Creation of a compact topologically nontrivial inflationary universe

In the paper

“Similarly, it was shown long ago that particle production in the very early universe can make the universe locally isotropic [23].However, this process could not make the universe globally isotropic because in the hot big bang scenario the universe consisted of many causally disconnected domains.But such effects may play important role in our scenario by making the initial small patch of the”

What the sources say

• ?Could not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  cites [23] de Oliveira-Costa A, 2004, Phys. Rev. sourceExperimental — accuracy not yet measured

In the paper

“As we already discussed in Section II, the probability of such event for V ≪ 1 is expected to be exponentially small, even though under certain conditions it might be greater than the probability given by the square of the tunneling wave function (1); see Eqs. (18) and (19) in [14].”

What the sources say

• ?Could not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  cites [14] sourceExperimental — accuracy not yet measured

In the paper

“Moreover, the effective energy associated with the curvature of 3D space in the open universe case decreases as a -2 , i.e. much more slowly than the energy of ordinary matter.Soon after the beginning of expansion, the curvature energy density becomes dominant, and the relative role of normal matter and of its density perturbations become insignificant.This is an additional reason to expect that”

What the sources say

• Partly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [22] sourceExperimental — accuracy not yet measured

In the paper

“After this work was completed we became aware of Ref.[26], where it was also found that the probability of quantum creation of compact flat and open dS universes (in the case K = 0, see below) is not exponentially suppressed, which agrees with[3] and with our results.”

What the sources say

• ?Could not verify

  Section 2 discusses compact flat and open universes and mentions the naturalness of finite spatial sections in quantum cosmologies, but it does not address their probability of quantum creation. Searches for exponential suppression and quantum nucleation found no passage establishing the claimed result for K = 0. (LLM, conf=0.78)

  cites [26] Barrow J, 2001, Class. Quantum Grav. sourceExperimental — accuracy not yet measured
• Not checked yetcites [3] Schwarzschild K, 1900, Vierteljahrschrift der Ast. Ges.

In the paper

“This is an important consideration, because inflation in the string theory landscape scenario is eternal [37,38].”

What the sources say

• Partly supported

  In “Open universes and the tunneling wave function” (page not supplied), Linde says that most versions of chaotic inflation enter a regime of eternal self-reproduction. Our copy does not connect that finding to a string theory landscape scenario, so it supports eternal inflation in the models discussed, but not the claim's specified setting. (LLM, conf=0.87)

  cites [37] Linde A D, 1998, Phys. Rev. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The Introduction and Concluding Remarks describe an open-universe model with old and new inflation, not a string-theory landscape scenario. The Concluding Remarks say that eternal inflation backward in time seems inconsistent with a finite bubble-nucleation rate, but do not establish whether inflation in a landscape scenario is eternal. Searched for string-theory landscape, eternal inflation, and future-directed inflation. (LLM, conf=0.76)

  cites [38] Bucher M, 1995, Phys. Rev. sourceExperimental — accuracy not yet measured

In the paper

“At a ≫ K V 1/6 the term Ka -2 is much smaller than a 4 V , and therefore the solutions of Eqs.(9) look the same as the solutions of Eq. ( 5), see Fig. 2.”

In the paper

“Meanwhile when one studies creation of a closed universe due to the tunneling from a = 0 to a = 3 V through the potential barrier V(a) = 6π 2 a 2 -2π 2 a 4 V , one finds that the potential is positive at small a. Therefore the description of tunneling begins under the barrier, where the wave function does not oscillate, so there are no incident and reflected waves.”

In the paper

“Meanwhile, as we have seen, there is no exponential suppression of creation of the low energy density inflationary universe if one considers compact open or flat universes.”

In the paper

“For large a, the solution of Eq. ( 5) can be easily obtained in the WKB (semiclassical) approximation, Ψ ∼ a -1 exp[±i 2afoot_2 √ V √ 3 ]; positive sign corresponds to an expanding universe.”

In the paper

“If one adds to V(a) the kinetic energy term -2π 2 K/a 2 , the effective potential V(a) becomes negative at small a, but one can show that for K < 1/192π 4 the solutions of the WDW equation remain non-oscillatory at small a, and the standard description of tunneling breaks down.”

In the paper

“What is most important to us here is that the action at the first (quantum mechanical) part of the evolution of the universe was O(1), i.e. for any V (φ) there was no exponential suppression of the probability of quantum creation of the universe associated with tunneling.”

In the paper

“However, for K > 1/192π 4 , the WKB approximation is applicable at small a, which leads to the existence of solutions oscillating at a < ∼ K 1/4 .In terms of the variable α = log a, one can interpret these solutions as waves coming from -∞ and almost completely reflected back from the barrier at a = (K/3) 1/4 .In this case one can use the standard quantum mechanical description of tunneling.”

In the paper

“However, once the universe grows larger than a ∼ V -1/6 , its action rapidly becomes exponentially large and its classical description becomes possible.”

In the paper

“The universe appears “from nothing” without tunneling and without exponential suppression of the probability of its creation.”

In the paper

“In other words, contrary to the usual expectations, at a < ∼ V -1/6 one cannot describe the universe in terms of a classical space-time even though the size of the universe at a ∼ V -1/6 is much greater than the Planck size, and the density of matter as well as the curvature scalar in this regime remains small, R = 4V ≪ 1.”

In the paper

“Thus without the help of inflation the effects considered above cannot solve the major cosmological problems.However, they can keep the universe sufficiently homogeneous until the onset of inflation.”

In the paper

“If a closed universe is born small, with the total kinetic energy of the scalar field being smaller than V -2 at the Planck time, then, at the classical level, it is going to collapse.It may survive due to tunneling, but the probability of this event is suppressed by exp -24π 2 V (φ) .”

In the paper

“The meaning of this result, to be discussed below in a more detailed way, is that at a ≫ V -1/6 the effective action corresponding to the expanding universe is very large, and the universe can be described in terms of classical space and time.”

In the paper

“One should note, however, that in the eternal inflation scenario [34,35] the problem of initial conditions may become irrelevant.”

What the sources say

• ?Not checked — no full text of the sourcecites [34] Vilenkin A, 1984, Phys. Rev. source
• ?Not checked — no full text of the sourcecites [35] Hartle J B, 1983, Phys. Rev. source

In the paper

“If the initial size of the universe was O(1), then at the time t ≫ 1 each particle (or a gravitational perturbation of metric) within one cosmological time would run all over the torus many times, appearing in all of its parts with nearly equal probability.This effect, called “chaotic mixing,” should lead to a rapid homogenization of the universe [5,6].”

What the sources say

• ?Not checked — no full text of the sourcecites [5] source
• ?Not checked — no full text of the sourcecites [6] source

In the paper

“Of course, there will be some suppression of the probability of inflationary initial conditions if an inflationary regime occurs only for a narrow range of initial values of the inflaton field.However, this phase space suppression is much milder than the exponential suppression of the type described by Eq. ( 1).”

In the paper

“Since the mass squared of the inflaton field is much smaller than V , and the size of the universe prior to inflation is smaller than H -1 , perturbations of this field behave as ultrarelativistic particles, the distribution of density of scalar perturbations becomes nearly homogeneous, and the energy density of the gradients of the scalar field will decrease as the energy of radiation (as a -4 )”

In the paper

“However, with a specific fine-tuning of inflationary potential [12], the inflationary stage can be made sufficiently short, in which case the remnants of the original anisotropy of the universe may become observable [6].”

What the sources say

• ?Not checked — no full text of the sourcecites [12] Lockhart C N, 1982, Phys. Rev. source
• ?Not checked — no full text of the sourcecites [6] source

In the paper

“Meanwhile at a < ∼ V -1/6 , the effective action becomes small, the classical description breaks down, and quantum uncertainty becomes large.”

In the paper

“However, in his papers Friedmann noted that even flat and open universes may be compact if they have nontrivial topology [1].”

What the sources say

• Not checked yetcites [1] Friedmann A, 1923, Mir Kak Prostranstvo i Vremya, The Universe as Space and Time

In the paper

“A similar result is valid for the open universe as well.”

In the paper

“One should note that here we ignored the Casimir effect, which may give an important quantum contribution O(a -4 ) to the vacuum energy density [3,4].Under certain conditions, this contribution may be negative, which will again forbid the classical evolution at a < O(H -1 ).However, this effect is suppressed by supersymmetry [3,4], it disappears in some anisotropic versions of toroidal compactifi”

What the sources say

• Not checked yetcites [3] Schwarzschild K, 1900, Vierteljahrschrift der Ast. Ges.
• ?Not checked — no full text of the sourcecites [4] Zeldovich Y B, 1984, Sov. Astron. Lett.

In the paper

“After that, inflation occurs in an expanding and cooling universe automatically, if the inflaton field did not strongly interact with matter and if from the very beginning it was staying at the flat (inflationary) region of the effective potential.”

In the paper

“Meanwhile, for 48K ≫ 1 the kinetic energy becomes Planckian when the universe is large in Planckian units, at a = K 1/6 ≫ 1, and the solution of the WDW equation remains semiclassical and oscillatory for all a.”

In the paper

“However, Casimir energy is suppressed by supersymmetry.In the absence of supersymmetry, this energy is O(a -4 ), so if a is somewhat greater than 1 at the Planck density, this energy always remains smaller than the thermal energy.”

What the sources say

• Not checked yetcites [3] Schwarzschild K, 1900, Vierteljahrschrift der Ast. Ges.
• ?Not checked — no full text of the sourcecites [4] Zeldovich Y B, 1984, Sov. Astron. Lett.

In the paper

“Usually, kinetic energy of the scalar field φ gives the leading contribution in this limit, since it scales as a -6 , i.e. much faster than the energy density of relativistic and nonrelativistic matter.”

In the paper

“Eqs. (5) differs from Eq. ( 3) not only by numerical coefficients, but mainly by the absence of the term 6π 2 a 2 , which was leading to the existence of the barrier in the effective potential V(a) for the closed universe.In the flat toroidal universe case there is no such barrier.”

In the paper

“The Hartle-Hawking wave function[17] yields a different result, P ∼ exp(+ 24π 2 V (φ)).In this case, the probability of inflation is also exponentially suppressed, as compared with the probability of living in the deepest minimum of V (φ).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [17] Sokolov D D, 1976, Sov. Astron.

In the paper

“If inflation is not eternal, then our investigation suggests that most probably we live in a flat or open compact universe with nontrivial topology.”