Black holes as possible sources of closed and semiclosed worlds

Quantum particle production immediately after the bounce can generate a finite period of exponential inflation consistent with the Planck 2015 observations.

“Quantum particle production immediately after the bounce can generate a finite period of exponential inflation [5] that is consistent with the Planck 2015 observations of the cosmic microwave background radiation [24].”

Such a closed universe might have originated as a baby universe from a bounce in the interior of a black hole existing in a parent universe.

“Such a universe might have originated as a baby universe from a bounce in the interior of a black hole existing in a parent universe [2][3][4][5].”

If our universe was formed in a black hole, then it must have increased its entropy and isotropized in the past to match the currently observed FLRW universe.

“If our universe was formed in a black hole, then it must have increased its entropy [5,33,34] and isotropized in the past to match the currently observed FLRW universe [35].”

The collapsing matter undergoes a nonsingular bounce and then expands as a new, closed universe whose total energy is zero.

“Instead, the collapsing matter undergoes a nonsingular bounce [21] and then expands as a new, closed universe [4,5,22] whose total energy is zero [23].”

The production rate of particles in a contracting or expanding universe can be phenomenologically given by 1/√-g d(√-g n_f)/dt = β H^4.

“The production rate of particles in a contracting or expanding universe can be phenomenologically given by 1 √ -g d( √ -gn f ) dt = βH 4 ,(33)”

If β is too big, the right-hand side of (38) could become positive, causing temperature to grow with increasing a, leading to eternal inflation.

“When a increases and if β is too big, then the right-hand side of ( 38) could become positive.In this case, the temperature would grow with increasing a, which would lead to eternal inflation [5].”

Because of particle production, which increases entropy, each cycle of expansion and contraction lasts longer and reaches a larger maximum of Y than the preceding cycle.

“Because of particle production, which increases entropy, each cycle of expansion and contraction lasts longer and reaches a larger maximum of Y than the preceding cycle [5,33].”

The universe may have several bounces and cycles until it reaches the size at which the cosmological constant becomes dominant and prevents the next contraction; then the cycles end and the universe begins indefinite expansion.

“The universe may have several bounces and cycles until it reaches the size at which the cosmological constant becomes dominant and prevents the next contraction.Then the cycles end and the universe begins indefinite expansion [5,33].”