Right-handed neutrinos as the source of density perturbations Lotfi - PowerPoint PPT Presentation

Right-handed neutrinos as the source of density perturbations Lotfi Boubekeur ICTP - Trieste. Based on: • LB and P. Creminelli , hep-ph/0602052 – PRD 73 (2006) 103516. Workshop on Cosmological Perturbations, GGI Firenze – 25 October, 2006. 1

Experiments Observations are getting more and more accurate → “Precision Cosmology” • Amplitude of fluctuations ∼ 10 − 5 • Scale dependence (tilt) � . 05 • Nature of fluctuations � � � � � δ ( n B /s ) � � ◮ Adiabatic? ζ � < 0 . 3 − 0 . 4 @ 2 σ � Seljak etal. n B /s � ζ � k 1 ζ � k 2 ζ � k 3 � k � 3 / 2 ≪ 10 − 5 ◮ Gaussian? � ζ � k ζ − � ◮ Tensors? r � . 22 2

Theory φ 2 ≪ V ( φ ). ˙ • Single field slow-roll inflation ζ ∼ V 3 / 2 M 3 P V ′ Additional scalars Lyth & Wands • The curvaton scenario Enqvist & Sloth Moroi & Takahashi ζ ∼ δσ σ ∗ • Inhomogeneous reheating Dvali, Gruzinov & Zaldarriaga Kofman ζ ∼ δ Γ φ Γ φ 3

(i) e.g. In string theory, there exist a lot of scalars (string moduli) that could be relevant for cosmology. (ii) They have distinctive experimental signatures in the CMB: • Non-Gaussianity • Correlated isocurvature perturbation • Typically no tensors. 4

(i) e.g. In string theory, there exist a lot of scalars (string moduli) that could be relevant for cosmology. (ii) They have distinctive experimental signatures in the CMB: • Non-Gaussianity • Correlated isocurvature perturbation • Typically no tensors. Departure from thermal equilibrium is required! 5

Out-of-equilibrium T 1 → a ( T 1 ) T 2 < T 1 → a ( T 2 ) In thermal equilibrium, due to adiabaticity, the scale factor a ∝ 1 /T ⇓ NO temperature perturbation can be produced. ⇓ Departure from thermal equilibrium is required! ↓ One can produce temperature fluctuations during baryogenesis. 6

Baryon Isocurvature • Produced baryon number is conserved after baryogenesis (out-of-equilibrium) → Baryon isocurvature. • In contrast with other types of isocurvature, e.g. CDM isocurvature, since CDM is a thermal relic → CDM ISO is erased due to thermal equilibrium. • Baryon isocurvature is correlated with curvature perturbation since produced during the same process. • Present limits on isocurvature are becoming more and more stringent. 7

Generation of the baryon asymmetry We consider the SM + 3 right-handed neutrinos (Type I seesaw + leptogenesis) � χ � � χ � N i N i + ( ∂χ ) 2 L = L SM + Y ij L i HN j + M i M P M P with M 1 > M 2 > M 1 ≡ M . Consider as usual the decay of the lightest N . The decay parameter � � � M 2 2 π 3 / 2 H ( T = M ) = ( Y † Y ) 11 · M Γ( T = 0) m 1 � g 1 / 2 √ ≡ 1 . 1 × 10 − 3 eV ≶ 1 , ∗ 8 π M P 45 where g ∗ ∼ 100, controls departure from thermal equilibrium. The baryon asymmetry is n B = − 28 m 1 ) n N 1 79 ǫ N 1 η ( � s ( T ≫ M ) , s � � 2 ( Y † Y where η is the washout parameter and ǫ N 1 is the CP parameter ∝ Im j 1 ]. 8

Generation of Density Perturbations We can parametrise curvature (temperature) fluctuations produced during RHN decay as ds 2 = − dt 2 + e 2 ζ ( � x ) a ( t ) 2 d� x 2 up to subleading O ( k/ ( aH )) terms. k is the comoving wavevector and H is the expansion rate. Salopek & Bond; Maldacena; Lyth etal. Thus x ) = a ( T low ) e ζ ( � a ( T high )( M, Γ) T high ≡ temperature before decay. T low ≡ temperature after decay. In our scenario, the only relevant parameter is � m 1 , so x ) = a ( T low ) e ζ ( � a ( T high )( � m 1 ) 9

Complete dominance limit • At T ≫ M , RHN are relativistic, they contribute 1 /g ∗ of the plasma density ρ ∝ a − 4 . (RD1) • At T ∼ M , RHN decouples from the plasma. • From T ≃ M/g ∗ until decay H ∼ Γ, the universe is dominated by RHN’s ρ ∼ ρ N ∝ a − 3 . (MD) • After that RHNs decay into radiation. (RD2) ⇓ a ( T low ) a ( T high ) ∝ M 1 / 3 Γ − 1 / 6 ∝ � m − 1 / 6 m ∗ /g 2 for m 1 ≪ � ∗ . � 1 We recover the standard result Dvali, Gruzinov, Zaldarriaga ζ = − 1 δ Γ 6 Γ 10

Density perturbations: The general case In general, one has to solve ρ γ ˙ + 4 Hρ γ = Γ ρ N � � ρ N ˙ + 3 1 + w N ( T/M ) Hρ N = − Γ ρ N 8 π H 2 = ( ρ N + ρ γ ) . 3 M 2 P 11

Density perturbations: The general case In general, one has to solve ρ γ ˙ + 4 Hρ γ = Γ ρ N � � ρ N ˙ + 3 1 + w N ( T/M ) Hρ N = − Γ ρ N 8 π H 2 = ( ρ N + ρ γ ) . 3 M 2 P Log � a � T low �� a � T high � T low � T high � 0.4 0.3 0.2 0.1 0 Log � m 1 � m � � � � � 7 � 6 � 5 � 4 � 3 � 2 � 1 0 12

Non-Gaussianity The non-linearity parameter f NL is defined as x ) − 3 5 f NL ( ζ 2 x ) − � ζ 2 ζ ( � x ) = ζ g ( � g ( � g ( � x ) � ) m ∗ ). In our case ζ = f (log � m 1 / � � δ � � 2 x ) = f ′ δ � m 1 x ) + 1 m 1 2( f ′′ − f ′ ) ζ ( � ( � ( � x ) , m 1 m 1 � � 13

Non-Gaussianity The non-linearity parameter f NL is defined as x ) − 3 5 f NL ( ζ 2 x ) − � ζ 2 ζ ( � x ) = ζ g ( � g ( � g ( � x ) � ) m ∗ ). In our case ζ = f (log � m 1 / � � δ � � 2 x ) = f ′ δ � m 1 x ) + 1 m 1 2( f ′′ − f ′ ) ζ ( � ( � ( � x ) , m 1 m 1 � � f ′′ − f ′ 0 f NL = − 5 f ′ 2 6 � 50 � 100 Experimental limit Creminelli etal. f NL � 150 − 27 < f NL < 121 @ 95% C.L. � 200 � 250 m 1 < 10 − 6 eV ⇒ m 1 < 10 − 6 eV � � 7 � 6 � 5 � 4 � 3 � 2 Log � m 1 � m � � � � 14

Correlated Baryon Isocurvature Non-Gaussianity constraint the RHN to be very out-of-equilibrium. Wash-out can be neglected. The simplest case, where ǫ N 1 is constant δ ( n B /s ) = − δs s = − 3 δT T = − 3 ζ RULED OUT n B /s In general � δ ( n B /s ) ζ = − 3 + δǫ N 1 /ǫ N 1 Can be � . 3 n B /s ζ • More generally, one can consider all the three RHN to produce both n B /s and ζ . Baryon number is washed out by the lightest RHN decay (at least partially) but ζ is not. • More flavor dependence in χ − N i couplings. Example: N 2 is way out-of-equilibrium → ζ and N 1 is close to equilibrium and produces baryon isocurvature. 15

Dynamics of the scalar χ So far, we assumed that the scalar is just frozen. However, its coupling to the plasma will produce a back-reaction. χ + M ′ T 3 = 0 ⇒ ∆ χ ∼ M ′ MT 3 • M ( χ/M P ) NN → ¨ φ + 3 H ˙ M P . H 2 M 2 M P M P During RHN domination: ∆ χ > M ′ M M P > M P ! given the constraints on GWs. Y 2 T 4 χ + Y ′ Y T 4 = 0 ⇒ ∆ χ ∼ Y ′ • Y ( χ/M P ) LHN → ¨ χ + 3 H ˙ M P H 2 M 2 M P Y P The displacement ∆ χ ≪ M P for small Yukawas. • χ will start oscillating when m χ > H . It must decay before dominating (moduli problem): very model dependent. 16

Conclusions • Modulated RHN decay as the source of density perturbations. • Adiabatic perturbations related to δ � m 1 / � m 1 . • Signatures: Non-Gaussianity + baryon isocurvature. m 1 < 10 − 6 eV. • Limits on NG requires N 1 to decay very out-of-equilibrium � • Baryon Isocurvature ∼ adiabatic → we must see something in the new data. • Evolution of the scalar: under control if only Yukawas are modulated. • Is it possible that χ is still around? (light) can it behave as a chameleon? Khoury & Weltman 17