Formation of Primordial Black Holes in Double Inflation

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1 Formation of Primordial Black Holes in Double Inflation Masahiro Kawasaki (ICRR and Kavli-IPMU, University of Tokyo) Based on MK Mukaida Yanagida, arxiv: MK Kusenko Tada Yanagida arxiv: Inomate MK Tada in preparation

2 1. Introduction Primordial Black Holes (PBHs) have attracted interest for many years Hawking (1971) PBHs can be formed by gravitational collapse of overdensity region with Hubble radius in the early universe PBHs with mass < 1015 g would have evaporated by now through Hawking radiation Hawking (1974) PBHs with larger masses can exist in the present universe but various constraints on their abundance are imposed PBHs can give a significant contribution to dark matter if MBH = g Large density fluctuations δ with O(0.1) are required for PBH formation but δ ~ O(10-5 ) on CMB scale 2

3 We consider double inflation (preinflation+new inflation) Preinflation (no specific model is required) accounts for perturbations on large scale observed by Planck New inflation ( after preinflation) with e-fold Nnew < 50 produces large curvature perturbations on small scales P (k) preinflation new inflation k CMB k PBH k This double inflation is realized in supergravity framework 3

4 Today s Talk 1. Introduction 2. PBH formation in radiation dominated universe 3. New inflation model and PBH formation 4. New inflation in supergravity 5. Production of gravitational waves 6. Conclusion 4

5 2. PBH formation in radiation dominated universe Region with Hubble radius collapses if its over-density is higher than δc ( 0.3) PBH mass M PBH ' 3.6M 2 k 10 6 Mpc 1 ' 4.5M PBH abundance is estimated by Press-Schechter formalism 2 T 0.1GeV PBH mass fraction β=ρ PBH(M)/ρ (M) = Z c d 2 1 p 2 2 (k) exp 2 2 (k) P (k) P (k) O(10 2 ) for PBH formation 2 (k) : variance of the comoving density perturbation coarse-grained on k 1 Present PBH fraction to DM f PBH (M) = PBH(M) ' (M) DM f PBH,tot = Z d log Mf PBH (M) 2 (k) = Z 1/2 MPBH M d log k 0 W 2 (k 0 /k) (k0 /k) 4 P (k 0 ) [ fraction per log M ] 5

6 3. New Inflation after Preinflation Potential for new inflation V (') = v 2 g' n 2 cv 2 ' Hubble Slow-roll parameter = 1 2 V 0 V H inf ' v2 p 3 2 = applev4 ' 2 n =3, 4, M p =1 c v 2 apple' 2ng 'n 1 v v 4 V (') ' = V 00 V = apple 2n(n 1)g 'n 2 v ) inflation Curvature perturbation P 1/2 = H inf 2 1 p ' p 3 v 4 c + applev 2 ' +2ng' n p 3 v 4 c ('. c v 2 ) P 1/2 O(0.1) for c v 4 PBH formation 6

7 New inflation after preinflation Initial value for the inflaton '? Interaction with the inflaton Hubble induced mass term Just before new inflation of preinflation Shape of power spectrum of curvature perturbations depends on κ > 0 or κ < 0 spectral index V H 2 ' 2 V ( )+ V H 2 ' 2 cv 2 ' + ) ' cv2 ' ini c v 2 H v 2 P 1/2 1 2 p 3 H 2 n s 1 ' 2 6 ' 3 c2 v 4 2apple 4n(n 1)g 'n 2 v 2 (e.g. V m 2 2 ' 2 ) v 4 c O(0.1) for c v4 7

8 κ < 0 κ ~0 power spectrum has a peak when V 00 0 ) n s 1=0 power spectrum is almost flat around ' ' ini V V V 00 0 PBHs with very wide range of mass are produced κ > 0 ' ' P PBHs with wide range of mass are produced apple. c 2 /v 4 v 4 1 V power spectrum takes the largest value at ' ' ini ' PBHs with narrow range of mass are produced P flat apple c 2 /v 4 1 P red-tilted n s 1 < 0 apple O(0.1) 8 ' ' '

9 Power spectrum of curvature perturbations Estimate power spectrum using slow-roll approximation ζ μ distortion of CMB due to Silk damping flat peak reenter the horizon before new inflation k[mpc -1 ] κ < 0 solid v = 10 4 apple = 0.44 c = g = dashed v = 10 4 apple = 0.18 c = g = MK Kusenko Tada Yanagida (2016) Another peak at k~106 Mpc -1 Hubble induced term cannot neglected at the beginning of new inflation, which flattens the potential However, it should be examined more carefully 9

10 Abundance of produced PBHs PBH fraction to DM in each logarithmic mass bin White Dwarf Kepler Femtolensing EROS/MACHO κ < 0 ΩPBH/ΩDM EGγ FIRAS WMAP Total PBH fraction to DM can be 1 Z Another peak at PBH / DM = M PBH [g] d log Mf PBH (M) ' 1 M PBH 30M MK Kusenko Tada Yanagida (2016) GW recently detected by LIGO/Virgo collaboration? 10

11 Abundance of produced PBHs MK Mukaida Yanagida (2016) For apple c 2 /v 4 1 PBHs with wide range of mass are produced For apple O(0.1) PBHs with very narrow range of mass are produced For both cases PBH can be DM κ ~ 0 apple c 2 /v 4 1 κ > 0 apple O(0.1) Kepler Hawking Femtolensing MACHO/EROS FIRAS WMAP3 NS in GCs Star Formation Ω PBH /Ω c v = c =0.6v 4 g = Kepler Hawking Femtolensing MACHO/EROS FIRAS WMAP3 NS in GCs Star Formation Ω PBH /Ω c v = c =0.4v 4 apple =0.25 g =

12 Another peak at large PBH mass The corresponding perturbations reenter the horizon before new inflation We need careful numerical calculation including all 1st order perturbations of metrics and scalar fields Inomate MK Tada (2016) Chaotic inflation + New inflation with V = 4 m 2 2 ' 2 H 2 ' 2 Peak height crucially depends on the Hubble induced term PBH DM Ω /Ω =0.58 c H PBH DM Ω /Ω =1 c H M [g] PBH M [g] PBH 12

13 4. New Inflation in Supergravity Potential of a scalar field in supergravity V ( )=e K (D W )K (D W ) Superpotential W (assuming Z 2nR R-symmetry) W ( )=v 2 Kähler potential Inflaton potential g n +1 Potential minimum n+1 K( )= 2 + apple V (') =v 4 hv (')i ' 3v 4 v 2 3 W 2 Inflaton ' = p 2Re apple 2 v4 ' 2 g 2 n/2 1 v2 n + g 2/n Izawa Yanagida (1997) V (') canceled by SUSY contribution µ 4 SUSY m 3/2 ' µ 2 SUSY/ p 3 ' v 2 v 2 D W W 2 1 g 1/n ' 13

14 New Inflation in Supergravity Constant term in superpotential Linear term Hubble induced term Inflaton ' obtains the Hubble induced mass during and after the first inflation(=preinflation) through the term Just before new inflation starts, the inflaton has the initial value Potential V lin = 2 p 2v 2 ' W = W ( )+c V ' e K (V pre + ) H 2 ' 2 O(1) V (') =v 4 ' i c v 2 2 p 2cv 2 ' No initial value problem apple 2 v4 ' 2 g p2 v PBH formation c v 4 14

15 SUSY breaking sector Dynamical SUSY breaking models W SUSY = 2 4 Z µ 2 SUSY = 2 4 If the origin of Z is destabilized due to a large Yukawa coupling (~ 4π ) (Z: SUSY breaking field) Izawa Yanagida (1996), Intriligator Thomas(1996) Chacko Luty Ponton (1998) hzi ' 4 W SUSY New inflation model (n=3) µ SUSY v 4/3 c v 4 3 (4 ) 2 c µ3 SUSY c µ 3 SUSY consistent 15

h 00 ~ k +2Hh 0 ~ k + k 2 h ~k = S( ~ k, t) GW h 2 10 8 (P /10 2 ) 2 f GW 2 10 9 Hz(M PBH /M ) 1/2 GWs can be probed

16 5. Production of gravitational waves PBHs form from large curvature perturbations 2nd order perturbations ~ O( ~k ~k ~ induce a k 0) source term of tensor perturbations Saito Yokoyama (2009) Bugaev Kulimai (2010) Moore Cole Berry (2015) h 00 ~ k +2Hh 0 ~ k + k 2 h ~k = S( ~ k, t) GW h (P /10 2 ) 2 f GW Hz(M PBH /M ) 1/2 GWs can be probed future detectors Pulsar timing experiments already give a stringent constraint on PBHs with M PBH M EPTA (2015) 16

17 6. Conclusion PBHs can be formed in double inflation (=preinflation + new inflation) The new inflation potential has linear and quadratic terms which play an important role in determining the initial value and amplitude of curvature perturbations In this model PBHs with wide range of mass can be produced and account for DM of the universe The model is realized in framework of supergravity Large curvature perturbations required for PBH production also produce gravitational waves which will be proved by future detectors 17

18 Backup 18

19 Power spectrum of curvature perturbations with double peaks R 10-6 κ=0.128 (ch=0.583) double peak μ-distortion k[mpc -1 ] 19

Non-Gaussianity and Primordial black holes Work in collaboration with Sam Young, Ilia Musco, Ed Copeland, Anne Green and Misao Sasaki

Non-Gaussianity and Primordial black holes Work in collaboration with Sam Young, Ilia Musco, Ed Copeland, Anne Green and Misao Sasaki Christian Byrnes University of Sussex, Brighton, UK Constraints on