Cosmological Inflation and primordial non-Gaussianities Sbastien - PowerPoint PPT Presentation

Cosmological Inflation and primordial non-Gaussianities Sébastien Renaux-Petel LPTHE - ILP LPSC, Grenoble. 05.02.2014

Outline 1. Description of inflation 2. Beyond the simplest models 3. Primordial non-Gaussianities 4. Quasi-single-field inflation

Outline 1. Description of inflation 2. Beyond the simplest models 3. Primordial non-Gaussianities 4. Quasi-single-field inflation

What is at the origin of all the structures in the universe?

Cosmic history Big Bang Structure LHC Nucleosynthesis formation Cosmic Microwave Inflation Background 3 main puzzles: Dark Matter, Dark Energy, Inflation: a period of accelerated expansion before the radiation era that solves the problems of the Hot Big Bang model

The horizon problem of the Hot Big-Bang model ... comoving (conformal) scale factor time d s 2 = − d t 2 + a ( t ) 2 d ⇥ x 2 = a ( � ) 2 � − d � 2 + d ⇥ x 2 � a H = ˙ cosmic time comoving Hubble scale distance a ( aH ) − 1

... solved by a schrinking comoving Hubble sphere Guth (80) d dt ( aH ) − 1 < 0

3 equivalent definitions of inflation d dt ( aH ) − 1 < 0 • Schrinking Hubble radius: (solving the horizon problem) − ¨ d a dt ( aH ) − 1 = • Accelerated expansion: ( aH ) 2 ˙ ¨ a H with � < 1 a = H 2 (1 − � ) and � ≡ − H 2 d s 2 ' � d t 2 + e 2 Ht d � Almost de Sitter: x 2 ✏ ⌧ 1 • Violation of strong energy condition: Big-Bang puzzles solved: p < − 1 ρ < − 1 3 ρ ⇔ w ≡ p ✓ a f ◆ & 60 N inf ≡ ln 3 a i

Slow-roll single field inflation • Simplest implementation of the above mechanism: scalar field with flat potential in Planck units  M 2 � 2 R − 1 Z d 4 x √− g P 2 g µ ν ∂ µ φ ∂ ν φ − V ( φ ) S = V ( φ ) ' 3 H 2 M 2 ◆ 2 M 2 p ✓ V , φ pl ⌧ 1 2 V V , φφ η ⌘ M 2 ⌧ 1 pl V reheating

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) δ T T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ Canonically h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) √ 2 ✏ ⇣ k v k = a normalized field k 2 � 2 a 2 H 2 � � v 00 v k ' 0 k + δ T sub − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ Quantization h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) (commutation relations) + choice of vacuum fix initial conditions δ T sub − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ Canonically h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) √ 2 ✏ ⇣ k v k = a normalized field k 2 � 2 a 2 H 2 � � v 00 v k ' 0 k + δ T sub − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ H h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) 4 ✏ k 3 (1 + ik ⌧ ) e − ik τ ⇣ k ( ⌧ ) ' p ˙ ζ = 0 δ T super − Hubble sub − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations 1 Gauge-invariant curvature perturbation ⇣ = + 2 ✏�� √ h ζ k ζ k 0 i = (2 π ) 3 P ζ ( k ) δ ( k + k 0 ) ˙ ζ = 0 δ T super − Hubble sub − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

From quantum to temperature fluctuations prediction observation H 4 P ζ ∼ p ˙ M 2 H ˙ ζ = 0 δ T super − Hubble T Tools: General Relativity and perturbative Quantum Field Theory in curved spacetime.

Inflation predicts universe on large scales is: homogeneous isotropic + density fluctuations are: flat adiabatic (no spatial variation of composition of the cosmic fluid) superhorizon at recombination almost scale-invariant almost Gaussian

Observations homogeneous l ( l + 1) C l / 2 π [ µK 2 ] flat adiabatic Gaussian scale-invariant isotropic superhorizon The simplest inflationary models are in full agreement with data

Outline 1. Description of inflation 2. Beyond the simplest models 3. Primordial non-Gaussianities 4. Quasi-single-field inflation

Microphysical origin of inflation? • So far, merely phenomenological description • Physics at the energy scale of inflation is unknown! Observational probe of very high-energy physics • Candidate physical theories motivate much more complicated dynamics than the simplest scenarios (toy models).

The Eta problem V ( φ ) ' 3 H 2 M 2 p ◆ 2 M 2 ✓ V , φ pl ⌧ 1 V 2 V , φφ η ⌘ M 2 ⌧ 1 pl V m 2 φ Why is the inflaton so light? H 2 ⌧ 1 η ⇡ like the Higgs hierarchy problem uv � H 2 m 2 φ ∼ Λ 2

The Eta problem V ( φ ) ' 3 H 2 M 2 p ◆ 2 M 2 ✓ V , φ pl ⌧ 1 V 2 V , φφ η ⌘ M 2 ⌧ 1 pl V m 2 φ Why is the inflaton so light? H 2 ⌧ 1 η ⇡ Supersymmetry ameliorates the problem m 2 φ ∼ H 2 but doesn’t solve it.

UV sensitivity of inflation L = − 1 O δ ( φ ) X 2( ∂φ ) 2 − V 0 ( φ ) + Λ δ − 4 δ Corrections to the low-energy Slow-roll action effective action Unless symmetry forbids it, ∆ V = cV 0 ( φ ) φ 2 presence of terms of the form Λ 2 ◆ 2 ✓ M P φ ∼ c V 0 ∆ m 2 Λ 2 ∼ c H 2 Λ Wilson coefficient c ∼ O (1) ∆ η & 1 + Sensitivity of slow-roll inflation Λ . M P to Planck-suppressed operators

Gravitational Waves CMB polarization P t ∼ H 2 Energy scale measures: of inflation M 2 p

Gravitational Waves CMB polarization observable if: Current constraints: r ≡ P t tensor-to-scalar-ratio & 0 . 01 r < 0 . 11 (95%CL) P ζ

The Lyth bound ✓ d φ ◆ 2 1 Field evolution r = 8 over 60 e-folds dN M p with dN ≡ Hdt ⇣ r ⌘ 1 / 2 ∆ φ ≈ M p 0 . 01 Lyth, 96 Observable gravitational waves require super-Planckian field-variation

The Lyth bound Observable GWs require a smooth potential over a range ∆ φ & M p Sensitivity to the UV-completion of large-field inflation

L ( X ≡ − 1 K-inflation 2 ∂ µ φ ∂ µ φ , φ ) Prototypical 1 ⇣p ⌘ L DBI = − 1 − 2 f ( φ ) X − 1 − V ( φ ) example: f ( φ ) ✓ 1 ◆ Z • Slow-roll regime: φ 2 ⌧ 1 f ˙ ˙ d t d 3 x a 3 φ 2 − V ( φ ) S = 2 φ 2 ⌧ 1 • ‘Relativistic’ DBI regime: s ⌘ 1 � f ˙ c 2 V ( φ ) = m 2 f ( φ ) = λ e.g: and 2 φ 2 φ 4 p m Condition for inflation: λ � 1 M P Inflation despite steep potential! Silverstein, Tong (04) overcomes the eta-problem?

Multifield inflation L = − 1 2 G IJ ( φ K ) ∂ µ φ I ∂ µ φ J − V ( φ I ) φ 2 ( δφ ) σ ⇣ = ( �� ) σ √ 2 ✏ ( δφ ) s Gordon et al, (00) θ φ 1 ✓ k 2 In general (bending trajectories): ◆ ζ ∝ ˙ ˙ θ ( δφ ) s + O super Hubble evolution of the a 2 H 2 curvature perturbation

An illustration McAllister, S.RP , Xu, JCAP , 12 P i P naive N e Hubble crossing naive; one-field; exact (6-field)

Mass scales in realistic set-up Hope: light inflaton, Find: many masses Planck-mass moduli of order H M P M P hard M moduli M moduli to achieve H H unnatural M φ (eta problem) M φ Quasi-single-field Chen, Wang 09

3 numbers to explain them all • Plethora of inflationary models versus three numbers ✓ k ◆ n s ( k � ) − 1 r < 0 . 11 (95%CL) P � ( k ) = A s ( k ⇥ ) k ⇥ k ? = 0 . 05 Mpc − 1 A s = (2 . 441 +0 . 088 Amplitude known since COBE − 0 . 092 ) × 10 − 9 n s = 0 . 9603 ± 0 . 0073 (68%CL) Planck 2013 Scale invariance ruled out at more than 5 sigma

How can we learn more?

Outline 1. Description of inflation 2. Beyond the simplest models 3. Primordial non-Gaussianities 4. Quasi-single-field inflation

Primordial non-Gaussianities • Gaussian approximation: freely propagating particles • Non-Gaussianities measure the interactions of the field(s) driving inflation. Discrimination amongst models which are degenerate at the linear level Particle physics Cosmology Gaussianities Non- Colliders

Beyond toy-models • Embedding inflation into high-energy physics requires the understanding of the cosmological perturbations generated in much more complicated scenarios than the simplest models: - multiple fields - non-standard kinetic terms - intermediate masses - modified gravity I have developped: • General formalisms -- analytical, numerical -- to predict cosmological observables (in particular NGs) in a wide variety of situations. • Applications to interesting early universe models.

Maldacena’s 2003 result Very small non-Gaussianities (much more quantitative statement actually!) UNDER HYPOTHESES • Single field It is now clear that • Standard kinetic term violating any of these assumptions might lead to • Slow-roll observably large NGs. • Initial vacuum state • Einstein gravity