LARGE Volume Models and Superstring Cosmophysics Joseph Conlon, Oxford University 3rd UTQuest Workshop, Hokkaido, 10th August 2012 Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Plan Plan of these two lectures: 1. The LARGE volume scenario (last time) 2. Applications to cosmology ◮ Cosmological moduli problem ◮ Dark radiation and N eff ◮ Inflation/susy tension ◮ Quantum Gravity Constraints on Inflation Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: LARGE Volume SM at local singularity: Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Moduli Stabilisation: LARGE Volume The basic mass scales present are (for V ∼ 3 × 10 7 l 6 s ) M P = 2 . 4 × 10 18 GeV. Planck scale: M S ∼ M P V ∼ 10 15 GeV. String scale: √ M KK ∼ M P V 2 / 3 ∼ 10 14 GeV. KK scale m 3 / 2 ∼ M P V ∼ 10 11 GeV. Gravitino mass � � M P ∼ 10 12 GeV. Small modulus m τ s ∼ m 3 / 2 ln m 3 / 2 m U ∼ m 3 / 2 ∼ 10 11 GeV . Complex structure moduli m τ b ∼ M P V 3 / 2 ∼ 4 × 10 6 GeV. Volume modulus M soft ∼ M P V 2 ∼ 10 3 GeV. Soft terms Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Cosmological Moduli Problem Review: Moduli are assumed to displace from their minimum after inflation. Neglecting anharmonicities their equation of motion is φ + 3 H ˙ ¨ φ + m 2 φ φ = 0 and so oscillations start at 3 H ∼ m . Moduli redshift as matter and come to dominate universe energy density. Hot Big Bang is recovered after moduli decay and reheat Standard Model. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Cosmological Moduli Problem Moduli can decay via 2-body processes, e.g. Φ → gg , Φ → qq , etc For direct couplings such as Φ Φ F µν F µν ∂ µ C ∂ µ C or 4 M P 2 M P the ‘typical’ moduli decay rate is m 3 1 φ Γ ∼ M 2 16 π P with a lifetime � 3 � 3 � 4 × 10 6 GeV � 40TeV 10 − 6 s τ ∼ 1 s ≡ m φ m φ Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Cosmological Moduli Problem The corresponding Hubble scale at decay is � 3 � m φ H decay ∼ 3 × 10 − 10 eV 4 × 10 6 GeV and so � 3 / 2 � � 1 / 4 = (1GeV) m φ V 1 / 4 3 H 2 decay M 2 � decay = P 4 × 10 6 GeV For masses less than ∼ 40TeV, the reheating temperature is too cool to allow for BBN. Even for heavier moduli, the reheating temperature is relatively low. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Coupling of Moduli in LVS The decay widths of moduli are determined by the strengths of their couplings to matter. Distinguish between local (‘small’) and global (‘bulk’) moduli and local and global matter. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Coupling of Moduli in LVS Couplings are √ ∼ 1 V 1 Local moduli to local matter on same cycle ∼ ≫ M s M P M P 1 Local moduli to bulk/ distant matter ∼ √ V M P 1 Bulk moduli to bulk matter ∼ M P 1 Bulk moduli to local matter ∼ M P These couplings determine the decay widths and moduli lifetimes. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Coupling of Moduli in LVS Moduli lifetimes are then M P (ln V ) 3 or M P (ln V ) 3 Γ τ s ∼ V 2 V 4 M P Γ U , S ∼ V 3 M P Γ τ b ∼ V 9 / 2 Bulk volume modulus outlives all other moduli by at least a factor √ V (ln V ) 3 ≫ 1. Therefore volume modulus τ b comes to dominate energy density of universe independent of post-inflationary initial conditions. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Cosmological Moduli Problem in LVS In sequestered scenario ( V ∼ 3 × 10 7 ): M S ∼ M P V ∼ 10 15 GeV. String scale: √ m 3 / 2 ∼ M P V ∼ 10 11 GeV. Gravitino mass � � M P ∼ 10 12 GeV. Small modulus m τ s ∼ m 3 / 2 ln m 3 / 2 m U ∼ m 3 / 2 ∼ 10 11 GeV . Complex structure moduli m τ b ∼ M P V 3 / 2 ∼ 4 × 10 6 GeV. Volume modulus M soft ∼ M P V 2 ∼ 10 3 GeV. Soft terms � 3 / 2 � m φ � 1 / 4 = (1GeV) V 1 / 4 3 H 2 decay M 2 � decay = P 4 × 10 6 GeV Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Cosmological Moduli Problem in LVS Moduli decays occur at � 3 / 2 � � 1 / 4 = (1GeV) m φ V 1 / 4 3 H 2 decay M 2 � decay = P 4 × 10 6 GeV This is well above BBN and so solves cosmological moduli problem. Note that the sequestered LVS scenario is crucial here. If m soft ∼ m 3 / 2 , then volume modulus has m τ ∼ 1MeV and τ decay > 10 11 years. Suppression of soft terms with relation to m 3 / 2 is what allows the volume modulus to avoid the cosmological moduli problem. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Cicoli, Conlon, Quevedo 1208.xxxx Higaki, Takahashi, 1208.xxxx Normally a systematic analysis of reheating in string models is very hard. Calabi-Yaus have O (100) moduli and generic models of have many moduli with comparable masses and decay widths - need to perform a coupled analysis. LVS has the single light volume modulus with a parametrically light small mass. Reasonable to expect modulus τ b to dominate the energy density of universe and be sole driver of reheating. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Focus on one particular observable: N eff . N eff measures the ‘effective number of neutrino species’ at BBN/CMB: in effect, any hidden radiation decoupled from photon plasma. Observation has a consistent preference at 1 → 2 σ level for N eff − N eff , SM ∼ 1 . Various measurements: ◮ BBN ◮ 3 . 7 ± 0 . 75 (BBN Y p ) ◮ 3 . 9 ± 0 . 44 (BBN, D / H ) ◮ CMB ◮ 4 . 34 ± 0 . 85 (WMAP 7 year, BAO) ◮ 4 . 6 ± 0 . 8 (Atacama, BAO) ◮ 3 . 86 ± 0 . 42 (South Pole Telescope, BAO) Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS We aim to study decay modes of τ b . Any decays of τ b to hidden radiation contribute to N eff − N eff , SM . To be hidden radiation , a field must remain relativistic up to CMB decoupling. This requires m � 10eV: axions are ideal candidates for such light and protected masses. For reheating by volume modulus decays, LVS has one guaranteed contribution to hidden radiation: bulk volume axion Im( T b ) which is massless up to effects exponential in V 2 / 3 ≫ 1. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Decay to bulk axion is induced by K = − 3 ln( T + ¯ T ). This induces a Lagrangian 3 3 4 τ 2 ∂ µ τ∂ µ τ + 4 τ 2 ∂ µ a ∂ µ a L = For canonically normalised fields, this gives � ∂ µ a ∂ µ a L = 1 2 ∂ µ Φ ∂ µ Φ + 1 8 Φ 2 ∂ µ a ∂ µ a − 3 M P 2 This gives m 3 1 Φ Γ Φ → aa = M 2 48 π P Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Decay to Higgs fields are induced by Giudice-Masiero term: H u H ∗ H d H ∗ T ) + ZH ∗ u H ∗ T ) + ZH u H d K = − 3 ln( T + ¯ u d d T ) + T ) + ( T + ¯ ( T + ¯ ( T + ¯ ( T + ¯ T ) Effective coupling is � ∂ µ ∂ µ Φ ∂ µ ∂ µ Φ � � Z 2 + H ∗ u H ∗ H u H d d 2 3 M P M P This gives Γ Φ → H u H d = 2 Z 2 m 3 Φ M 2 48 π P Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Other decays: ◮ Decays to SM gauge bosons are loop suppressed and so � α � 2 m 3 φ negligible, Γ ∼ 4 π M 2 P ◮ Decays to SM fermions are chirality suppressed and so negligible, Γ ∼ m 2 f m φ M 2 P ◮ Decays to MSSM scalars are mass suppressed and so m 2 Q m φ ˜ negligible, Γ ∼ P . M 2 ◮ Decays to RR U(1) gauge fields are volume suppressed and m 3 φ negligible Γ ∼ P . V 2 M 2 ◮ Decays to bulk gauge bosons are not suppressed but are model dependent. ◮ Decays to other axions are not suppressed but are model dependent. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Important points are: ◮ The only non-suppressed decay modes to Standard Model matter are to the Higgs fields via the Giudice-Masiero term. ◮ There is always a hidden radiation component from the bulk axion. ◮ Both rates are roughly comparable and unsuppressed. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
Reheating and N eff in LVS Assuming Z = 1 and just volume axion gives BR (Φ → hidden) = 1 3 Volume axion remains massless and is entirely decoupled from Standard Model. This branching ratio corresponds to N eff ∼ 4 . 7. This is approximately the right order if observational hints of dark radiation persist. Note hidden radiation also follows only from volume modulus couplings - it does not assume TeV-scale susy. Joseph Conlon, Oxford University LARGE Volume Models and Superstring Cosmophysics
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