Primordial Black Holes Dark Matter from Axion Inflation

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1 Primordial Black Holes Dark Matter from Axion Inflation Francesco Muia University of Oxford Based on: PBH Dark Matter from Axion Inflation V. Domcke, FM, M. Pieroni & L. T. Witkowski arxiv: [astro-ph.co]. String Pheno 2017 Virginia Tech, 04/07/2017

2 Motivation String theory predicts the existence of many axions.

3 Motivation String theory predicts the existence of many axions. Axions are well motivated candidates to drive inflation.

4 Motivation String theory predicts the existence of many axions. Axions are well motivated candidates to drive inflation. Axions generically couple to U(1) gauge fields through Chern-Simons terms

5 Motivation String theory predicts the existence of many axions. Axions are well motivated candidates to drive inflation. Axions generically couple to U(1) gauge fields through Chern-Simons terms Can we extract predictions from these models? Can we learn something about string theory?

6 Primordial Black Holes [Zeldovich, Novikov, 67] [Hawking, 71] [Carr and Hawking, 74] REQUIREMENTS & PROPERTIES Formed during radiation domination.

7 Primordial Black Holes [Zeldovich, Novikov, 67] [Hawking, 71] [Carr and Hawking, 74] REQUIREMENTS & PROPERTIES Formed during radiation domination. Planck time pre-bbn

8 Primordial Black Holes [Zeldovich, Novikov, 67] [Hawking, 71] [Carr and Hawking, 74] REQUIREMENTS & PROPERTIES Formed during radiation domination. Planck time pre-bbn (Meta-)Stability: BHs evaporate through Hawking radiation. such PBHs survive till today and can compose dark matter

9 REQUIREMENTS & PROPERTIES [Carr et al., 10, 17] Can PBHs compose a sizeable fraction of dark matter? Dynamical Lensing Large Scale Structure Evaporation Accretion

10 REQUIREMENTS & PROPERTIES [Carr et al., 10, 17] Can PBHs compose a sizeable fraction of dark matter? sub-lunar intermediate mass

11 PBH production [Garcia-Bellido et al., 96] IDEA a PBH is formed when a mode re-enter the horizon if the related density perturbation is above a certain threshold INFLATION RADIATION MATTER N { formation of PBHs with mass mode leaves the horizon mode re-enter the horizon structure formation (accretion?) t

12 PBH production [Garcia-Bellido et al., 96] IDEA a PBH is formed when a mode re-enter the horizon if the related density perturbation is above a certain threshold INFLATION RADIATION MATTER N { formation of PBHs with mass mode leaves the horizon mode re-enter the horizon structure formation (accretion?) t N = number of e-foldings (before the end of inflation) at which a given mode left the horizon

13 PBH production [Peloso et al., 11] Consider the curvature perturbation on uniform-density hypersurfaces. (spatially flat gauge)

14 PBH production [Peloso et al., 11] Consider the curvature perturbation on uniform-density hypersurfaces. (spatially flat gauge) Probability of forming PBHs with mass upon re-entry of the mode threshold probability distribution

15 PBH production [Peloso et al., 11] Consider the curvature perturbation on uniform-density hypersurfaces. (spatially flat gauge) Probability of forming PBHs with mass upon re-entry of the mode threshold probability distribution E.g.: gaussian distribution

16 PBH density [Carr et al., 10, 17] = fraction of the universe in PBHs of mass at the formation Hubble patches with

17 PBH density [Carr et al., 10, 17] = fraction of the universe in PBHs of mass at the formation Hubble patches with Fraction of PBH dark matter today (neglecting accretion)

18 PBH density [Carr et al., 10, 17] = fraction of the universe in PBHs of mass at the formation Hubble patches with Fraction of PBH dark matter today (neglecting accretion) Total fraction of PBH dark matter today

19 Need large perturbations at the CMB scales COBE normalisation the spectrum is locally almost flat

20 Need large perturbations at the CMB scales COBE normalisation the spectrum is locally almost flat assume we can extrapolate the spectrum up to very small scales the fraction of PBH dark matter is completely negligible

21 Need large perturbations at the CMB scales COBE normalisation the spectrum is locally almost flat assume we can extrapolate the spectrum up to very small scales the fraction of PBH dark matter is completely negligible need a mechanism that enhances the power spectrum at scales smaller than CMB

22 Axion inflation coupled to gauge fields GENERIC MODEL [Sorbo et al., 09]

23 Axion inflation coupled to gauge fields GENERIC MODEL [Sorbo et al., 09] GAUGE FIELDS assuming inflating background increases towards the end of inflation

24 Axion inflation coupled to gauge fields GENERIC MODEL [Sorbo et al., 09] GAUGE FIELDS assuming inflating background increases towards the end of inflation TACHYONIC INSTABILITY gauge fields production exponential amplification of gauge field modes towards the end of inflation governs the instability

25 Equations of motion INFLATON new friction term

26 Equations of motion INFLATON new friction term - Hubble friction dominates at CMB scales (around N = 60). - As increases, the new friction term becomes important. - The inflaton speed increase slows down Additional e-foldings.

27 Equations of motion INFLATON new friction term - Hubble friction dominates at CMB scales (around N = 60). - As increases, the new friction term becomes important. - The inflaton speed increase slows down Additional e-foldings. FRIEDMANN always negligible

28 Perturbations INFLATON [Sorbo et al., 09] [Peloso et al., 11] [Linde and Pajer, 13] source for scalar power spectrum

29 Perturbations INFLATON [Sorbo et al., 09] [Peloso et al., 11] [Linde and Pajer, 13] source for scalar power spectrum Power spectrum

30 Perturbations INFLATON [Sorbo et al., 09] [Peloso et al., 11] [Linde and Pajer, 13] source for scalar power spectrum Power spectrum Blue spectrum exactly what is needed for PBH production [Domcke et al., 15] COBE normalisation

31 Interesting phenomenology Chiral GW spectrum [Sorbo, 11] [Sorbo et al., 12] [Domcke et al., 15]

32 Interesting phenomenology Chiral GW spectrum [Sorbo, 11] [Sorbo et al., 12] [Domcke et al., 15] Large non-gaussianities [Sorbo et al., 12]

33 Interesting phenomenology Chiral GW spectrum [Sorbo, 11] [Sorbo et al., 12] [Domcke et al., 15] Large non-gaussianities [Sorbo et al., 12] Can we learn something from all these features combined (tensor-to scalar ratio, chiral GWs, non-gaussianities)?

34 plateau in the scalar power spectrum [Domcke et al., 15]

35 plateau in the scalar power spectrum at small N, PBHs of critical mass are produced E.g. for [Domcke et al., 15]

36 plateau in the scalar power spectrum at small N, PBHs of critical mass are produced E.g. for [Domcke et al., 15] totally negligible

37 plateau in the scalar power spectrum at small N, PBHs of critical mass are produced E.g. for [Domcke et al., 15] totally negligible coupling to gauge fields is useful to rise the spectrum, but we need a mechanism to suppress it at small scales

38 Simplest extension non-canonical kinetic term

39 Simplest extension non-canonical kinetic term The presence of K implies that the tachyonic instability is governed by results depend on the behaviour of K

40 Simplest extension non-canonical kinetic term The presence of K implies that the tachyonic instability is governed by results depend on the behaviour of K Attractors at strong coupling [Linde et al., 13] canonical kinetic terms

41 non-gaussianities evolution of

42 non-gaussianities evolution of Scalar spectrum COBE

43 PBH production Only PBHs with mass contribute to dark matter.

44 the instability is turned off towards the end of inflation

45 the power spectrum features a peak the instability is turned off towards the end of inflation Increasing and the instability starts and is turned off earlier. GW production always negligible in the case interesting for PBHs.

46 the power spectrum features a peak the instability is turned off towards the end of inflation Increasing and the instability starts and is turned off earlier. GW production always negligible in the case interesting for PBHs.

47 PBH production ruled out Increasing and shifts the peak towards larger mass values. We neglected NS capture constraints. The case with canonical kinetic terms is ruled out by PBH overproduction.

48 Conclusions and outlook Models of axion inflation with coupling to gauge fields are extremely interesting from a phenomenological point of view potentially observable chiral GWs, non-gaussianities

49 Conclusions and outlook Models of axion inflation with coupling to gauge fields are extremely interesting from a phenomenological point of view potentially observable chiral GWs, non-gaussianities A simple extension allows for PBH dark matter

50 Conclusions and outlook Models of axion inflation with coupling to gauge fields are extremely interesting from a phenomenological point of view potentially observable chiral GWs, non-gaussianities A simple extension allows for PBH dark matter - (P-)Reheating (generic tension with dark radiation?). - String theory embedding. - Extension to non-abelian gauge fields.

51 Conclusions and outlook Models of axion inflation with coupling to gauge fields are extremely interesting from a phenomenological point of view potentially observable chiral GWs, non-gaussianities A simple extension allows for PBH dark matter - (P-)Reheating (generic tension with dark radiation?). - String theory embedding. - Extension to non-abelian gauge fields. Thank you!

52 Neutron stars capture Neutron stars: The presence of a PBH inside a NS leads to its rapid destruction by the accretion of the star matter onto the PBH [Kouvaris et al., 04, 11, 12] Capture rate depends on the DM density Assuming that cores of globular clusters possess the DM densities exceeding several hundred would imply that PBHs are excluded as comprising all of the dark matter in the mass range [Capela et al., 13] HOWEVER Observations of globular clusters show no evidence of [Ibata et al., 12] significant dark matter content in such systems [Bradford et al., 11]

53 Are we neglecting something? Yes, several things - Critical collapse. typically O(1) corrections - Accretion and mergers. critical mass at equality During matter domination PBHs of mass merge and become stable. All PBHs become heavier. - Non sphericity. generically increases the threshold Proof-of-principle that these models can give rise to a sizeable amount of PBH dark matter

54 Perturbations revisited [Peloso et al., 11] [Linde and Pajer, 13] INFLATON small correction (slow-roll) At horizon crossing in the gauge field regime Not a gaussian! [Garcia-Bellido et al., 16]