Searching for Axion Dark Matter with CMB Birefringence

Searching for Axion Dark Matter with CMB Birefringence and Background Photon Resonance ar. Xiv: 1811. 07873 ar. Xiv: 1907. 04849 Günter Sigl & Pranjal Trivedi University of Hamburg II. Institute for Theoretical Physics and Hamburg Observatory 15 th Rencontres du Vietnam on Cosmology, ICISE, Quy Nhon, Vietnam 11 -17 August 2019

What is Dark Matter? Bertone 18 Tait 14 Pranjal Trivedi (Hamburg)

Dark Matter Primordial black holes WIMPs Axions or ALPs (Axion-like particles) Pranjal Trivedi (Hamburg)

Dark Matter Primordial black holes WIMPs Axions or ALPs (Axion-like particles) Carr 19 Pranjal Trivedi (Hamburg)

Dark Matter Primordial black holes Baudis 14 Pranjal Trivedi (Hamburg) WIMPs Axions or ALPs (Axion-like particles)

Slide: Guenter. Sigl Pranjal Trivedi (Hamburg) 6

Slide: Guenter. Sigl Pranjal Trivedi (Hamburg) 7

DM and Axions and ALPs Pranjal Trivedi (Hamburg)

Pranjal Trivedi (Hamburg) 9

Overview of Current Constraints on Axion-Photon Coupling Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence 10

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) Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 resonance for or with growth rate and relative width Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

Resonance Enhancement by Galactic Axion Condensate numerical solution including logarithmic dependencies: axion condensate size R R = 1 kpc R = 10 kpc Lower end of ma range set by lowest available radio frequency Pranjal Trivedi (Hamburg) Higher end of ma range set by nonrelativistic axion temperature staying below the condensate critical temperature Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 γray opacity (Hess collaboration 2013, Meyer 2012) Also, constraints will tighten by another x 2 -3 from integrating over DM profiles e. g. NFW, Burkert Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

Axion Stars, Axion Miniclusters, Axion Decay Axion stars can be stable on dilute branch of MR 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 unlikely to 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 contribute to photon background enhancement only at ma > e. V Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

Birefringence constraints • Birefringence constraints: upto 4 orders improvement over Chandra cluster x-ray constraints • Complementary to helioscopes, haloscopes, LSW experiments in g aγ vs ma 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 x 5 Lite. BIRD, x 500 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, De. Rocco & Hook 18, Nagano 19) Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

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 > μe. V, 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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence

Summary- Resonance and Birefringence: Strong probes of ultra-light Dark Matter • Condensate axion DM can produce parametric resonance and enhance background photons • Cosmic birefringence constraints are upto 4 orders stronger than x-ray AGN in cluster constraints. • Radio to optical background data and upper limits imply a constraint gaγ ~ 10 -14 Ge. V-1 in mass windows over broad mass range 0. 1 μe. V – 10 e. V • Mass scales probed by CMB in log (ma/e. V) gaγin Ge. V-1 -27 to -24 10 -18 -10 -12 • Can probe classical QCD axion models 10 -5 – 10 -3 μe. V • CMB-S 4, COr. E, SKA 2 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 Pranjal Trivedi (Hamburg) Axion-Like Dark Matter Constraints from Parametric Resonance & CMB Birefringence