MASAHIDE YAMAGUCHI. Quantum generation of density perturbations in the early Universe. (Tokyo Institute of Technology)

Transcription

1 Quantum generation of density perturbations in the early Universe MASAHIDE YAMAGUCHI (Tokyo Institute of Technology) New Generation Quantum Theory -Particle Physics, Cosmology, and Chemistry-

2 Contents Introduction Our Universe has fruitful structure Inflationary Universe Vacuum energy density Generation of primordial perturbations Primordial density perturbations Primordial tensor perturbations (gravitational wave) Cosmic microwave background anisotropies Summary

3 Introduction

4 Our Universe has fruitful structure The Cosmic Perspective, Bennett et al. Why and how was this kind of structure formed?

5 Formation of structure The structures of the Universe such as stars and galaxies are formed from the primordial density fluctuations, which grow due to the instabilities of gravity. Talk by Prof. Taruya How do you confirm the presence of such primordial density fluctuations?

6 Recombination Around 380,000 year, free electron combines with proton to form hydrogen atom so that photon freely travels, which can be observed as cosmic microwave background.

7 Cosmic microwave background anisotropies WMAP This is a snapshot of the Universe around 380,000 year. We can observe primordial perturbations of order of Then, how were such primordial density fluctuations generated???

8 Inflation practically erases any perturbations You may wonder if the sources of these structures (primordial density perturbations) have existed since the onset of the Universe. This is not the case because inflation effectively erases any structure. (a: scale factor, size of the Universe) (usual (non-relativistic) matter) (inflation energy)

9 Inflationary expansion Microscopic scale Size of galaxy expansion during second Any structure is effectively erased.

10 Inflationary Universe

11 Inflation connects small scales to large scales. Microscopic scale e.g m Size of galaxy During inflation, quantum effects are very important.

12 Inflation is caused by unusual energy The expansion of the Universe is determined by not energy but energy density of the Universe from general relativity simply because, unless the Universe is finite, the total energy diverges. For usual matter, the energy density decreases as the Universe expands because the volume increases. In order to keep inflation long, the energy density of the Universe must be almost constant even though the Universe expands rapidly!! Is there such an energy?

13 Position (potential) energy density = energy determined by state

14 Position (potential) energy density does not decrease as the Universe expands. Energy density of standard matter decreases as the Universe expands. (credit: J.Yokoyama) Position(potential) energy density is determined by a state so that it does not necessarily decrease as long as the state does not change.

15 Vacuum Classically, vacuum is just an empty state. Quantum mechanically, vacuum is a state, in which no real particle exists but a pair of virtual particle and anti-particle is created due to uncertainty principle. Vacuum can have its energy density, which causes inflation.

16 Quantum field theory Quantum mechanics : uncertainty principle Special relativity : mass-energy equivalence Quantum field theory : Virtual particles are continuously created even in a vacuum state, in which no real particle exists. Then, vacuum fluctuates and has energy, which is confirmed as Casimir effects.

17 Casimir effects Area : S Energy for electromagnetic (or scalar) field : separation : a Without boundary (plate), any mode is allowed. Vacuum energy With boundary (plate), only some modes are allowed.

18 Effective action Classically : Effective action : Γ(φ) Action : Euler-Lagrange equation: Quantum mechanically: Effective action Γ(φ) : State of vacuum (vacuum expectation value of a scalar field) Legendre transformation Euler-Lagrange equation including quantum effects :

19 inflation Starobinsky, Guth, Sato Simplest case: Vacuum energy density : V(φ) Slow-roll inflation V(φ) If kinetic term is negligible, the energy density is dominated by the potential energy. State of vacuum (vacuum expectation value of a scalar field) (a : scale factor, H : Hubble parameter) The Universe expands exponentially, which is called inflation.

20 From inflation to big-bang After the rapid expansion (inflation) ends, the vacuum energy is released as the latent heat (called re heating) so that the hot and dense Universe (Big-bang Universe) is realized. Vacuum energy density : V(φ) Decay into radiation inflation oscillation ρ Reheating : Γ = H (start of big-bang cosmology) inflation oscillation Radiation Dominant State of vacuum (vacuum expectation value of a scalar field) te tr t time

21 Generation of primordial perturbations

22 Primordial density fluctuations The position,φ, fluctuates quantum mechanically. Vacuum energy density Uncertainty principle These quantum fluctuations are stretched to cosmological scales thanks to inflationary expansion, and become seeds to produce stars and galaxies. microscopic scale inflation vacuum state (expectation value of scalar field) cosmological scale How are these fluctuations transformed into density fluctuations?

23 V Primordial density fluctuations II ρ Γ = H (Almost Gaussian) fluctuates inflation oscillation phi inflation oscillation(md) RD te tr t time Density fluctuation Almost scale invariant fluctuations are predicted.

24 Primordial gravitational waves

25 Three dynamical degrees of freedom During inflation, we have three dynamical degrees of freedom : One scalar degree of freedom causing inflation Gravity itself has two dynamical degrees of freedom

26 General Relativity (1915) General relativity enabled us to describe the dynamics of spacetime itself. Einstein equation Spacetime Matter Young Albert Einstein in Munich Equation of motion(geodesic)

27 Gravitational waves Spacetime has its own dynamical degree of freedom (GW): Even without matter, spacetime can fluctuate and its fluctuation propagates. Image credit: R. Hurt Caltech/JPL. Very recently, LIGO team detected such a gravitational wave directly. In this case, GWs are generated by the merger of the black holes.

28 Primordial tensor fluctuations (gravitational waves) (Starobinsky) Vacuum fluctuates quantum mechanically. Vacuum energy density Geometry itself fluctuates (irrelevant to scalar dynamics) vacuum state (expectation value of scalar field) (directly probes the energy density of the Universe) Such vacuum fluctuations generate not only density fluctuations, but also ripples of spacetime, i.e. gravitational waves as quantum gravity effects (quantization of spacetime).

29 Generic predictions of inflation Spatially flat universe Almost scale invariant, adiabatic, and Gaussian primordial density fluctuations Almost scale invariant and Gaussian primordial tensor fluctuations (gravitational waves) Generate anisotropies of CMB.

30 Inflation makes our Universe spatially flat observable region The Universe becomes effectively flat due to rapid expansion Predict spatially flat Universe

31 These primordial fluctuations generate cosmic microwave background anisotropies.

32 Recombination Around 380,000 year, free electron combines with proton to form hydrogen atom so that photon freely travels, which can be observed as cosmic microwave background.

33 Temperature anisotropy CMB MAP by PLANCK Planck 2015 results. I

34 (Angular) powerspectrum of temperature fluctuations observed by PLANCK Anugular power θ Angle θ~ 180 / l Red line : prediction by inflation Blue points : observation by PLANCK Large scale Small scale well consistent

35 Constraints on density and tensor perturbations from the PLANCK satellite Observational constraints : Theoretical predictions : As predicted by inflation, density perturbations are almost scale invariant (ns=1). This deviation is important which implies inflation is dynamical. (TT+lowP+lensing) Unfortunately, primordial GWs are not yet observed, which constrains inflation models. Planck 2015 results. XX

36 Parameter dependence Abundance of dark matter Abundance of nucleons Total energy density Geometry of our Universe

37 Present state of our Universe 13.8 billion years old Dark matter Nucleons Dark energy We do not know the identification of more than 95% of content. As predicted by inflation We do not know when inflation happened & which field caused inflation.

38 Summary Our Universe has a fruitful structure, which is formed from primordial perturbations through gravitational instabilities. Such primordial perturbations are generated as quantum fluctuations during inflation. These primordial perturbations are tested by the observations of cosmic microwave background anisotropies. Unfortunately, primordial tensor perturbations (GWs) have not yet been observed, whose detection determines when inflation happened and is an evidence of quantum gravity effects.