The self-interacting (subdominant) curvaton

Size: px

Start display at page:

Download "The self-interacting (subdominant) curvaton"

Bryce Hall
5 years ago
Views:

1 Corfu The self-interacting (subdominant) curvaton Kari Enqvist Helsinki University and Helsinki Institute of Physics in collaboration with C. Byrnes (Bielefeld), S. Nurmi (Heidelberg), A. Mazumdar (Lancaster), G. Rigopoulos (Helsinki), O. Taanila (Helsinki), T. Takahashi (Saga)

2 curvaton schematically curvaton: massless field during inflation with ρ << ρ φ ENERGY DENSITY slow roll inflaton curvaton oscillation inflaton decays curvaton decays curvaton not moving flat spectrum time

3 1. Curvaton dominant at decay all matter from curvaton matter inherits perturbation from the curvaton. Curvaton not yet dominant at decay decay products thermalize with inflaton decay products curvaton perturbation can be dominant if δρ ρ 10 5 such that δρ ρ tot = 10 5 and inflaton perturbation small curvaton perturbation generated during curvaton oscillation from inflationary seed

4 simplest potential V = 1 m δ δ = curvaton must decay: φ initial value higher order operators must exist: φ + + self-interactions

5 even weak interactions cosmologically important: - large field values probe interaction terms - interactions non-linearities curvature perturbation at constant ρ hypersurface ς = N separate universe formalism ( ) N = N( ) = ln a / a depends on the field 0 initial condition during curvaton oscillations N O but N O 5 (10) (10 ) non-linearities: sensitivity to the initial condition - in particular: non-gaussianity

6 ( ) ( ) ς = N ' δ + N '' δ + N ''' δ f 9 g NL 1 5 NL 1 = ς ς ς ς gaussian g NL : connected part of 4-point correlator τ NL : disconnected part ςς spectrum ςςς bispectrum ςςςς trispectrum =0 for gaussian perturbation non-gaussianity of the primordial perturbation very important observable perhaps the single most interesting that Planck will measure

7 9 < f <111 Limits: NL < g NL < single-field inflation fnl O( ε ) 1 multi-field inflation fnl O(1) Planck expected to set limit to f 5 NL preheating may generate large non-gaussianities

8 non-gaussianity in curvaton models r rdec = d ' = d osc 3ρ 4ρr + 3ρ decay =0 for quadratic case f NL can be large ' + + '' r r ' = = osc non-quadratic case: more complicated

9 Assume small deviation from quadratic form = + λ 1 4 V m m m p s λ m p measures the strength of interaction small: s<</p non-integer p log

10 = + λ 1 4 V m m m p n=p f NL g NL s = 0. s = 0.1 s = n s = 0. s = 0.1 s = f NL r=0.01

11 The spectral index of f NL n f NL = df NL d ln k Sefusatti et al, JCAP 091:0,009. future resolution 50 1 n f NL 0.05 f f NL sky

12 If deviations are not always small numerics V 1 λ = m + M 4+ n n Equations of motion: 3H 0 = && + 3 H +Γ & + m + λ n ( ) ( ) & ρ = 4Hρ +Γ & r = ρ + ρ r r n 3 initial condition: =, = + + H π inflation

13 curvature perturbation is = N N ς + ( ) ( ) for fixed m, n, free parameters are H ρ V( ), r = 1 ρr 3H natural value of r? FP P p exp V( ) eq find Γ at equal ρ such that ς = π 3H 4 V flat distribution up to ( ) H 8π 4 not quantum fluctuation = classical force V ' H 3

14 Four phases: slow roll non-quadratic oscillation ρ a n+ 4 6 n+ 6 quadratic oscillation ρ a 3 decay Γ H scan through parameter space, adjust parameters such that ς = 10-5

16 perturbation sensitive to parameters:

17 contraint on Γ curvaton must decay before CDM freeze-out M WIMP T freeze perturbations adiabatic 0 T O(10) GeV freeze Tfreeze Γ H freeze 10 M 15 GeV spectrum scale invariant: V '' < 10 H

18 log r dec V = 1 λ=10 m 7 + λ 4 m= 10 8 non-quadratic term irrelevant r scale invariance high probability: V<H 4 white is ruled out H

19 when non-linearities important, N shows oscillations n = 4, m= 10 1

20 ALLOWED REGIONS 1 n= 4, m= 10 M V < H correct amplitude f NL, g NL curvaton decay

21 TeV scale curvaton? if one assumes quadratic potential: ς H r 10 = eff 5, r eff r dec = ρ ρ + ρ correct perturbation amplitude, non-gaussianity, decay before DM freeze-out r purely quadratic potential not consistent if m ~TeV

22 n=4 r initial non-quadratic domination decay time limit non-gaussianity H GeV only n = 4 consistent 8 1 V = m +, m= O(1) 4 M TeV

23 allowed regions n=4

24 What could the TeV scale curvaton be? obvious candidates: MSSM flat directions - can one have the required small Γ? KE, Mazumdar, Taanila

25 conclusion ignore curvaton self-interaction at your peril rich phenomenology signature: large non-gaussianity comp. bispectrum w. trispectrum spectral index

Completing the curvaton model Rose Lerner (Helsinki University) with K. Enqvist and O. Taanila [arxiv: ]

Completing the curvaton model Rose Lerner (Helsinki University) with K. Enqvist and O. Taanila [arxiv:1105.0498] Origin of? super-horizon Origin of (almost) scale-invariant? perturbations Outline What