[Paper Review] Inflation as a Solution to the Early Universe Entropy Problem

Pisin Chen, Po-Shen Hsin+1 more|arXiv (Cornell University)|Dec 5, 2012

Advanced Thermodynamics and Statistical Mechanics40 references3 citations

TL;DR

This paper proposes that inflation itself dynamically generates the low initial entropy required by the thermodynamic arrow of time, resolving the early universe entropy problem. Using a nonlinear generalized Chaplygin gas model, it shows that cosmological entanglement entropy rapidly decreases during inflation to a minimum before rising monotonically, implying that low entropy is not an initial condition but a dynamical outcome of inflationary expansion.

ABSTRACT

There exists the "entropy problem" of the early universe, that is, why did the universe begin with an extremely low entropy and how did it evolve into such high entropy at late times? It has been long believed that inflation cannot be the solution since it requires an extremely low entropy to ever occur. However, we point out that since the inflation is always accompanied with a horizon, the correct probability of inflation is associated with the quantum entanglement entropy, which should in principle be larger than what considered previously. This motivates us to reexamine the issue by computing the evolution of the cosmological entanglement entropy in the early universe. We invoke a toy model of nonlinear generalized Chaplygin gas (GCG), which has the advantage of providing a smooth and unitary transition between the inflation epoch and the radiation dominant era. We found that soon after the onset of the inflation, the total entanglement entropy rapidly decreases to a minimum, and it rises monotonically afterwards throughout the remainder of the inflation and the radiation epochs. This indicates that the universe does not need to begin with an extremely low entropy; its smallness can be naturally induced by the dynamics of inflation itself. We believe that our computation largely captures the essential feature of entropy evolution and can provide us insights beyond the toy model.

Motivation & Objective

• To resolve the longstanding entropy problem in the early universe, where the universe began with extremely low entropy despite inflation requiring a special initial condition.
• To challenge the conventional view that inflation cannot solve the entropy problem due to its need for a low-entropy initial state.
• To propose that the correct probability measure for inflation should be based on quantum entanglement entropy associated with the cosmological horizon, not classical initial conditions.
• To demonstrate that inflation can naturally induce a low-entropy state through its dynamical evolution, rather than requiring it as a pre-existing condition.
• To provide a mechanism in which entropy decreases during inflation and then increases, thereby naturally accounting for the thermodynamic arrow of time

Proposed method

• Employ a toy model of nonlinear generalized Chaplygin gas (GCG) to describe a smooth, unitary transition from inflation to radiation-dominated era.
• Compute the evolution of cosmological entanglement entropy using a bipartite entanglement formalism between observable and unobservable regions.
• Use the entanglement entropy as the key measure of probability for inflation, arguing it is higher than previously assumed due to the presence of a cosmological horizon.
• Model the scalar field dynamics with a potential $ V = V_0 e^{- u heta} $, incorporating quantum corrections via noise and diffusion kernels in loop calculations.
• Analyze the time evolution of the entropy using effective field theory techniques, including higher-order loop corrections through diagrammatic rules.
• Use parameter space analysis to show that inflation can emerge from a non-inflationary expanding phase when kinetic energy is suppressed relative to potential energy

Experimental results

Research questions

• RQ1 Can inflation naturally produce the low initial entropy required for the thermodynamic arrow of time, rather than requiring it as a special initial condition?
• RQ2 Does the presence of a cosmological horizon increase the probability of inflation through quantum entanglement entropy, challenging previous assumptions?
• RQ3 How does the entanglement entropy evolve during inflation and the subsequent radiation-dominated era in a unitary, smooth model?
• RQ4 Can a decrease in entanglement entropy during inflation be a generic feature of non-equilibrium quantum cosmology, even if thermodynamic laws do not yet apply?
• RQ5 What is the role of quantum corrections and nonlinear interactions in modifying the entropy evolution at early times?

Key findings

• The cosmological entanglement entropy rapidly decreases soon after the onset of inflation, reaching a minimum before monotonically increasing throughout the remainder of inflation and the radiation epoch.
• This decrease implies that the low initial entropy required for the thermodynamic arrow of time is not an initial condition but a dynamical consequence of inflation itself.
• The probability of inflation is higher than previously thought because it is governed by quantum entanglement entropy associated with the cosmological horizon.
• The model shows that a finite range of parameters allows inflation to begin after a non-inflationary expanding phase, broadening the viable parameter space.
• Higher-order quantum corrections to inhomogeneous entropy are non-perturbative and require numerical lattice methods due to infinite vertex types from the exponential potential.
• The entropy decrease during inflation is a correction to the area law, analogous to results in Susskind’s work, suggesting a deeper connection to quantum gravity