Searching for Axion Dark Matter with

1. Searching for Axion Dark Matterwith CMB Birefringence Background Photon Resonance and arXiv:1907.04849 arXiv:1811.07873 Günter Sigl & Pranjal Trivedi Pranjal Trivedi University of Hamburg II. Institute for Theoretical Physics and Hamburg Observatory 15th Rencontres du Vietnam on Cosmology, ICISE, Quy Nhon, Vietnam 11-17 August 2019

2. What is Dark Matter? Bertone 18 Tait 14

3. Dark Matter Primordial black holes Axions or ALPs (Axion-like particles) WIMPs

4. Dark Matter Primordial black holes Axions or ALPs (Axion-like particles) WIMPs Carr 19

5. Dark Matter Primordial black holes Axions or ALPs (Axion-like particles) WIMPs Baudis 14

6. Slide: GuenterSigl

7. Slide: GuenterSigl

8. DM and Axions and ALPs

10. Overview of Current Constraints on Axion-Photon Coupling Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

11. Axion-Photon Coupling (not absolutely DARK matter) Axion-like particles (ALPs) are a pseudo-scalar field which couples to EM Axion-photon coupling constant Equation of Motion for photon field A(t,r) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

12. Photon Propagation in Axion Background Equation of Motion for photons is a Mathieu equation (resonance possible) q is a dimensionless parameter: controls resonance growth rate & width Solve Mathieu equation via Floquet theorem Find Parametric resonancefor or with growth rate and relative width Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

13. Resonant Enhancement of Photon Flux Radiation flux received will have an Enhancement factor f produced by parametric resonance amplification Rough Estimate: assuming q is constant over total path length R R (ignoring logarithmic dependencies) This assumes an axion condensate of size R Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

14. Resonance Enhancement by Galactic Axion Condensate numerical solution including logarithmic dependencies: axion condensate size R R = 1 kpc R = 10 kpc Higher end of marange set by non-relativistic axion temperature staying below the condensate critical temperature Lower end of marange set by lowest available radio frequency Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

15. Detailed Constraints: Background Flux Observations &Limits • Observations and Limits on Background flux: Radio-IR-Optical  Possible Flux Enhancement • Observed Wavebands  Axion-Photon Coupling constraints over Axion mass windows Radio background: Extragalactic excess background (ARCADE 2) or CMB Radio upper limit: sky noise temperature Optical-IR background: CIB detections or integrated number counts (Madau & Pozzetti 2000) Optical-IR upper limit: CIB uncertainty or γ-ray opacity (Hess collaboration 2013, Meyer 2012) Also, constraints will tighten by another x 2-3 from integrating over DM profiles e.g. NFW, Burkert Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

16. Galactic Axion Condensate Parametric Resonance constraints depend crucially on the existence of a mono-energetic axion condensate, of size R • Zero mode of axion dark matter must contribute significantly to ρa • Described by a classical field a(t,r) which evolves at rate Γevol< Γc(resonant growth rate) Γc • Above the Jeans scale, time evolution ~ free fall time • τff~ R/v ~ 103 R >> Γc-1 • However, adiabaticity is violated on lines of sight where small scale structure evolves with rates • Γevol> Γc • corresponding to structures on length scales R < where such gaγ constraints can’t be derived Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

17. Axion Stars, Axion Miniclusters, Axion Decay Axion stars can be stable on dilute branch of M-R relation Axion miniclusters can form once axion field starts to oscillate at Tosc set by H(Tosc) ~ ma We find axion stars and miniclusters are unlikelyto lead to significant enhancement of background flux. Visinelli 2018 Spontaneous decay or stimulated decay of a single axion in a photon field is distinct from parametric resonance of photons propagating in an axion background We find spontaneous or stimulated decay of a single axion in a photon field can contributeto photon background enhancement only at ma > eV Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

18. Birefringence: Photon Dispersion Relation From Equation of Motion for photons (Mathieu equation) we can derive Dispersion relation – NL coupling of photon and axion field Phase difference between Left and Right Circular Polarized photons axion density and field value axion DM fraction Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

19. Birefringence: Axion-Photon Coupling constraints Using a conservative limit from current CMB observations Polarization reduction factor (‘washout’ effect, Fedderke 19) a oscillation during recombination F is axion DM fraction: 10-2 to 10-1 over the range Hlozek 14, 18 CMB power spectrum Kobayashi 17 Lyman Alpha forest Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

20. Birefringence constraints • Birefringence constraints: upto 4 orders improvement over Chandra cluster x-ray constraints • Complementary to helioscopes, haloscopes, LSW experiments in gaγvsma parameter space • Can improve gaγ constraints for DM fraction as low as 10-8 • Independent of any assumption about magnetic fields • Future CMB obs can improve constraints by x5 LiteBIRD, x500 PICO • CMB Birefringence constraints: expected to be more robust than astrophysical polarized sources – PPDs (Fujita 19), AGN (Ivanov 19) • Time oscillation of local axion field ‘AC oscillation’ (Fedderke 19) not a factor for these very low ma • Laboratory measurements of axion birefringence proposed via laser interferometers • (Obata 18, Liu 18, DeRocco & Hook 18, Nagano 19) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

21. Clarify Random Walk in Birefringence Angle We clarify the discussion regarding random walk in birefringence angle (Fedderke+ 19; Arvanitaki+ 10; Finelli & Galaverni 09, Harari & Sikivie 92, Carroll 90) • CMB Birefringence: no random walk, • local minus emission values of axion field • Analyze photon equation of motion using (u,v) coordinates: • u = z-t • v = z+t • Find non-linear terms (eg. neglected by Fedderke 19) do not cancel but are suppressed by (ma/k) • For CMB: ma << k where constraints are interesting. • At ma > μeV, random walk from NL terms possible but constraints too weak to be of interest • Discontinuities in axion gradient (domains or cosmic strings) could also lead to random walk • Multiple axions (from string theory) coupled to EM could also lead to random walk type enhancement Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

22. Summary- Resonance and Birefringence: Strong probes of ultra-light Dark Matter • Condensate axion DM can produce parametric resonance and enhance background photons • Radio to optical background data and upper limits imply a constraint gaγ ~ 10-14 GeV-1 in mass windows over broad mass range 0.1 μeV – 10 eV • Can probe classical QCD axion models 10-5 – 10-3μeV • Cosmic birefringence constraints are upto 4 orders stronger than x-ray AGN in cluster constraints. • Mass scales probed by CMB • in log (ma/eV) gaγin GeV-1 • -27 to -24 10-18-10-12 • CMB-S4, COrE, SKA2 can all improve by 1-2 orders of mag. in axion-photon coupling Both independent of magnetic fields, probe new parts of axion parameter space Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence