Emergence of Fluctuations from a Tachyonic Big Bang

1. Emergence of Fluctuations from a Tachyonic Big Bang Sugumi Kanno McGill University work with Robert H. Brandenberger & Andrew R. Frey PRD 76, 083524 (2007); arXive:0706.1104 [hep-th]

2. Introduction One of the most important problems in cosmology is the existence of singularity. There have recently been several proposals to study the resolution of cosmological singularities in string theory. Postulating a tachyon condensate phase of closed string in the very early universe is one of these new proposals. McGreevy & Silverstein (2005) We will make a first attempt to connect such an early stringy phase of cosmology to the origin of cosmological fluctuations In particular, we will consider two possible cosmological implications. Trans-Planckian problem The initial conditions for string gas cosmology

3. Comoving present horizon size Trans-Planckian problem Length Scale Initial conditions are set deep inside the horizon in the Planck Phase Planck Phase Still in Planck Phase time Inflation ends Present day Need quantum gravity Can we see the trans-Planckian physics?

4. Even if without the inflation, thermal fluctuations of string gas created in the Hagedorn phase may produce the curvature perturbations with a flat spectrum consistent with the current observations. Nayeri et al. (2006) Comoving present horizon size Structure formation scenario in String Gas Cosmology Length Scale Length Scale Thermal distribution of string gas Quasi-static Hagedorn phase Quasi-static spacetime Radiation & Matter Inflation time Present day No trans-Planckian problem. However, how can we realize the thermal equilibrium of string gas?

5. General relativity (String scale) String theory + Tachyon Effects Conformal inv. General relativity (near the singularity) String theory = finite Singularity at the beginning of the universe Let us consider the flat toroidal universe Non-linear sigma model approach is a good approximation Spacetime Metric Einstein eq. The path integral diverges However, this can be avoided by considering the effects of tachyon.

6. Tachyon condensation in field theory Ex) Higgs Mechanism Field theory In the high temperature phase, the ground state is a symmetric point. As the temperature goes down, the effective potential changes to a double well potential. The symmetric point becomes tachyonic. Tachyon indicates an instability of the vacuum. eventually, the field rolls down to the true ground state. Tachyon Tachyon Condensation As a result, the symmetry is spontaneously broken. In string theory, tachyon can change the geometry.

7. Tachyon condensation in string theory closed tachyon modes open string tachyon modes Tachyon Condensation Tachyon Tachyon Condensation Tachyon Ex) Implies the annihilation of spacetime Ex) Implies the pair-annihilation of branes

8. 0 To describe this, we take a model <--- No Tachyon (future) = <--- Tachyon condensates (All modes: massive & frozen) (past) Resolution of the singularity by tachyon condensation McGreevy & Silverstein (2005) We assume a winding tachyon state exists. Mass for the winding mode Tachyon appears Tachyon Condensation Phase Tachyon Tachyon Condensation The tachyon condensation is supposed to lifts the closed stiring degrees of freedom, this leads to a phase of nothing. Thus, the closed string tachyon condensation resolves the singularity We will show the cosmological fluctuations emerge in a thermal state.

9. Our Scenario time Standard cosmology Inflation / String gas cosmology We consider around this period Weak tachyon condensation phase Strong tachyon condensation phase

10. Details

11. Gauge choice : Static gauge fixed E.O.M. Need to Solve model Need to know parameters : Consider a small scale Action Neglect cosmic expansion Tachyon We want the worldsheet Hamiltonian to obtain the string state. Momentum conjugate for t Tachyon In the weak tachyon condensation phase, we can treat tachyon contribution as a perturbation

12. determined (Late time) We concentrate on the massless modes eigenvalue of the operator Equations of motion for fluctuations We expand in Fourie modes: Mode functions: Const. of integration Weak Tachyon Condensation Phase: Maching to the usual mode excitation and ignore all other oscillators. Then, the worldsheet Hamiltonian becomes Wave eq.

13. In general, does not coincides with T Bogoliubov coefficients Using the variables out in Tachyon Condensation Tachyon free Incident wave transmitted reflected This implies particle creation. Bogoliubov coefficients (Scattering problem) What we need is to calculate the reflection coefficient in this potential.

14. (Past) Thermal fluctuations emerge Let us expand the field operator by in and out mode functions We assume the state is in vacuum The number density of created string modes Planck distribution with temperature given by We have shown that cosmological fluctuation modes emerge from the tachyon condensate phase in a thermal state.

15. discussion Case of connection to inflation scenario If the initial tachyon phase is connected to late time cosmology via a period of cosmological inflation and an e-folding number is larger than the minimal number to solve the problems of standard cosmology, we would see trans-Planckian signature in CMB. Otherwise, our analysis support the use of the Bunch-Davis vacuum for fluctuations Case of connection to string gas cosmology If the tachyon phase is a precursor phase of the quasi-static Hagedorn phase, our result naturally gives the initial condition for string gas cosmology in which the fluctuations are assumed to be thermal.