Supergravity and inflationary cosmology Ana Achúcarro

Supergravity and inflationary cosmology Slow roll inflation with fast turns: Features of heavy physics in the CMB with J-O. Gong, S. Hardeman, G. Palma, S. Patil 1005.3848 (PRD 2011); 1010.3693 (JCAP 2011); 1109.xxxx In memoriam Sjoerd Hardeman (1982-2011) Ana Achúcarro (Univ. Leiden / UPV-EHU Bilbao) COSMO 11, Porto, 22/8/11

Observations of the Cosmic Microwave Background anisotropies make a convincing case for inflation

Inflation (accelerated expansion) -dilutes massive relics (e.g. monopoles) -solves horizon problem -solves flatness problem if it lasts long enough (~ 55 e-folds) -gives mechanism for approximately scale invariant, gaussian, adiabatic primordial inhomogeneities (of quantum origin) -produces a background of gravitational waves

Coming soon: CMB polarization, tensor modes, non-gaussianity? (gravitational waves, multi-field inflation, cosmic strings) Planck WMAP-7 from Urrestilla, Mukherjee, Liddle Bevis, Hindmarsh, Kunz 0803.2059

Single-field inflation assumes all other fields are decoupled from the inflaton during inflation. Not so easy to achieve in realistic particle physics models e Extremely difficult in 4D SUGRA and even harder in string theory (because gravity couples to all fields) Gravity is strong at those energies Supersymmetry breaking gets transmitted to all fields inflation is UV sensitive It opens the possibility to detect heavy fields that interact with the inflaton

Image: WMAP The dream

The dream in Elm Street The theorists nightmare The observers nightmare Image: WMAP

The observers nightmare

The dream in Elm Street The theorists nightmare The observers nightmare Image: WMAP

In QFT we expect heavy degrees of freedom to decouple from the low energy dynamics of light ones We can integrate out the effect of heavy fields to get an effective action for the light degrees of freedom Corrections are suppressed by O ( k 2 / M 2 ) But sometimes the prefactors are large

An inflationary trajectory with bends (straight = autoparallel w.r.t. sigma model metric in field space) One field much heavier than the other. Light field rolls slowly down a valley with steep walls. c.f. Chen & Wang 2010 ; Tolley & Wyman 2010 ; Peterson & Tegmark 2010 ; Cremonini, Lalak, Turzynski 2011; Shiu Xu 2011; Baumann Green 2011

Turning trajectories have been studied extensively in the context of inflation with many light fields multifield inflation in the slow roll regime under the assumption of slow/mild turns. Gordon Wands Bassett Maartens 2001 Lalak Langlois Pokorski Turzynski 2007 Groot Nibbelink van Tent 2001, 2002 Peterson Tegmark 2011 The effect of the turn is to couple the adiabatic and isocurvature modes. The curvature perturbation does not remain constant on superhorizon scales, it is sourced by the isocurvature mode. Chen Wang 2010 (M ~ H, quasi single field inflation, equilateral NG) Here we are interested in the effect of very heavy fields (M > H) on the (single) inflaton. In this case, strong turns are consistent with slow roll. The heavy fields are excited and leave an imprint on the primordial spectrum: non-decoupling. The isocurvature mode is very massive, it decays.

Get corrections to the action of order ( turn rate / heavy mass ) 2 or In slow roll inflation In supergravity: Expect masses of order H M 2 ~ O ( H 2 ) the eta problem in SUGRA and field space curvatures of order ~ O ( 1 / M cutoff 2 ) ~ κ -2 κ can be much smaller than M Pl

SUSY/SUGRA actions are entirely determined by three functions: Focus on neutral scalar fields, no gauge fields - need only K, W

N=1 SUGRA with neutral, scalar fields - + fermions Kähler metric (of scalar manifold) Inverse Kähler metric Kähler-covariant derivative Metric and potential controlled by two functions K, W

N=1 SUGRA with neutral, scalar fields - + fermions

Truncating heavy fields at their critical points is a dangerous approximation to make in supergravity inflation. Even if masses and couplings look safe, it misses the effects of turns in the inflationary trajectory -- which are generic unless the critical points are supersymmetric along the whole trajectory -- even after SUSY breaking! Consistent decoupling requires (counterintuitive) direct couplings in the superpotential Sufficiently heavy fields can still be integrated out to get an effective single-field description the corrections due to a turn can be packaged as a (scale-dependent) reduction in the speed of sound of the adiabatic perturbations during inflation Turns generate features in the power spectrum and correlated non-gaussianity that are potentially observable in the CMB

To understand the effect of turns, consider inflation with real scalar fields that span a manifold with metric Gordon Wands Bassett Maartens 2001; Groot Nibbelink Van Tent 2001, 2002;

Action Equations of motion Background

Slow roll, with strong turns - Enforce adiabatic evolution: In a multifield context, everyone agrees about << 1 near-de Sitter background (adiabatic evolution) beyond that, it is letter soup (WARNING: even mean different things to different authors! ) Rule of thumb: slow roll is needed only in tangential direction / derivatives

Eqs. of motion -- tangential projection (single-field inflation) tangential projection Eqs. of motion -- normal projection 2 x kinetic energy radius of turn normal projection

Slow roll parameters << 1 << 1 Project: Not necessarily small (sharp turns are consistent with slow roll inflation)

Perturbations (scalar) Gauge invariant combination (Sasaki Mukhanov) Quantize as coupled oscillators (I, α = 1 n ) Two field case: I = T,N; α = heavy, light

Two field case (allow both signs for turn rate to get continuous def. of normal) see also Tsavara van Tent 1012.6027

Turns are defined with respect to the geodesics of the sigma model metric, irrespective of whether the kinetic terms are canonical or not If the critical points of the potential (the valley ) track a geodesic, these non-decoupling effects from turns disappear. In this case, truncation of the heavy fields is a much better approximation

If the critical points of the potential (the valley ) track a geodesic, these non-decoupling effects from turns disappear. In this case, truncation of the heavy fields to get a single-field description is a much better approximation In Supergravity, this happens if the Kahler invariant function Is such that G heavy = 0 and light G heavy = 0 e.g. if it is separable: Counterintuitive Holds approximately in Large Volume Scenarios and not in KKLT-based models. AA Hardeman Sousa PRD 08; AA Hardeman Oberreuter Schalm van der Aalst 1108.2278 Davis Postma 08 ; Kallosh Linde Olive Rube 2011

Perturbations, parallel and normal coupled by the turning rate Equations of motion (α = heavy, light)

Note the mass of the perturbations is not really given by a b V : The mass matrix Ω contains the tensor a b V, projected, but if M is large and ζ ~ const, the physical mass of the light field is and of the heavy field (independent of ) (reduced by the turning)

If M 2 >> H 2, a sufficiently heavy field can still be integrated out -- At quadratic order get an effective single-field theory with a reduced speed of sound for the adiabatic mode c.f. Tolley Wyman 2010 Expect features in the spectrum and non-gaussianity (equilateral) Creminelli 2003

Power spectrum curvature isocurvature interested in at the end of inflation

Constant turn - spectrum renormalized, no features (constant M, η : constant c s )

Fake primordial spectra - blue:two-field system red: effective theory (slowroll) =2

A proper toy model Non-canonical sigma model metric + easy potential Since turning is defined w.r.t. geodesics of γ ab, potential valleys with ψ= const = 0 are turning if Γ(χ) non-trivial

Hlosek et al 2011 (ACT) Still no evidence of features in the power spectrum

Summary (0) Single field inflation is succesful (so far) but difficult to embed in a UV complete theory (String Theory) (1) Truncating (as opposed to integrating out) heavy fields at their minima misses the coupling effect of turns (curvature and isocurvature perturbations coupled, masses are not given by a b V ) (2) Turns (including sharp ones) are generic in SUGRA (+ ST) (3) They are consistent with slow roll (4) Their effects are of order (5) If the heavy fields are very heavy (M>>H) they can be integrated out. The net effect is a reduced speed of sound for the adiabatic perturbations (6) Expect features (damped oscillations) in the power spectrum correlated with (equilateral) non-gaussianity on the same scales.