The end of inflation. Peter Adshead University of Illinois at Urbana-Champaign

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1 The end of inflation Peter Adshead University of Illinois at Urbana-Champaign

2 (Gauge-preheating and gravitational wave production at) The end of (axion) inflation Peter Adshead University of Illinois at Urbana-Champaign

3 Constraining axion inflation with gravitational waves across 29 decades in frequency Peter Adshead University of Illinois at Urbana-Champaign with J.T. Giblin, M. Pieroni, and Z. Weiner arxiv: arxiv:

4 Constraining axion inflation with gravitational waves across 29 decades in frequency Peter Adshead University of Illinois at Urbana-Champaign Tom Giblin (Kenyon College) Mauro Pieroni (Imperial College) Zach Weiner (UIUC)

5 We re pretty sure inflation, or something like it, happened

6 What happens at the end of inflation We Don t Know!

7 Reheating? Super-horizon adiabatic modes are insensitive to processes happening on sub-horizon scales Only impact is on the unknown expansion history We don t know exactly where on the potential the fluctuations are generated Reheating could provide clues for unification of inflation and SM

8 Whatever energy drives the accelerated expansion must* be directly coupled to matter (SM?) to reheat the Universe

9 Inflaton-matter interactions Assume inflation driven by an axion/pseudoscalar Shift-symmetry severely restricts allowed interactions Only derivative couplings allowed to other degrees of freedom L int = 8f µ F µ F + i C µ 5 µ f µ A A ^ A ^ A ] From an EFT perspective, these interactions must be in the theory

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sha1_base64="6fscwlrreisfvotazdhjgrng/uu=">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</latexit> Reheating: the old story (Abbot, Farhi, Wise 82; Albrecht, Steinhardt, Turner, Wilczek 82 ) Coherent inflaton oscillations look like a collection of massive particles at rest Axion decays to photons Reheating occurs when: H 1 1 Reheating is a slow, smooth, perturbative process A A T / a 3/8 T RH T / a 1 T RH f 109 GeV But of course, this picture is incomplete (Traschen & Brandenberger 90; Shtanov, Traschen & Brandenberger 94; ; Linde, Kofman & Strobinsky 94 )

11 Linear analysis Axially coupled gauge fields are asymmetrically amplified after (and during) axion inflation ~ A(, x) r ~ A(, x) =0 In circular polarization 2 A ± k + k k f Tachyonic enhancement for modes: A ± A ± rad e 2 H! f ah! H ± 2 A ± k =0 f H 1 < k ah < f Largest amplifications when axion rolls the fastest H Linear theory quickly invalid -Numerical simulations required!

12 Re-scattering during inflation V These gauge fields can source (non-gaussian) density 2 +2aH@ + a 2 V 00 = f (E B he Bi) BUT: largest effects occur when inflaton rolls fastest!

13 Black-Holes near the end of inflation To date, the tightest bounds on the coupling arise from estimates of primordial black hole abundances A ± A ± rad e 2 f H ± 2 f H PBH bound f 25m pl <latexit sha1_base64="ittdd/dqf+t+kngxo2kp2jishqw=">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</latexit> N (Linde, Mooj, Pajer 12) We consider couplings well below these

14 Gauge preheating Lower couplings Higher couplings Gauge field modes rapidly produced as inflation ends gauge/ Transition to radiation domination becomes almost instantaneous w = hpi / h i gauge/ gauge/ w w = hpi / h i h i As gauge-fields backreact axion oscillations are strongly damped h i (Mpl) w = hpi / h i h i (Mpl) h i (Mpl) N = ln(a) N = ln(a) N = ln(a)

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sha1_base64="nr7xbxkyssp57t8nbdhffschdei=">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</latexit> GWs from Gauge-Preheating During reheating, axion oscillates and both gauge-helicities generated Rapidly decaying amplitude favors 1st oscillation A + h L h R V ( )= 1 2 m2 2 f (.1M pl) 1 <latexit sha1_base64="qasz//ga/zldzifqcfne74a9vog=">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</latexit> Adshead, Giblin, & Weiner (arxiv: ) Sources a significant topological charge sufficient for gravitational leptogenesis Alexander, Peskin, Sheikh-Jabbari 2004, Adshead, Long & Sfakianakis 2017

17 Generation of gravitational waves stronger coupling larger redshifted to today vacuum fluctuations frequency observed today Adshead, Giblin, & Weiner (arxiv: )

18 <latexit sha1_base64="cmonl+rsawlws2pfr3assesqhbk=">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</latexit> <latexit sha1_base64="axyvc2cbv4s3pyu1k3wctsbdkbo=">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</latexit> <latexit sha1_base64="rex6ephkpwmhrcybqmco9qqr/jy=">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</latexit> <latexit sha1_base64="qolkagl0mqwxatjb+anuqrpebni=">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</latexit> <latexit sha1_base64="83a0h/4w8lapcomyjwhxohrykvs=">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</latexit> Gravitational waves and Neff Peak GW frequency is set by the scale of the source f 1 H end Amin et al. (arxiv: ) Energy density in GW today GW,0 (f ) rad,0 2 2 T TT tot But this radiation; assuming only the SM SMr,0 + GW,0 = 2 15 " # 4 3 Ne 11 T 4 Gravitational waves contribute to Neff: GW,0 = 7 4/3 4 (N e 3.046) = N e,0 8 11

19 <latexit sha1_base64="kmxuxbfyr4kusmtxmuqttjzdlh4=">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</latexit> Complete preheating and gravitational wave production 1.0 max ( gauge/ ) efficient resonance backscattering slow tachyonic resonance 0.2 chaotic 10 6 Planck CMB S4 gw,0h V ( )= 1 2 m2 2 Planck COrE + Euclid CMB-S /f (M 1 pl )

20 <latexit sha1_base64="axyvc2cbv4s3pyu1k3wctsbdkbo=">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</latexit> Dependence on Energy Scale 1.0 Quasi-universality GW production efficiency depends on energy scale max ( gauge/ ) Lower energy-scales require larger preheating amplification and larger gw,0h Planck CMB S4 couplings Larger couplings mean higher momenta become tachyonic /f (M 1 pl ) m = M pl m = M pl m = M pl m = M pl m = M pl Planck COrE + Euclid CMB-S H end <latexit sha1_base64="qolkagl0mqwxatjb+anuqrpebni=">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</latexit> f GW,0 (f ) rad,0 2 2

21 Dependence on potential shape Weak shape dependence All models can completely preheat, and produce detectable GWs max ( gauge/ ) chaotic monodromy Starobinsky D-brane hilltop, p = 4, v =4M pl hilltop, p = 4, v =2M pl GW production efficiency correlated most strongly with scale gw,0h Planck bound COrE + Euclid CMB-S /f (m 1 pl ) Future CMB measurements will rule out/probe preheating efficiency >85% in high-scale models (r > 10-3 )

22 Gauge preheating already constrained by Planck! 10 6 Planck gw,0h CMB S4 Increasing r chaotic Starobinsky monodromy hilltop (p = 4, v =4M pl ) hilltop (p = 4, v =2M pl ) D-brane Planck COrE + Euclid CMB-S max gauge / Gravitational-wave production efficiency (roughly) correlated with tensor-to-scalar ratio

23 Robustness ~1% axion fluctuations remain at the end of the sim. -dominate energy density after 5 e-folds! -But: extremely large gauge-field occupation numbers ~10 12 lead to huge Bose-enhanced decay width Couplings to charged matter generate currents that suppress gauge field production -A more serious worry, though could have a dark U(1) kinetically mix with hyper charge Gravitational back reaction? -More work required stay tuned!

24 Summary Gauge-preheating after axion inflation can be extremely violent Gravitational waves from gauge-preheating will place the tightest bounds on axial couplings to U(1) gauge fields through Neff Gravitational-wave production efficiency (roughly) correlated with tensor-to-scalar ratio Future measurements of r and Neff will constrain axion inflation across 29 decades in frequency!