Inflation as a Solution to the Early Universe Entropy Problem

Inflation as a Solution to the Early Universe Entropy Problem Pisin Chen Phys. Dept. & LeCosPA, NTU KIPAC, Stanford University PC, P.-S. Hsin, Y. Niu, arXiv:1212.1087 IEU Cosmology Conference, Seoul. Korea, June 3-5, 2013 IEU Cosmology Conference

Thermodynamic Time Asymmetry • Thermodynamic law dictates natural process to evolve toward higher entropy. • Oldness of universe very low entropy at beginning “(Low) Entropy Problem” • Don Page (echoed by Sean Carroll}: Inflation cannot by itself solve the problem. • “Special” initial condition required: small kinetic energy • beg for even lower entropy to be accounted for. (R. Penrose, R. Wald, S. Carroll, D. Page, B. McInnes, B. Greene,…) IEU Cosmology Conference

We will demonstrate… • Inflation occurred with a probability that is higher than what is commonly believed. • Subsequently a lower entropy state is dynamically induced by inflation itself. • A large amount of entropy is generated after it reaches a minimum during inflation. The secret lies in Entanglement Entropy. IEU Cosmology Conference

How to Measure Probability? • System states {1, 2, 3,…N} • Equal weight (generic): equal probability • Unequal weight: one state can be much more probable than others. • Different measure different probability • Equal: special initial condition, hard to occur • LQG measure: not so special, higher probability (Ashtekar & Sloan 2011) IEU Cosmology Conference

How to Measure Probability? • Different probability measures are equivalent to different ways of counting entropies. • Three possible measures: - Thermal entropy Ill-defined for lack of universal temp. during infla. - Statistical entropy Not applicable due to long-range gravitational int. - von Neumann Entanglement entropy Most suitable IEU Cosmology Conference

Entanglement Entropy • When inflation occurs, a horizon is formed: Hilbert spaces in observable and unobservable regions are quantum mechanically entangled. • We suggest that a more appropriate way to measure probability of inflationary metric configuration is through entanglement entropy: • Existence of horizon enhances entanglement entropy: inflation has better probability to occur according to this more rigorous measure. IEU Cosmology Conference

Inaccessible Particle Horizon • Light path: • Farthest that light can travel: • For rapid expansion, the integral converges and light can only travel finite coordinate distance particle horizon! • For slower expansions,light can travel to farther distances IEU Cosmology Conference

Tracing Out Hilbert Space Outside Particle Horizon t Light travels beyond x accessible up to x a' t slice a IEU Cosmology Conference

Entanglement & Entropy Problem • Bi-partite entanglement entropy of (3+1)-spacetime QFT system:(Ryu and Takayanagi 2006) • l ~ a : length of the boundary (particle horizon) • c0<0 for a wide class of bosonicsystems • Decreasing entropy at the onset of inflation leads to a low entropy state, which ameliorates the entropy problem IEU Cosmology Conference

Homogeneous vs. Inhomogeneous Entangled Entropy Two contributions to the entropy of the Universe: • Homogeneous The von Neumann entropy measures the entanglement due to evolution of background metric; probability of different histories. • Inhomegenous Entanglement between opposite momentum sectors in the universe. IEU Cosmology Conference

To investigate whether there is indeed a decreasing entanglement entropy, we present a concrete computation using quantum mechanics (Canonical Quantum Gravity) IEU Cosmology Conference

Model We invoke the following model to track entropy: • Early universe as a quantum system • Unitarity, standard framework • Generalized Chaplygin Gas: smoothly patches inflation and radiation eras without phase singularity. inflation Example: β=-1, γ=-2 radiation IEU Cosmology Conference

Result(I): Homogeneous EE • Solving Wheeler-deWitt (WDW) equation under FRW metric and minisuperspace treatment with spatial dependence suppressed. • Total action: IEU Cosmology Conference

Early time approximation WKB approx. wavefunction for WDW; Entanglement between inside and outside horizon IEU Cosmology Conference

Result(I): Homogeneous Part of EE • Late time (radiation dominant era) approx. Indicates the decrease of entropy during transition from flation to radiation IEU Cosmology Conference

Relation to the Area Law • Leading term in the regularized entanglement entropy is proportional to the boundary area. • The calculated homogeneous entanglement entropy in the semi-classical region agrees with area law. Takayanagi et al (2009),Iwashita et al (2006), Muller & Lousto (1995)... IEU Cosmology Conference

Result(II): Inhomogeneous EE • Distribution of wavepacket in a fully QM treatment IEU Cosmology Conference

Result(II): Inhomogeneous EE • Tree-level cosmological perturbation • Entanglement between opposite momenta IEU Cosmology Conference

Revisit of Homogeneous EE under QM Correction IEU Cosmology Conference

Is Decreasing Entropy Physical? • Non-equilibrium effect • Quantum fluctuation (e.g. Boltzmann’s brain) • Early particle production in observable region As the system in observable region dissipates, its density matrix decreases, indicating slow-down of particle production (moving toward equilibrium) IEU Cosmology Conference

Conclusion • Entanglement entropy as probability measure suggests inflation does not need special initial condition. • Numerical computation shows a low entropy state is induced during inflation. Possibly from non-equilibrium physics. • Subsequent evolution of entropy is shown to be increasing, which is consistent with thermodynamic time arrow. IEU Cosmology Conference

Future Directions • Numerical study of the decrease using effective field theory and replica method • Apply our method of calculating entanglement entropy from canonical quantum gravity to other gravitational systems, e.g. Black Hole IEU Cosmology Conference

Happy Birthday, Alex! IEU Cosmology Conference

Inflation as a Solution to the Early Universe Entropy Problem