Phenomenology of Axion Inflation

Transcription

1 Phenomenology of Axion Inflation based on Flauger & E.P Flauger, McAllister, E.P., Westphal & Xu Barnaby, EP & Peloso to appear Enrico Pajer Princeton University Minneapolis Oct 2011

2 Outline 1 Motivations 2 Review 3 Gravitational Waves at Interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

3 Outline Motivations 1 Motivations 2 Review 3 Gravitational Waves at Interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

4 Motivations Tensor modes and the Lyth bound Assuming slow-roll inflation and N CMB e-foldings dφ = dn r 2ɛ dn M pl 8 φ r N CMB > M pl Measuring tensor modes puts a lower bound on the range of variation of the inflaton [Lyth 98] In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem. This is the main motivation to consider axion inflation Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

5 Motivations Tensor modes and the Lyth bound Assuming slow-roll inflation and N CMB e-foldings dφ = dn r 2ɛ dn M pl 8 φ r N CMB > M pl Measuring tensor modes puts a lower bound on the range of variation of the inflaton [Lyth 98] In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem. This is the main motivation to consider axion inflation Schematically Tensor modes High scale Large field more UV-sensitive Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

6 UV-sensitivity Motivations EFT approach: learn about higher scales studying UV-sensitive observables. Inflation is a UV-sensitive mechanism. Schematically V (φ) = 1 2 m2 φ 2 + n φ n λ n M n 4 pl Within string theory and supergravity many models suffer from an η-problem. Invoke a shift symmetry to protect flatness Study all the couplings allowed by the symmetry Find a UV embedding in which the symmetry is realized Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

7 Axion Inflation Motivations Many realizations: Shift symmetry protects the flatness of the potential. E.g. Natural Inflation with non-perturbative effects [Freese et al 90] Superplanckian axion decay constants f are elusive. [Banks et al. 03] Multiple axions can avoid this problem: [Peloso et al 04], Dante s Inferno [Berg et al 09], N-flation [Dimopoulos et al 05] Axion mixing with a 4-form [Kaloper & Sorbo 08] Axion monodromy from controlled explicit shift-symmetry breaking [Silverstein & Westphal (1+McAllister)] Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

8 Axion Inflation Motivations Many realizations: Shift symmetry protects the flatness of the potential. E.g. Natural Inflation with non-perturbative effects [Freese et al 90] Superplanckian axion decay constants f are elusive. [Banks et al. 03] Multiple axions can avoid this problem: [Peloso et al 04], Dante s Inferno [Berg et al 09], N-flation [Dimopoulos et al 05] Axion mixing with a 4-form [Kaloper & Sorbo 08] Axion monodromy from controlled explicit shift-symmetry breaking [Silverstein & Westphal (1+McAllister)] Logic Tensor modes Large field Shift symmetry Shift-symmetric couplings Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

9 Motivations The effective potential Inflaton action has more than just the slow-roll potential as consequence of the shift-symmetry L = 1 2 φ2 V sr (φ) 1 ( ) φ 4 F 2 Λ 4 cos αφ f 4f F F Oscillating (but monotonic) potential f M pl many short ripples, stronger coupling α O(1) in generic EFT (we will compute it in string theory) Any shift-symmetric model (large field) should come with these couplings Tensor modes correlate with other observables Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

10 Outline Review 1 Motivations 2 Review 3 Gravitational Waves at Interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

11 Review Correlated Observables Observable tensor modes (r.01) naturally correlate with 1 Non-perturbative oscillatoric contribution leading to Oscillations in the two point function Detectably large and oscillatoric three point function (resonant non-gaussianity) 2 Coupling to gauge fields leading to Additional efoldings close to the end of inflation due to the strong backreaction Additional contribution to scalar and tensor power spectra with strong running Scale dependent equilateral non-gaussianity from inverse decay Gravitational waves detectable at interferometers such as LIGO/VIRGO Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

12 Review Background equations Extra terms from the tachyonic gauge fields φ + 3H φ + V = α f E B 3H 2 = 1 M 2 p [ 1 2 φ 2 + V + 1 ] 2 E 2 + B 2 Gauge fields sources grow [Anber & Sorbo 08, Barnaby & Peloso 10] since ξ α φ 2fH E B 4 H ξ 4 e2πξ E 2 + B 2 4 H ξ 3 e2πξ Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

13 Review Numerical background evolution Inflation lasts longer due to extra friction in = 2.5 = H / V /f < E.B > / V / M p N N Additional O(10) efoldings have important consequences. Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

14 CMB Phenomenology Review The scalar power spectrum is (for φ M pl f and Λ 4 /(V f) 1) ( ) k ns 1 ( )] φk P s (k) = A s [1 + δn s cos k f δn s 3 Λ4 2πf V f 2ɛ Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

15 Review Observational constraints on the spectrum The best fit next to the unbinned WMAP5 data looks like C 2Π ΜK C 2Π ΜK The improvement of the fit is not statistically significant. The bound of WMAP5 data on the parameters of the model is roughly Λ 4 /(V M pl ) < 10 4 Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

16 Review Resonant non-gaussianity Large non-gaussianity from modulations Modulations on the potential violate slow roll and can induce large non-gaussianity. Resonant non-gaussianity [Chen et al. 08]. They are very large and are not scale invariant. Resonant non-gaussianity is orthogonal to any other known shape. No constraints on it yet. Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

17 Review Resonant of non-gaussianity Direct analytical computation [Flauger & Pajer 10] ζ k1 ζ k2 ζ k3 = (2π) 7 4 δ 3 (k 1 + k 2 + k 3 ) ζ k1 2 f res k2 2 k2 3 ( ) ( ) 2ɛ sin f log K/k + f k i 2ɛ cos 2ɛ k j f log K/k f res 3 2πΛ 4 8V f ( ) 3/2 2ɛ. f i,j Large resonant non-gaussianity Liner in Λ 4 as for the spectrum Spectrum and bispectrum are correlated and observable. Non-scale-invariant due to the sinusoidal oscillation Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

18 Review Inverse Decay in Axion Monodromy r Inverse decay A 2 δφ generates running of the spectral tilt and non-gaussianity All effects are controlled by ξ φα 2Hf Current bound ξ < 2.6 from non-gaussianity % CL 1000 WMAP WMAP7+BAO+H p=2 68% CL f NL id p= n s f / M p Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

19 Review What is the coupling in string theory? Axion inflation in string theory with a monodromy from an NS5-brane [McAllister, Silverstein & Westphal 08]. The DBI action after S-duality gives S = d 4 x g [ B4 F µν F µν C4 ] F µν Fµν, B Two regimes 1 τ 2 (2π) 3 g s g2 g s τ 2 + (2πφ/f) 2, C C 0g 2 sφ (2π) 2 f, C 0 g s 1 ξ M 2 pl 2φ 2 C 0g s C 0 g s C 0 g s 1 ξ M 2 pl 2φ 2 (C 0g s ) 3 (C 0 g s ) , Observable only for C 0 g s 7 In a toy IIB flux compactification this happens.5% of the time Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

20 Review Summary of Scalar Observables Remarkably, the coupling to a D5-brane would be α 2πg s v2 s.06 Summarizing, all signals are competitive Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

21 Gravitational Waves at Interferometers Outline 1 Motivations 2 Review 3 Gravitational Waves at Interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

22 Gravitational Waves at Interferometers It looks vary hard... The standard vacuum contribution from inflation is quite small Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

23 Gravitational Waves at Interferometers But is it theoretically possible? Conservatively, consider Advanced LIGO s sensitivity around 10 2 Hz Not to stop inflation requires There is a viable window! Ω GW Ω R,0 12π 2 h 0 2 > M 2 plḣ2 3M 2 pl H2 h < h 2 1 LISA/ELISA and Einstein Telescope will broaden this window Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

24 Gravitational Waves at Interferometers Numerical Results Axion inflation with α f φf f is the existence proof Current f NL limit 1e-08 1e-10 N CMB = 60 LISA AdvLIGO CMB Adv LIGO GW h 2 1e-12 = 2.66 = 2.33 ET ET 1e-14 1e-16 = N CMB (p=1) 1e-12 1e-10 1e-08 1e f / Hz Signal at LIGO/VIRGO correlated with non-gaussianity in CMB Visible for N 60 Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

25 Gravitational Waves at Interferometers What about the Scalars? Perturbation theory requires ζ 2 1 In the weak backreaction regime P ζ P T ɛ 2 In the strong backreaction regime again P ζ P T ɛ 2. One ɛ from δφ = ζ 2ɛ. The other? Close to the end of inflation ɛ.1, so perturbation theory is OK (but close). Also tensors from particle production scale the same. There should be a reason... Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

26 Gravitational Waves at Interferometers Summary Observable tensor modes, through symmetry arguments, correlate with Oscillation in the spectrum Resonant non-gaussianity Running of spectral tilt Inverse decay equilateral NG Gravitational waves at interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24

27 Gravitational Waves at Interferometers Summary Observable tensor modes, through symmetry arguments, correlate with Oscillation in the spectrum Resonant non-gaussianity Running of spectral tilt Inverse decay equilateral NG Gravitational waves at interferometers Enrico Pajer (Princeton) Phenomenology of Axion Inflation UMN / 24