Primordial Gravitational Waves in String Theory

Transcription

1 Primordial Gravitational Waves in String Theory Susha Parameswaran University of Liverpool String Phenomenology th June 2016 Based on: Phys.Lett. B759 (2016) , Karta Kooner, S.L.P. and Ivonne Zavala JCAP 1604 (2016) no.04, 008, S.L.P., Gianmassimo Tasinato and Ivonne Zavala GRF Gravity Essay, S.L.P. and Ivonne Zavala Susha Parameswaran Primordial Gravitational Waves in String Theory 1/11

2 Three results on the possibility of primordial gravitational waves in string theory 1. Examples of string axions with axion decay constants f /M pl > 1, in contrast to expectations from Weak Gravity Conjecture. 2. Validity of 4D EFT and control over all model building steps during inflation from string theory puts upper bound on r Subleading contributions to V (φ) in stringy Natural or φ 2 Inflation can lower r back into favour of string theory and observations. Susha Parameswaran Primordial Gravitational Waves in String Theory 2/11

3 Primordial gravitational waves, M inf and φ Current bound on primordial gravitational waves is r 0.07, with r 10 2 in 5 yrs, r 10 3 BICEP 15/Planck in 20s. Primordial gravitational waves are related to: Energy density during inflation: M inf V 1/4 inf ( r ) 1/ GeV 0.1 M inf M GUT for values as small as r 10 5! Inflaton field range during inflation: φ ( r ) 1/2 2 M pl 0.01 Lyth 96 Super-Planckian field ranges are necessary for observable pgws difficult to suppress quantum corrections to V inf (φ) which would violate slow roll conditions. Susha Parameswaran Primordial Gravitational Waves in String Theory 3/11

4 Examples of large field axion inflation If inflaton is an axion, shift symmetry can protect slow roll V (φ) from higher-derivative corrections over large field ranges. Natural Inflation φ an open or closed string axion and shift symmetry broken non-perturbatively by instantons: Freese, Frieman, Olinto 90 V (φ) = Λ 4 (1 cos ( )) φ f Slow roll conditions satisfied for f, φ 4M pl, consistency with n s from Planck constrains f, φ 6.8M pl (95%CL). Mononomial Inflation φ an open or closed string axion and shift symmetry broken spontaneously by fluxes ( axion monodromy ) e.g. V (φ) = 1 2 m2 φ 2 Linde 83, Kaloper & Sorbo 08 Westphal & Silverstein 08 Marchesano, Shiu & Urganga 14,... Slow roll conditions satisfied for φ 15M pl (independently of f ). Susha Parameswaran Primordial Gravitational Waves in String Theory 4/11

5 Planck 2015 φ 2 and Natural Inflation are strongly disfavoured compared to Starobinsky/Higgs inflation r 0.1 too large. More about this later... Susha Parameswaran Primordial Gravitational Waves in String Theory 5/11

6 1. No-go for large f /M pl from string theory? Weak gravity conjecture - to avoid stable black hole remnants, a theory of quantum gravity coupled to an Abelian gauge theory in 4D must contain a particle satisfying m M pl g. Arkani-Hamed, Motl, Nicolis & Vafa 06 Susha Parameswaran Primordial Gravitational Waves in String Theory 6/11

7 1. No-go for large f /M pl from string theory? Weak gravity conjecture - to avoid stable black hole remnants, a theory of quantum gravity coupled to an Abelian gauge theory in 4D must contain a particle satisfying m M pl g. Arkani-Hamed, Motl, Nicolis & Vafa 06 Generalisation to axions and instantons - a 4D quantum gravity theory with an axion, must contain an instanton with action S cl M pl /f. Susha Parameswaran Primordial Gravitational Waves in String Theory 6/11

8 1. No-go for large f /M pl from string theory? Weak gravity conjecture - to avoid stable black hole remnants, a theory of quantum gravity coupled to an Abelian gauge theory in 4D must contain a particle satisfying m M pl g. Arkani-Hamed, Motl, Nicolis & Vafa 06 Generalisation to axions and instantons - a 4D quantum gravity theory with an axion, must contain an instanton with action S cl M pl /f. For axion with f > M pl, non-perturbative instanton contributions to its potential will be O(1): Banks, Dine, Fox & Gorbatov 03 e n M pl f e inφ bumps in V (φ) effectively limit axion field range. Susha Parameswaran Primordial Gravitational Waves in String Theory 6/11

9 1. No-go for large f /M pl from string theory? Weak gravity conjecture - to avoid stable black hole remnants, a theory of quantum gravity coupled to an Abelian gauge theory in 4D must contain a particle satisfying m M pl g. Arkani-Hamed, Motl, Nicolis & Vafa 06 Generalisation to axions and instantons - a 4D quantum gravity theory with an axion, must contain an instanton with action S cl M pl /f. For axion with f > M pl, non-perturbative instanton contributions to its potential will be O(1): Banks, Dine, Fox & Gorbatov 03 e n M pl f e inφ bumps in V (φ) effectively limit axion field range. In other words, large f /M pl is not possible in perturbative limits of string theory supported by all known string constructions when conjecture was made. Susha Parameswaran Primordial Gravitational Waves in String Theory 6/11

10 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

11 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < (2π) 2 g θθ l 2 Φ Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

12 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < 4 for torus Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

13 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < 4r 2 0 L 2 for KS warped throat Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

14 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < 4r 0u L 2 for warped resolved conifold Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

15 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < 4r 0u L 2 for warped resolved conifold Probe D5-brane at tip of warped resolved conifold allows f 6.8M pl consistently with supergravity approximation (g s 0.3, ( ls L )2 0.3) S cl > M pl /f?! Kenton & Thomas 14; Kooner, SLP & Zavala 15 Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

16 A Go-Go for large f /M pl in string theory? Avgoustidis & Zavala 08 Kenton & Thomas 14 Kooner, SLP & Zavala 15 Open string axions from probe Dp-brane wrapping warped throat. Figure from Dias, Frazer & Liddle On brane, there is a 4D gauge field and axion (θ position/wl): g 2 4 = (2π) h (3 p)/4 0 g s nv p 3 and f 2 M 2 pl = 1 g s nv p 3 2 h(p 3)/4 0 g θθ ls 2 V6 w Weak gravity conjecture m < M pl g 4 upper bound on f /M pl : f 2 M 2 pl < 4r 0u L 2 for warped resolved conifold Probe D5-brane at tip of warped resolved conifold allows f 6.8M pl consistently with supergravity approximation (g s 0.3, ( ls L )2 0.3) S cl > M pl /f?! Kenton & Thomas 14; Kooner, SLP & Zavala 15 Backreaction? Do instantons couple to axions with a suppressed f < f, to ensure S cl < M pl /f? Susha Parameswaran Primordial Gravitational Waves in String Theory 7/11

17 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

18 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Then r 0.1(M inf /M gut ) 4 implies: ( r ( Minf ) M mod ) 4 ( ) 4 ( Mmod Mkk M kk M s ) 4 ( gs V6 ) 4 Due to fourth powers, bound is very sensitive to numerical factors, and mild changes in g s, curvature and mass hierarchies. Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

19 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Then r 0.1(M inf /M gut ) 4 implies: ( r ( Minf ) M mod ) 4 ( ) 4 ( Mmod Mkk M kk M s ) 4 ( gs V6 ) 4 Due to fourth powers, bound is very sensitive to numerical factors, and mild changes in g s, curvature and mass hierarchies. Assuming mass-squared hierarchies and g s 0.2 gives: r Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

20 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Then r 0.1(M inf /M gut ) 4 implies: ( r ( Minf ) M mod ) 4 ( ) 4 ( Mmod Mkk M kk M s ) 4 ( gs V6 ) 4 Due to fourth powers, bound is very sensitive to numerical factors, and mild changes in g s, curvature and mass hierarchies. Assuming mass-squared hierarchies and g s 0.25 gives: r 0.07 Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

21 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Then r 0.1(M inf /M gut ) 4 implies: ( r ( Minf ) M mod ) 4 ( ) 4 ( Mmod Mkk M kk M s ) 4 ( gs V6 ) 4 Due to fourth powers, bound is very sensitive to numerical factors, and mild changes in g s, curvature and mass hierarchies. Assuming mass-squared hierarchies and g s 0.1 gives: r Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

22 2. Upper bound on r from validity of 4D EFT Observations imply single field, slow roll inflation within 4D EFT. This suggests a hierarchy of scales within string models: e.g. Baumann & McAllister g where M s = M s pl. 4πV6 M inf < M mod < M kk < M s M pl Then r 0.1(M inf /M gut ) 4 implies: ( r ( Minf ) M mod ) 4 ( ) 4 ( Mmod Mkk M kk M s ) 4 ( gs V6 ) 4 Due to fourth powers, bound is very sensitive to numerical factors, and mild changes in g s, curvature and mass hierarchies. Assuming mass-squared hierarchies and g s 0.1 gives: r Observable pgws would be right at the limits of 4D EFT, and depend sensitively on numerical factors and/or moduli stabilisation! Susha Parameswaran Primordial Gravitational Waves in String Theory 8/11

23 3. Subleading effects and φ in axion inflation Leading axion potentials are due to non-trivial vevs (φ 2 inflation) or non-perturbative effects (natural inflation). Susha Parameswaran Primordial Gravitational Waves in String Theory 9/11

24 3. Subleading effects and φ in axion inflation Leading axion potentials are due to non-trivial vevs (φ 2 inflation) or non-perturbative effects (natural inflation). Subleading instanton effects give contributions to V (φ): ( ) nφ Λ 4 n cos f n Susha Parameswaran Primordial Gravitational Waves in String Theory 9/11

25 3. Subleading effects and φ in axion inflation Leading axion potentials are due to non-trivial vevs (φ 2 inflation) or non-perturbative effects (natural inflation). Subleading instanton effects give contributions to V (φ): ( ) nφ Λ 4 n cos f n Corrections change the shape of the potential, depending on their frequency and amplitude. If corrections dominate new minima introduced inflaton trapped in local minimum and slow roll inflation stops. V(ϕ) Banks, Dine, Fox & Gorbatov 03 ϕ Susha Parameswaran Primordial Gravitational Waves in String Theory 9/11

26 3. Subleading effects and φ in axion inflation Leading axion potentials are due to non-trivial vevs (φ 2 inflation) or non-perturbative effects (natural inflation). Subleading instanton effects give contributions to V (φ): ( ) nφ Λ 4 n cos f n Corrections change the shape of the potential, depending on their frequency and amplitude. With tiny modulations inflaton s background trajectory is hardly affected, but imprints seen in CMB large, possibly oscillating, running of scalar spectral index. V(ϕ) ϕ Westphal, Silverstein & McAllister 08 Kobayashi & Takahashi Kappl, Nilles & Winkler 15 Choi & Kim 15 Susha Parameswaran Primordial Gravitational Waves in String Theory 9/11

27 3. Subleading effects and φ in axion inflation Leading axion potentials are due to non-trivial vevs (φ 2 inflation) or non-perturbative effects (natural inflation). Subleading instanton effects give contributions to V (φ): ( ) nφ Λ 4 n cos f n Corrections change the shape of the potential, depending on their frequency and amplitude. If corrections are subleading, but significant sharp cliffs and gentle plateaus sufficient inflation for reduced field range V(ϕ) E.g. tune to give natural inflation with f M pl, φ M pl and: n s = , r = , α s = , β s = ϕ Susha Parameswaran Primordial Gravitational Waves in String Theory 9/11

28 Conclusions 1. Obtained f /M pl > 1 from open string axions on a probe Dp-brane in non-trivial warped sugra geometries. Consistency with axionic WGC? 2. Observable PGWs from string theory are difficult we cannot rely on the hierarchy M inf M mod M kk M s M pl which would keep the string compactification, moduli stabilisation and the 4D EFT under control during inflation. 3. Natural inflation and φ 2 inflation can be restored into the favour of string theory and observations and with distinctive signatures by including subleading corrections to inflaton potential - φ 1, r , α s Susha Parameswaran Primordial Gravitational Waves in String Theory 10/11

29 A WORKSHOP ON STRING INFLATION AFTER PLANCK Liverpool, 7th-9th September 2016 Researchers will come together to work towards an understanding of cosmic inflation from string theory, in the light of the most recent cosmological observations. There will be plenty of time for discussion and collaboration throughout the programme. Participants include: Ana Achucarro Cliff Burgess Renata Kallosh* Antony Lewis Andrei Linde* Fernando Quevedo* Diederik Roest Gianmassimo Tasinato Alexander Westphal Moonlight Mersey, Keith Drury Organisers: Steve Abel Ruth Gregory Susha Parameswaran Radu Tatar Ivonne Zavala * tbc For more information and to register susha@liv.ac.uk