Chaire Galaxies et Cosmologie Inflation and new paradigms Françoise Combes Overview Whyyj inflation? Observational justification History of the model Principle of « slow roll » inflation Hybrid inflation, eternal inflation, Curvaton Inflation in string theory Observat iona l constra ints : Pl anck 2015 Critics and problems -Alternatives? Why is inflation needed? Exponential expansion (~1030) between 10-36s and 10-32s the problems of horizon, of homogeneity the problem of universe flatness ppp(g)roblem of monopoles (+strings, textures, etc..) Problem of monopoles (and other textures) • At very high energy in the very hot Big-Bang, all forces of physics are unified (GUT) T = 1014 GeV • Then occur several breaks of symmetry in cascade, and in particular the electro-magggpnetic group • At each symmetry break, magnetic monopoles are created (stable) • The energy of a monopole ~ 1016 GeV, mass ~ 1.8x101.8 x 10-8 g • With one per horizon , ~17x101.7 x 1065 g/cm3 (GUT epoch) , -15 3 -29 3 then 10 g/cm today >> c =10 g/cm Monopole, in Onion shape 15 ~10 x mp The horizon problem • The horizon at the CMB epoch was < 2° -5 • Why TCMB is the same within 10 everywhere? (regions non causally linked) Homogeneity 14 -35 TGUT=10= 10 GeV, at t=10 s and today -4 TCMB = 2..04 10 eV (2 .77K) Expansion of a= 4 1026 Horizon(GUT)=3 10-25cm Homogeneity (t=0) ~102cm!! Inflation solves the horizon problem In absence of inflation, the horizon is cdt/a(t) 2/3 1/3 l (tdec,0) = 2ctdec/adec, and the ratio a l(t0,tdec) = 3c/adectdec t0 1/3 R =2/3(= 2/3 (tdec/t0) =0. 02<< 1 4 R becomes 4 10 , i.e. Universe horizon 2x106 mooewre with inflati on . today During inflation, the horizon in comoving coordinates contracts! (system at rest % expp)ansion) Time Elementary region causally linked tdec Inflation dilutes also the magnetic monopoles Guth (1997) RfReferen tiltial at rest The observer accompanies the inflation of space The horizon is constant Comoving referential The obse rve r is at rest The horizon shrinks The inflation solves the problem of flatness Whatever initial conditions The exponential expansion of a factor ~1030, reduces the curvature term kc2/a2 by a factor 1060 Inflation, source of fluctuations at t < 10-32s today The scalar field which is the source of inflation is called inflaton The universe is empty at the start (just contains vacuum fluctuations) Corresponds to the de Sitter solution After the era ditddominated bditiby radiation, then by matter, the Universe becomes empty again (at 70%?) & starts another inflation Fluctuations of quantum origin Quantum Mechanics (QM): virtual particles in the vacuum During inflation,,g regions causally connected, are suddenly disconnected: particles cannot annihilate any more WlthWavelength (d)(mode) Quantic ~a~exp(Ht) Horizon =c/H ~ cste Frozen waves > horizon Creation of gravit waves (tensor mode) Black hole Temperature ~1/H Kinney 2003 10 Inflation between t~10-35s GUT sca le Until t=70/H~10-32s H= 21053km/s/Mpc ! a(t) eHt = 2.5 x1030 The temperature at the end of inflation is the same, bfthbecause of the latent heat liberated in the phase transition T= 1014 GeV Otherwise T~1/a(t) Amplitude of perturb. ~same whthhen they cross the horizon Inflation: the only model for the anisotropies of the cosmic background Before Planck wihWMAPith WMAP + Ground experiments Eliminates the generation of fluctuations by cosmic defects Guth 2007 Conservation of energy? Nothing is created from nothing! nihil fit ex nihilo Parmenides (greek philosopher, ~500 av J-C), Lucrece (R ome ~100 av. J -C), de Rerum Natura Scalar field (from GUT?) has the property to be in equilibrium in a false vacuum, where E ≠ 0 Then the field could slowly roll towards the true vacuum E=0 Negative pressure of false vacuum P=-c2 AiiActs as a negative gravity The universe starts very small ~10-25cm, Its size increases by 1030, and its energy of 1090 (volume); but its gravitational energy is very negative, and compensates exactly. The energy of all the created matter is taken on the gravitational energy Inflation GUT: GrandUnificationofforces GUT: Gaussian fluctuations, with a power spectrum The fluctuations are self -similar, with no characteristic size Except at horizon crossing Power law with flat slope ns = 1 + O(10-2) Compatible with Planck (2015) ns = 0.966 + 0.006 Adiabatic fluctuations In the case of simple inflation, one predicts: --A flat universe,,g homogeneous and isotro pic --Gaussian and adiabatic fluctuations, with a flat spectrum --Spectrum slope ns = 1 + 0.1 Scalar field? All gauge bosons correspond to « vectors » of spin 1 The graviton has spin 2 HhHas a tensor character As a scalar (spin 0) there is only the Higgs boson, could it be related to the inflaton? Non-gaussianity Amplitude quantified by the coefficients fNL computed from the 3 -point correlations Or also called « bi-spectrum » B(k1,k2,k3) =<(k1)(k2)(k3)> = 3 3 fNL(2 (k1+k2+k3)b(k1,k2 ,k3) (k) is the Fourier transform of the fluctuation, and b(k1,k2,k3) defines the shape of the triangles Local shape of fNL Equilateral shape Komatsu 2008 Results from Planck The gaussianity is confirmed at the level of 0.03%, but finer constraints could reveal the cosmological model The gravitational lenses generate some non-gaussianity Thissusbecoecedbeoe must be corrected before making gees the test local f NL = 272.7 + 585.8, equil f NL = -42 +75, ortho f NL = -25 + 39 In the future, better constraints Flatness at 0.01%, and non-ggyaussianity at 0.005% (fNL~5) Inflation confirmed, but ekpyrotic or cyclic scenario in difficulty Some words of history • Theory of Landau-Ginzburg, of symmetry breaking (1950) for superconductors: phase transition of 2nd order, order parameter Minimisation of Lagrangian: yields an order parameter cancelling for T= Tc • Inflation proposed by Alexei Starobinski (1979/80, URSS) and Alan Guth (1980/81, USA). But the Guth mechanism requires a modification to get out of inflation New inflation, proposed by A. Linde, A. Albrecht, P. Steinhardt independantly in 1982 • The first inflationary models: phase transition of 1st order, then of 2nd order • Eventually without phase transition at all, as in the chaotic inflation, supposed deriving from chaotic initial conditions Potential Depends on the ambiant temperature with respect to Tc Criticl temperature Tc~3 1014 GeV Schema for an inflation with tunnelli ng eff ect The thermal fluctuations +tunnelling effect transition false true vacuum, terminating inflation in certain regions, or “bubbles”. All terminates when the expandi ng b ubbl es t ouch each oth er, merge and heat the matter Schema for a chaotic inflation Wihithout ph ase transi iition, if Ec << V Requires that the field is homogeneous on scales >> horizon!! New potential In fact these models do not work, too inhomogeneous, not efficient for the re-heating The potential must have a smaller slope (slow roll) The inflaton decays into photons, and matter particles The quantum oscillations create initial perturbations Constant energy during inflation, efficient heating of matter bifltby inflaton, or Hi ggs b oson ? New and old inflation Smooth exit from inflation Inflation scenario -33 -5 94 3 Quantum, Lp= 10 cm, Mp= 10 g, = 10 g/cm Problems of models with phase transition The bubbles have a too fast expansion, Leaving the universe devoid of structures Fine tuning is necessary to avoid the collisions between bubbles (forming monopoles, domains, etc.) Fine tun ing of th e mech ani sm to exihflit the false vacuum, metastabl e Once the fine tuningg,g is done, to agree with the CMB , the bubbles collide too frequently Use a field potential with a slow roll instead of tunneling effect (solves the absence of monopoles, or cosmic defects) Use quantum fluctuations as initial conditions (avoids fine tuning) Inflation as an harmonic oscillator V() = m2/2 2 V’() = m2 V’’() = m2 Eternal Inflation generated by the quantum fluctuations several expansions possible Chaotic inflation Linde 1986 The equations Energy density V() = m2/2 2 Einstein equation H2 = 8G/3 H2 = ( a / a ) 2 = 8G m2/6 2 X Klein-Gordon slow roll (Relativistic Shrödinger) with V’ = m2 = 3H, k=m2 Similar to the equation of an harmonic oscillator with friction (Hubble friction) xx kx 0 Principle of the inflation Large values of field + large values of H large friction The field varies veryyy, slowly, therefore its value in energy is quasi constant a(t) eHt In this case , there is no false vacuum , nor phase transition Conditions for inflation There must exist a “slow roll”, therefore a slow decrease of the potential , but how much? Requires H ~constant, or –dH/dt << H2 2 2 2 2 2 H = V /(3 Mp ) –dH/dt /H = Mp /2 (V’/V) = 2 2 = Mp /2 (V’/V) << 1 2 = Mp V’’/V << 1 N=ln(af/ai) V/V’ Si V() = m2/2 2 V’() = m2 V’’() = m2 2 = 2 (Mp/) << 1 >> Mp Chaotic or eternal inflation It i s diffi cult t o st op i nfl ati on everywh ere. O ne can st op it i n a bubble in particular, produce a re-heating, and the creation of particles in a universe , but space continues its expansion elsewhere Each region of the Universe evolves independantly, according to the Initial values of quantum parameters The i nfl ati on self -maitiintains, i n a ch aoti c way, and und dfidtiefined time There is no start, no end eternal inflation (Linde 1986) Inevitable! Guth 2007 Evolution of the inflaton field Because of quantum fluctuations, the probability to come back to large values of is not zero These regions produce a strong inflation and involve a large fraction of the volume Film A.