Baryogenesis via Cosmic Quantum Fluctuation Adrian Manning School of Physics, University of Sydney ARC Centre of Excellence for Particle Physics at the Terascale Based on arXiv:1506.01511 OUTLINE 1 The Problem - Matter/Anti-Matter Asymmetry 2 The Model - Baryogenesis as a Quantum Fluctuation 3 Plausibility - Can it work? MATTER/ANTI-MATTER ASYMMETRY • The Observable Universe is predominantly made of matter • Big Bang Nucleosynthesis (BBN) - Requires a baryon asymmetry: (nB−n¯B) −11 ηB = s ≈ 8:6 × 10 • The Standard Model has no mechanism in which to generate this amount of asymmetry with standard cosmology • There are potential solutions: • Leptogenesis • GUT Theories • Extra Particles, Forces, Interactions Baryogenesis as a Quantum Fluctuation 1 / 11 MATTER/ANTI-MATTER ASYMMETRY • The Observable Universe is predominantly made of matter • Big Bang Nucleosynthesis (BBN) - Requires a baryon asymmetry: (nB−n¯B) −11 ηB = s ≈ 8:6 × 10 • The Standard Model has no mechanism in which to generate this amount of asymmetry with standard cosmology • There are potential solutions: • Leptogenesis • GUT Theories • Extra Particles, Forces, Interactions Baryogenesis as a Quantum Fluctuation 1 / 11 MATTER/ANTI-MATTER ASYMMETRY • The Observable Universe is predominantly made of matter • Big Bang Nucleosynthesis (BBN) - Requires a baryon asymmetry: (nB−n¯B) −11 ηB = s ≈ 8:6 × 10 • The Standard Model has no mechanism in which to generate this amount of asymmetry with standard cosmology • There are potential solutions: • Leptogenesis • GUT Theories • Extra Particles, Forces, Interactions Baryogenesis as a Quantum Fluctuation 1 / 11 MATTER/ANTI-MATTER ASYMMETRY • The Observable Universe is predominantly made of matter • Big Bang Nucleosynthesis (BBN) - Requires a baryon asymmetry: (nB−n¯B) −11 ηB = s ≈ 8:6 × 10 • The Standard Model has no mechanism in which to generate this amount of asymmetry with standard cosmology • There are potential solutions: • Leptogenesis • GUT Theories • Extra Particles, Forces, Interactions Baryogenesis as a Quantum Fluctuation 1 / 11 SAKHAROV CONDITIONS Typical extensions to the SM involve mechanisms which provide the following: • B violation • C and CP violation • Departure from thermal equilibrium Can we achieve the asymmetry without these conditions? Baryogenesis as a Quantum Fluctuation 2 / 11 PROPOSED SOLUTION • Assume an inflationary epoch, with no initial baryon asymmetry • Propose that hBi = 0 • In general we expect hB2i 6= 0 • Expect hB2i to grow during the inflationary epoch • Propose that this quantum fluctuation is large enough at the end of inflation to give rise to the observed baryon asymmetry Baryogenesis as a Quantum Fluctuation 3 / 11 PROPOSED SOLUTION • Assume an inflationary epoch, with no initial baryon asymmetry • Propose that hBi = 0 • In general we expect hB2i 6= 0 • Expect hB2i to grow during the inflationary epoch • Propose that this quantum fluctuation is large enough at the end of inflation to give rise to the observed baryon asymmetry Baryogenesis as a Quantum Fluctuation 3 / 11 PROPOSED SOLUTION • Assume an inflationary epoch, with no initial baryon asymmetry • Propose that hBi = 0 • In general we expect hB2i 6= 0 • Expect hB2i to grow during the inflationary epoch • Propose that this quantum fluctuation is large enough at the end of inflation to give rise to the observed baryon asymmetry Baryogenesis as a Quantum Fluctuation 3 / 11 PROPOSED SOLUTION • Assume an inflationary epoch, with no initial baryon asymmetry • Propose that hBi = 0 • In general we expect hB2i 6= 0 • Expect hB2i to grow during the inflationary epoch • Propose that this quantum fluctuation is large enough at the end of inflation to give rise to the observed baryon asymmetry Baryogenesis as a Quantum Fluctuation 3 / 11 PROPOSED SOLUTION • Assume an inflationary epoch, with no initial baryon asymmetry • Propose that hBi = 0 • In general we expect hB2i 6= 0 • Expect hB2i to grow during the inflationary epoch • Propose that this quantum fluctuation is large enough at the end of inflation to give rise to the observed baryon asymmetry Baryogenesis as a Quantum Fluctuation 3 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -OVERVIEW • Use an inflationary epoch approximated by de-Sitter space • Introduce a new complex scalar field, φ^(x) which caries unit baryon charge • Impose U(1)B global symmetry representing baryon number which is strictly conserved • Calculate the baryonic charge uncertainty in φ^(x) at the end of inflation • Estimate the size of the baryonic fluctuations over the size of the observable universe after inflation • Can the baryon asymmetry be the result of a large scale quantum fluctuation? Baryogenesis as a Quantum Fluctuation 4 / 11 MODEL -DETAILS • Inflationary action in conformal time: Z 00 3 µν ∗ a 2 ∗ 1 S = d x dη η @µΦ @ν Φ + − (ma) Φ Φ a = − a ηH • With comoving field operator ^ 1 ^ ^ ^ Φ = p Φ1 + iΦ2 = a(η)φ 2 • Comoving charge operator ^ ^ ^ ^ ^ Q(η;~x) = Φ2@ηΦ1 − Φ1@ηΦ2 Baryogenesis as a Quantum Fluctuation 5 / 11 MODEL -DETAILS • Inflationary action in conformal time: Z 00 3 µν ∗ a 2 ∗ 1 S = d x dη η @µΦ @ν Φ + − (ma) Φ Φ a = − a ηH • With comoving field operator ^ 1 ^ ^ ^ Φ = p Φ1 + iΦ2 = a(η)φ 2 • Comoving charge operator ^ ^ ^ ^ ^ Q(η;~x) = Φ2@ηΦ1 − Φ1@ηΦ2 Baryogenesis as a Quantum Fluctuation 5 / 11 MODEL -DETAILS • Inflationary action in conformal time: Z 00 3 µν ∗ a 2 ∗ 1 S = d x dη η @µΦ @ν Φ + − (ma) Φ Φ a = − a ηH • With comoving field operator ^ 1 ^ ^ ^ Φ = p Φ1 + iΦ2 = a(η)φ 2 • Comoving charge operator ^ ^ ^ ^ ^ Q(η;~x) = Φ2@ηΦ1 − Φ1@ηΦ2 Baryogenesis as a Quantum Fluctuation 5 / 11 MODEL -DETAILS • Evaluate Charge-Charge correlator at the end of inflation over a comoving scale, ` = j~x − ~yj Z ¯ 2 3 3 ^ ^ Q` = d x d y W`(~x)W`(~y)hQ(ηinf;~x)Q(ηinf;~y)i • Gaussian window function 1 −|~xj2=2`2 W`(~x) = 3 e (2π) 2 `3 • Charge-Charge correlator @2 @ @ hQ^ (x)Q^ (x0)i = 2 G(x; x0) G(x; x0) − G(x; x0) G(x; x0) @η@η0 @η0 @η Baryogenesis as a Quantum Fluctuation 6 / 11 MODEL -DETAILS • Evaluate Charge-Charge correlator at the end of inflation over a comoving scale, ` = j~x − ~yj Z ¯ 2 3 3 ^ ^ Q` = d x d y W`(~x)W`(~y)hQ(ηinf;~x)Q(ηinf;~y)i • Gaussian window function 1 −|~xj2=2`2 W`(~x) = 3 e (2π) 2 `3 • Charge-Charge correlator @2 @ @ hQ^ (x)Q^ (x0)i = 2 G(x; x0) G(x; x0) − G(x; x0) G(x; x0) @η@η0 @η0 @η Baryogenesis as a Quantum Fluctuation 6 / 11 MODEL -DETAILS • Evaluate Charge-Charge correlator at the end of inflation over a comoving scale, ` = j~x − ~yj Z ¯ 2 3 3 ^ ^ Q` = d x d y W`(~x)W`(~y)hQ(ηinf;~x)Q(ηinf;~y)i • Gaussian window function 1 −|~xj2=2`2 W`(~x) = 3 e (2π) 2 `3 • Charge-Charge correlator @2 @ @ hQ^ (x)Q^ (x0)i = 2 G(x; x0) G(x; x0) − G(x; x0) G(x; x0) @η@η0 @η0 @η Baryogenesis as a Quantum Fluctuation 6 / 11 MODEL -DETAILS • Two-point Function: 0 ^ ^ 0 ^ ^ 0 G(x; x ) = hΦ1(x)Φ1(x )i = hΦ2(x)Φ2(x )i 3~ Z d k ~ 0 = Φ (η)Φ∗(η0)eik·(~x−~x ) (2π)3 k k • de-Sitter mode