Gravitational Waves from Inflation and Primordial Black Holes Marco - PowerPoint PPT Presentation

Gravitational Waves from Inflation and Primordial Black Holes Marco Peloso, University of Padua GW from axion inflation • GW from primordial black holes (PBH) • Characterization of the stochastic GW background (SGWB) • Barnaby, Bartolo, Bertacca, De Luca, Domcke, Figueroa, Franciolini, Garc ´ ıa-Bellido, Lewis, Matarrese, Nardini, Pajer, Pieroni, Racco, Ricciardone, Riotto, Sakellariadou, Sorbo, Tasinato, Unal

GW as a probe of inflation a ∝ e Ht = e − N We give time in terms of e − foldings : − ∝ a ≃ e − 60 a end CMB modes produced at N ≃ 60 before the end of inflation, when wavelength horizon They only probe CMB and Large Scale Structure N = 56 − 63 in excellent agreement with inflation. However, only probe λ ≃ 10 2 − 10 5 Mpc ≃ − Smaller scales / later times λ ≃ 10 3 − 10 9 km es essentially unprobed. time inflation matter/radiation We can probe N = 15 − 28 Development of GW interferometers f ≃ 10 8 Hz N = 0 ↔ opens a new window on much smaller scales

GW production during inflation ij + 2 a ′′ 2 a h ij + k 2 h ij = T TT h ′′ ij M 2 p Several mechanisms result in Amplification of vacuum modes from sourced GW during inflation. inflationary expansion guaranteed Subject to the same limits as vacuum modes at CMB scales signal, but too small for present and next generation detectors Quantum -6.0 Signal must be blue to be aLIGO 2 Ω GW ] Fluctuations -8.0 Ω GW ∝ 1 /k 2 Log[h 0 visible at interferometers (MD modes) -10.0 LISA -12.0 scale-invariant (RD modes) Natural property in r e d t i l t e d ( q u a s i - ) -14.0 s c a l e - i n v a r i a n t ( R D m o d e s ) axion inflation -16.0 -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 10.0 Log[f] D. Figueroa

Axion inflation V Freese, Frieman, Olinto ’90, . . . 1.5 Main theoretical di ffi culty 1.0 is to keep the potential flat 0.5 against radiative corrections Φ 2 4 6 • Coupling to matter invariant under φ → φ + constant ∆ L = ∂ µ φ ψγ 5 γ µ ψ ¯ Coupling to fermions : f ∆ L = φ F µ ν ≡ − 4 ∂ µ φ f F µ ν ˜ to gauge fields : f ϵ µ ναβ A ν ∂ α A β φ ψ Loops with these couplings ∂ µ φ ψ ∂ µ φ ψ do not modify the potential ∆ V = 0 φ ψ

φ f F ˜ Vector production from F Turner, Widrow ’88 Garretson, Field, Carroll ’92 Anber, Sorbo ’06 Originally studied for magnetogenesis. Here, generic U(1) φ F ˜ F breaks parity, ̸ = results for two polarizations � � ∂τ 2 + k 2 ∓ ak ˙ ∂ 2 φ + left handed A ± ( τ , k ) = 0 f d − right handed Physical ρ in one mode 1e+09 � + vacuum 1e+08 One tachyonic helicity at horizon crossing • 1/H 4 d (E 2 +B 2 /2) / d log k 1e+07 1e+06 Then diluted by expansion 100000 • 10000 1000 Max amplitude A + ∝ e ˙ φ • 100 � = 5 10 0.01 0.1 1 10 100 a H / k

δ A • The produced A + modes source inflaton perturbations δφ δφ through inverse decay. These modes are highly non-gaussian. δ A � � recall L ⊃ − φ F ˜ F ∼ 10 16 GeV This imposes f > Barnaby, MP ’10 f � � Planck ’15 The amplified gauge fields also produce GW, though A + A + → h L • Barnaby, MP ’10 Sorbo ’11 ˙ φ grows during inflation (inflation ends Bartolo et al ’16; LISA cosmology WG because ˙ φ too large) ⇒ Blue GW and potentially visible at interferometers Cook, Sorbo ’11; Barnaby, Pajer, MP’11; Domcke, Pieroni, Bin´ etruy ’16; . . . Signal is chiral h L ≫ h R and highly non-Gaussian, ⟨ h 3 ⟩ ∼ ⟨ h 2 ⟩ 3 / 2

V ( φ ) from shift symmetry Due to ∝ e ˙ φ , signal very sensitive to the inflaton potential Domcke, Pieroni, Bin´ etruy ’16 N 60 50 40 30 20 10 0 V ( φ ) = 1 2 m 2 φ 2 10 - 9 � 2 � � � − � � 2 � 3 φ V ( φ ) = V 0 1 − e 10 - 14 GW h 2 � 4 � 2 � � � � � � φ 10 - 19 V ( φ ) = V 0 1 − v 10 - 24 � 3 � 2 � � � φ � V ( φ ) = V 0 1 − v 10 - 29 10 - 15 10 - 10 10 - 5 10 0 10 5 f [ Hz ] N = number of e-folds before the end of inflation when a mode is produced. Di ff erent experiments probe di ff erent ranges of V ( φ )

A L As in all mechanisms of GW from inflation, • δφ h L , the key di ffi culty is to produce observable GW without overproducing density perturbations A L • For a monomial V ( φ ), PBH bounds prevent GW from being observable at aLIGO and LISA Linde, Mooij, Pajer ’13 � GW h 2 P Ζ aLIGO 10 � 6 0.1 LISA 0.001 10 � 9 PBH limit f � � 10 N ∼ 15 − ln 10 � 5 10 � 12 100 Hz 10 � 7 Ξ CMB � 1.66 Ξ CMB � 1.66 10 � 15 10 � 9 30 20 f 10 � 18 N 10 � 11 10 � 14 10 � 10 10 � 6 Hz 0.01 100 60 50 40 30 20 10 Due to ∝ e ˙ φ , significant di ff erences from a minor change of V • Garcia-Bellido, do, MP, Unal ’16 0.1 � GW h 2 9 aLIGO 10 � 6 0.001 PBH limit 8 LISA Φ 1 V � M 3 Mp 10 � 9 Φ 2 10 � 5 7 Ξ CMB � 2.41 6 10 � 12 10 � 7 Ξ max � 4.43 Ξ CMB � 2.41 5 Ξ max � 4.43 10 � 9 10 � 15 30 4 20 10 � 9 � 8 � 7 � 6 � 5 � 4 f 10 � 11 N 10 � 18 60 50 40 30 20 10 Hz Φ � Mp 10 � 14 10 � 10 10 � 6 0.01 100

• Mechanism for a peaked distribution of PBH 0.1 0.001 PBH limit 10 � 5 Ξ CMB � 2.41 10 � 7 Ξ max � 4.43 10 � 9 N 10 � 11 60 50 40 30 20 10 ! If su ffi ciently large, at horizon re-entry, d H the perturbation collapses to form a Primordial Black Hole (PBH) Matter / Radiation Inflation A significant fraction of the mass in the horizon collapses M λ into the PBH. So, parametrically, λ ↔ M PBH

PBH dark matter • Zel’dovich, Novikov ’67 PBH and PBH-DM long standing idea • Hawking ’71; Carr ’75; Chapline ’75 Recent interest due to lack of detection of particle Bird et al ’16; • 16; Clesse, Garc ´ ıa-Bellido ’16; candidates, and LIGO / VIRGO events 16; Sasaki et al ’16 • 2 windows, one at ∼ 10 − 12 M ⊙ , and (possibly) one at ∼ 10 − 100 M ⊙ . ∼ 10 15 10 18 10 21 10 24 10 27 10 30 10 33 10 36 10 0 SNe Credit: G. Franciolini, update EROS / MACHO g 10 - 1 k b UFD - of Carr, Kuhnel, Sandstad ’16 γ HSC OGLE G E 10 - 2 and Inomata et al ’17 CMB 10 - 3 10 - 4 Limits from capture from NS and WD 10 - 5 not shown due to uncertainty in DM 10 - 6 10 - 18 10 - 15 10 - 12 10 - 9 10 - 6 10 - 3 10 0 10 3 astrophysical abundance, and on nuclear physics Cut on HSC and on limits from femtolensing of Capela, Pshirkov, Tinyakov ’13 γ -ray bursts. Schwarzschild radius PBH < λ γ Montero-Camacho, Fang, Vasquez, Katz, Kopp, Sibiryakov, Xue ’18 z, Silva, Hirata ’19

PBH enhanched δρ GW ← → Whenever δρ present GW produced • 1) during inflation, by the same source that produced δρ 2) by δρ at horizon re-entry after inflation Mechanism 2 is unavoidable and model-independent • ζ ζ Standard gravitational interaction: h i h i h i ⇒ = ζ ζ Technical (but important !) point. Power spectrum � δρ 2 � � � controls • the amount of GW. Full statistics of δρ relevant for PBH abundance. 0.1 P Ζ � Gaussian � Stronger constraint on P δρ sourced in 0.001 axion infaltion (non-gaussian statistics) P Ζ P Ζ � Χ 2 � 10 � 5 ⇒ Fewer GW 10 � 7 10 22 10 26 10 30 10 34 � � g �

� 10 − 12 M ⊙ f GW ∼ 1 λ ∼ 3 mHz M M λ M ∼ 10 M ⊙ f GW ∼ nHz PTA! ⇒ M ∼ 10 − 12 M ⊙ f GW ∼ mHz LISA! ⇒ Garc ´ ıa-Bellido, MP, Unal ’17 SKA 10 � 6 PTA LISA SKA 10 � 8 Gauss � Ind � Gauss � Ind � 10 � 8 � GW h 2 � GW h 2 10 � 10 10 � 10 Χ 2 � Prim � 10 � 12 Χ 2 � Prim � 10 � 12 10 � 14 10 � 14 10 � 16 0.01 1 10 � 6 10 � 4 12 10 � 7 10 � 11 10 � 10 10 � 9 10 � 8 10 � 6 � f � Hz f � Hz From axion inflation Gaussian δρ

Measurement of the SGWB SGWB from cosmological sources superimposed with astrophysical one. Potential observables to disentangle them Current LIGO bounds 10 − 5 O1 (2 σ ) Spectral shape Ω GW ( f ) O1+O2 (2 σ ) • 10 − 6 Design (2 σ ) Ω BBH+BNS+NSBH Ω BBH+BNS (Median) Net Polarization Ω GW , λ • 10 − 7 Ω BBH+BNS (Poisson) Ω GW Statistics � � Ω n � � 10 − 8 • GW 10 − 9 Directionality x ) Ω GW ( ⃗ • 10 − 10 10 1 10 2 10 3 f (Hz) Measurement of GW polarization Crowder, Namba, Mandic, c, Mukohyama, MP ’12 � α f � − 8 Assume Ω GW , L = Ω α and Ω GW , R = 0 � 10 100 Hz − 10 10 Amplitude needed to detect Ω GW � � − 12 10 and exclude Ω GW , R = Ω GW , L at 2 σ − 14 10 2 nd Gen. H1 − L1 2 nd Gen. H1 − L1 − V1 − K1 3 rd Gen. − 16 10 − 3 − 2 − 1 0 1 2 3 �

One more motivation for an Australian detector ! � � ∆ t detector i ∆ t detector j � d f � � M ij,R ( f ) P GW , R ( f ) + M ij,L ( f ) P GW , L ( f ) � = t t f ∆ M = M R − M L measure of chirality maximized for anti-podal detectors 0.05 0.00 Δ ℳ - 0.05 - 0.10 LL - P - 0.15 Antipodes 0 100 200 300 400 f [ Hz ]