primordial non-gaussianities in future probes, see [SG et al., arxiv:1506.05251, accepted by PRD]. Thank you for the attention!