Holographic Model of Cosmic (P)reheating

Transcription

1 Holographic Model of Cosmic (P)reheating Yi-Fu Cai 蔡一夫 University of Science & Technology of China New perspectives on Cosmology, APCTP, Feb 13 th 2017 In collaboration with S. Lin, J. Liu & J. Sun, Based on ,

2 Outline What is cosmic (p)reheating? A pedagogical description of Perturbative Reheating A QFT description of Nonperturbative Preheating Addressing preheating at strong coupling A holographic description of Cosmic Preheating Conclusions

3 What is cosmic (p)reheating? Story goes back to the Inflationary Big Bang

4 Chronicle of inflationary big bang s Birth Inflation begin s Inflation end Hot big bang

5 Inflationary Cosmology Guth 1981; Starobinsky 1980; Sato 1981; Fang 1981; Linde 1982; Consider Its cosmic evolution follows the Friedman equation and the Klein- Gordon equation: This model yields an accelerating phase at high energy scale, when the amplitude of the scalar is larger than the Planck mass. Chaotic inflation: Linde 1983

6 Solution to Horizon Problem Cosmic Time 13.8 billion years 370,000 years Big Bang

7 Solution to Horizon Problem Cosmic Time 13.8 billion years 370,000 years Inflation ~ seconds Big Bang

8 Inflationary Cosmology Solved the horizon, flatness, monopole problems. Primordial fluctuations lead to the formation of LSS, LSS CMB Nearly scale invariant and adiabatic power spectrum of primordial perturbations.

9 The End of Inflation Our universe was cold and empty Dominated by φ s field condensate Energy remain restored inside φ s potential Q: How to initiate the hot big bang? Reheating

10 The End of Inflation Our universe was cold and empty Dominated by φ s field condensate Energy remain restored inside φ s potential Q: How to initiate the hot big bang? Reheating Old viewpoint of Reheating Instantaneous phase transition Abbott, Farhi, Wise 1982; Dolgov, Linde 1982; Dynamics mainly depends on the temperature

11 Modern viewpoint of (P)reheating Physics of (P)reheating can be extremely fruitful A series of dynamical stages exist before the thermalization Inflaton oscillations Dolgov, Kirilova, 1990; Traschen, Brandenberger 1990; Kofman, Linde, Starobinsky 1994; Resonant particle excitations Big Bang begins

12 Modern viewpoint of (P)reheating Physics of (P)reheating can be extremely fruitful A series of dynamical stages exist before the thermalization Connecting the end of inflation with the beginning of hot big bang The origin of all elementary particles in the universe However, unclear issues remain

13 Unclear issues of (P)reheating Preheating involves more parameters. Namely, the equation of state parameter: w the sound speed parameter: c s the uncertainty of e-folding number: ΔN They are important to precision cosmology.

14 Unclear issues of (P)reheating Preheating involves QFT description under extreme environments: extremely high energy scales: ~10 12 GeV extremely violent instability: Mathieu equation extremely nonlinear dynamics: Turbulence with re-scattering They require delicate selection of model parameters to guarantee a successful preheating.

15 A pedagogical description of Perturbative Reheating

16 Phase of post-inflationary oscillations Near the minimum, the inflaton oscillates with a gradually damping amplitude following: The background universe behaves as a pressure-less one.

17 Two-field reheating model Consider that the inflaton couples with an entropy field via a toy model: The equation of motion in Fourier space are:

18 Two-field reheating model Dynamics of the inflaton s energy density follows, The energy transfer is realized from the field condensate φ to the particle χ via the channels φφ χχ and φ χχ. Respectively, the cross section and decay rate are given by,

19 Two-field reheating model Dynamics of Perturbative Reheating: When H>Γ, ρ φ ~ a -3 ~ t -2 When H<Γ, ρ φ ~ e -Γt At the moment of decay, there is Thus, the reheating temperature is approximately

20 Two-field reheating model Dynamics of Perturbative Reheating: When H>Γ, ρ φ ~ a -3 ~ t -2 When H<Γ, ρ φ ~ e -Γt At the moment of decay, there is Thus, the reheating temperature is approximately Failure of decay! Decay via φ χχ is incomplete. The process of the annihilation becomes nonlinear, nonperturbative & far from thermal equilibrium.

21 A QFT description of Nonperturbative Preheating Honorable researcher: Lev Kofman

22 Cosmic Preheating with QFT description For the same model without φχχ term, we rescale The equation of motion becomes

23 Cosmic Preheating with QFT description For the same model without φχχ term, we rescale The equation of motion becomes Solving Mathieu Equation

24 Cosmic Preheating with QFT description For the same model without φχχ term, we rescale The equation of motion becomes Solving Mathieu Equation There exist unstable phases to enhance the χ field exponentially when q>1

25 Cosmic Preheating with QFT description Narrow Resonance with q<1: Broad Resonance with q>1:

26 Cosmic Preheating with QFT description The modes of χ undergo parametric resonance: Each time φ crosses the bottom, the number density of χ particles will increase for all modes within the resonance band.

27 Cosmic Preheating with QFT description The modes of χ undergo parametric resonance: Each time φ crosses the bottom, the number density of χ particles will increase for all modes within the resonance band. Comments: CYF, Brandenberger, Zhang 2011 The above result is generic to both inflation and bounce cosmologies

28 Cosmic Preheating with QFT description The modes of χ undergo parametric resonance: Each time φ crosses the bottom, the number density of χ particles will increase for all modes within the resonance band. Comments: The above result is generic to both inflation and bounce cosmologies Condition of broad resonance leads to a lower bound for the coupling parameter g Condition of controllable back-reaction leads to an upper bound for g

29 Cosmic Preheating with QFT description The modes of χ undergo parametric resonance: Each time φ crosses the bottom, the number density of χ particles will increase for all modes within the resonance band. Comments: The above result is generic to both inflation and bounce cosmologies Condition of broad resonance leads to a lower bound for the coupling parameter g Condition of controllable back-reaction leads to an upper bound for g Typically, a successful preheating with QFT description roughly requires:

30 Holographic description of cosmic preheating

31 Motivations Cosmic preheating has already become highly nonperturbative and nonlinear even at the weakly coupled case No first principle guarantees that the couplings between the inflaton and other fields were weak Lessons from heavy ion collisions reveal that a physical system at high energy scales may be strongly coupled However, the QFT treatment fails to characterize cosmic preheating at strong coupling

32 A holographic model Holographic principle connects a QFT system at strong coupling with a gravitational environment at weak coupling by mapping it to the boundary. Since preheating occurs in an expanding universe, we should study within the AdS-FRW geometry, which can be conformally mapped to the AdS-Schwarzschild background. We consider a holographic superconductor model Ψ: dual to the inflaton, (Ψ + is vev and Ψ - source); A M : dual to (fermionic) entropy fields, in particular, A t

33 Phase diagram analysis In analogy to holographic superconductors, there is a PT at a critical chemical potential. Above it, the system is dominated by the field condensate of inflaton; while, below it, the system is dominated by entropy field.

34 Phase diagram analysis In analogy to holographic superconductors, there is a PT at a critical chemical potential. Above it, the system is dominated by the field condensate of inflaton; while, below it, the system is dominated by entropy field. The order of the PT depends on the choice of model parameter: n. Namely, it is 2 nd order for n = 2 and 1 st order for n = 3. For n = 3, the bulk background yields two solutions, Sol1: Sol2: a vanishing source Ψ - = 0 but a nonzero vev Ψ + 0

35 Phase diagram analysis In analogy to holographic superconductors, there is a PT at a critical chemical potential. Above it, the system is dominated by the field condensate of inflaton; while, below it, the system is dominated by entropy field. The order of the PT depends on the choice of model parameter: n. Namely, it is 2 nd order for n = 2 and 1 st order for n = 3. For n = 3, the bulk background yields two solutions, Sol1: Sol2: a vanishing source Ψ - = 0 but a nonzero vev Ψ + 0 The phase diagram can be characterized by the difference of free energy density.

36 Phase diagram analysis The difference of free energy density takes PT occurs along the lower curve ΔW > 0: metastable state with nonzero vev ΔW < 0: stable state with vanishing vev

37 Quasi-normal mode analysis One can study the detailed evolution of PT by analyzing the QNMs We turn on pert modes Then we study the frequencies of these modes in Fourier space by taking the form of

38 Quasi-normal mode analysis The frequency of QNMs as functions of wave number k and the inflaton s vev Ψ +, respectively: The amplification of entropy field is the most efficient at small k regime; A larger vev of the inflaton triggers a more dramatic energy transfer, as the imaginary part of frequency is linear to the inflaton s vev.

39 Cosmological implications The boundary of AdS-FRW corresponds to a 4D FRW universe We focus on the a t component of the QNMs, which is related to the entropy field creation Mapping to the boundary, one gets Divided by the boundary area, the density of entropy field takes

40 Comparison with preheating at weak coupling Results: Holographic preheating Preheating at weak coupling Comments:

41 Comparison with preheating at weak coupling Results: Holographic preheating Preheating at weak coupling Comments: Preheating at strong coupling is featured by continuous particle production;

42 Comparison with preheating at weak coupling Results: Holographic preheating Preheating at weak coupling Comments: Preheating at strong coupling is featured by continuous particle production; The number density during preheating contains 1/a 3 factor due to the damping from cosmic expansion;

43 Comparison with preheating at weak coupling Results: Holographic preheating Preheating at weak coupling Comments: Preheating at strong coupling is featured by continuous particle production; The number density during preheating contains 1/a 3 factor due to the damping from cosmic expansion; A large inflaton s vev tends to trigger a rapid growth of entropy field. However, for strong coupling, the exponent of matter creation grows as the vev linearly; for weak coupling, the vev appears merely in power law function.

44 Conclusions The history of cosmic (p)reheating is a key element to initiate the hot big bang It attempts to explain the origin of all elementary particles as observed today It contains rich dynamics, including perturbative particle production, nonperturbative resonance, re-scattering, fragmentation, turbulence, thermalisation So far most of attention was paid on preheating at weak coupling, otherwise, the QFT description would fail A holographic description was proposed to characterize the preheating at strong coupling

45 Conclusions In holographic preheating particles were produced continuously in contrast to discontinuous excitations at weak coupling The scenario of holographic preheating can initiate fruitful studies from many perspectives: To include the bosonic entropy fields To explore more information about the QNMs To examine the backreaction of cosmological perturbations To connect with fundamental theories To search for possible observable signatures: GWs, cosmological collider signals,

46 The Cosmology Group at USTC Based on the CAS key laboratory of Galaxy and Cosmology, our research interests includes, Cosmology (theory, numerics, observations) Quantum/Classical Gravity physics Dark Energy, Dark Matter Galaxy formation and evolution Supermassive black holes, AGN We invite applicants for postdoc/faculty positions in relevant fields, in particular, the CMB physics. The successful applicants will join an exciting group of the Ali CMB project, and, will extensively interact with other groups. Thanks!