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Cited by 91Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical Physics

UNIVERSE IN A BLACK HOLE IN EINSTEIN–CARTAN GRAVITY

Open access
Popławski, Nikodem·2016·The Astrophysical Journal
DOI 10.3847/0004-637x/832/2/96

Published version of a preprint

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Abstract

The conservation law for the angular momentum in curved spacetime, consistent with relativistic quantum mechanics, requires that the antisymmetric part of the affine connection (torsion tensor) is a variable in the principle of least action. The coupling between the spin of elementary particles and torsion in the Einstein–Cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin fluid, and thus avoids the formation of singularities in black holes. The collapsing matter in a black hole should therefore bounce at a finite density and then expand into a new region of space on the other side of the event horizon, which may be regarded as a nonsingular, closed universe. We show that quantum particle production caused by an extremely high curvature near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) of this universe. This scenario can thus explain inflation without a scalar field and reheating. We show that, depending on the particle production rate, such a universe may undergo several nonsingular bounces until it has enough matter to reach a size at which the cosmological constant starts cosmic acceleration. The last bounce can be regarded as the big bang of this universe.

AI snapshot

Written from the paper’s full text.

TL;DR

In Einstein–Cartan gravity, spin–torsion repulsion prevents singularities, so a black-hole interior can bounce into a new closed universe; quantum particle production near the bounce can generate entropy and a finite inflationary expansion without a scalar field. Depending on the production rate, the universe may undergo several nonsingular bounces, with the last bounce regarded as its big bang.

Key findings

  • Spin–torsion coupling in the Einstein–Cartan theory generates gravitational repulsion at extremely high densities, replacing black-hole and big-bang singularities with nonsingular bounces; collapsing matter can expand into a closed universe on the other side of the event horizon.
  • Quantum particle production near a bounce can create enormous amounts of matter, produce entropy, and generate a finite period of exponential expansion (inflation) without a scalar field or reheating.
  • For standard-model particles with \(g_b=28\) and \(g_f=90\), the paper reports \(T_{\max}=1.15\times10^{32}\) K, \(|H|_{\max}=4.75\times10^{45}\) s\(^{-1}\), \(t=8.1\times10^{-43}\) s, \(\Omega_{\min}-1=5.7\times10^{-36}\), and \(N_{\max}=10^{52}\).
  • For a stellar black hole with Schwarzschild radius \(a_i=10^4\) m, it finds \(T_i=1.38\times10^{12}\) K and \(a_{\min}=1.19\times10^{-16}\) m; particle production requires \(a_i/a_i\sim >10^{10}\) and gives \((\Omega_{\min}-1)\sim/(\Omega_{\min}-1)<10^{-55}\), solving the flatness and horizon problems.
  • Inflation appears as a special case: if \(\beta\) is slightly less than \(\beta_{\rm cr}\), the universe expands exponentially at nearly constant energy density; \(\beta_{\rm cr}\approx1/929\) for \(g_{b1}=9\). \(\beta=0\) gives infinite cycles, \(0<\beta<\beta_{\rm cr}\) finite cycles, \(\beta\approx\beta_{\rm cr}\) one bounce plus inflation, and \(\beta>\beta_{\rm cr}\) eternal inflation.

Methods

  • Theoretical derivation in the Einstein–Cartan–Sciama–Kibble theory: torsion is related algebraically to spin, fermionic matter is approximated as a spin fluid, and a closed homogeneous isotropic FLRW universe is used with Friedmann equations including torsion.
  • The analysis uses standard-model thermal degrees of freedom (\(g_b=28\), \(g_f=90\); \(g_{b1}=9\)) and reference cosmological values \(T_{\rm eq}=8820\) K and \(\Lambda/\kappa=5.24\times10^{-10}\) Pa; no observational dataset is analyzed.
  • Main derivations cover bounce conditions, oscillatory dynamics, particle production and entropy growth, and the inflationary condition; the paper cites numerical confirmation in Desai & Popławski (2016).

Limitations

  • Stated: the scenario would be more complete if the spin–torsion coupling were used beyond the point-particle spin-fluid approximation and combined with a Dirac-spinor description; Dirac spinors should be treated as anticommuting fields to see whether the cusp-like bounce can be smoothed out.
  • Stated: \(K\) should ultimately be derived from quantum field theory in Riemann–Cartan spacetime; the paper uses a simple phenomenological form. The formation of trapped surfaces and wormhole throats could be explored numerically.
  • Stated: the paper notes a philosophical problem it cannot solve—what started the entire process if the black hole creating our universe exists in a larger universe also created inside a black hole. Evident from the text: the main dynamics assume a homogeneous and isotropic FLRW universe for simplicity, although the black-hole interior is expected to be initially inhomogeneous and anisotropic.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3847/0004-637x/832/2/96

Cites

80 of 80 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

39 of 111 cited sources checked · 19 supported · 1 flagged · accuracy not yet measured

  • Premisecitation

    At extremely high densities in black holes and the very early universe, the minimal spinor-torsion coupling manifests as gravitational repulsion, which avoids the formation of singularities from fermionic matter.

    “At extremely high densities existing in black holes and in the very early universe, the minimal spinor-torsion coupling manifests itself as gravitational repulsion, which avoids the formation of singularities from fermionic matter (Kopczyński 1972(Kopczyński , 1973;;Trautman 1973;Hehl et al. 1974;Gasperini 1986;Brechet et al. 2008;Popławski 2010bPopławski , 2012aPopławski , 2013c;;Magueijo et al.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Kopczyński 1972 source
    • cites Trautman 1973 source
    • cites Popławski 2010b source

      Section IV (p. 6) describes a repulsive torsion-induced four-fermion interaction that balances gravitational attraction. The Discussion (p. 6) connects spin and torsion to averting cosmological singularities and proposes that they prevent singularities in self-gravitating fermionic matter, even inside an event horizon. But the paper calls the latter conclusion a conjecture; the claim presents it as established. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
  • Premisecitation

    The nonsingular bounce scenario solves the flatness and horizon problems in cosmology.

    “In addition to eliminating the initial singularity, this scenario solves the flatness and horizon problems in cosmology (Popławski 2010c(Popławski , 2011a(Popławski , 2012a(Popławski , 2012b(Popławski , 2013b;;Magueijo et al. 2013;Alexander et al. 2014;Bambi et al. 2014).”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites Popławski 2010c source
    • cites Magueijo et al. 2013 source

      Section 4 (p. 7) says the spinor model is, “in a sense,” a solution to the flatness problem because it precludes spatial curvature. Section 5.2 (p. 9) describes a nonsingular bounce, but the paper does not say that the bounce solves the horizon problem; the claim attributes more to this source than it establishes. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites Bambi et al. 2014 source

      The Abstract describes a nonsingular bounce in a collapsing cloud, supporting that part of the attribution. The passages on apparent horizons concern trapped surfaces and black-hole formation, not the cosmological horizon problem; our copy does not show that the bounce solves either the flatness or cosmological horizon problem. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
  • Premisecitation

    In general relativity, the singularity forms before the collapse has completed.

    “In general relativity, the singularity forms before the collapse has completed (Landau & Lifshitz 1975;Hochberg & Visser 1998).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Landau & Lifshitz 1975

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

    • cites Hochberg & Visser 1998 source

      Section 6.1.1 (p. 24) discusses a collapsing background in a dynamic wormhole model, but does not say when a singularity forms. Section 4.1.1 (p. 14) mentions gravitational collapse and singularity theorems while explicitly distinguishing its wormhole analysis from claims about singularities. Searches for singularity formation and the timing of gravitational collapse found no passage addressing the cited claim. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
  • Premisecitation

    At macroscopic scales, fermions can be averaged and described as a spin fluid.

    “At macroscopic scales, such particles can be averaged and described as a spin fluid (Kopczyński 1972(Kopczyński , 1973;;Trautman 1973;Hehl et al. 1974;Kuchowicz 1978;Gasperini 1986;Brechet et al. 2008;Popławski 2009Popławski , 2010cPopławski , 2011a)).”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Kopczyński 1972 source
    • cites Trautman 1973 source
    • cites Popławski 2009 source
  • Premisecitation

    Quantum effects in the presence of an extremely strong gravitational field cause an intense particle production, which creates an enormous amount of mass without changing the total energy (matter plus gravitational field) in the black hole.

    “Quantum effects in the presence of an extremely strong gravitational field cause an intense particle production, which creates an enormous amount of mass (Parker 1968(Parker , 1969;;Zel'dovich 1970;Parker 1971aParker , 1971b;;Zel'dovich & Starobinskii 1977) without changing the total energy (matter plus gravitational field) in the black hole (Popławski 2014).”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Parker 1968 source
    • cites Zel'dovich 1970

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

    • cites Popławski 2014 source
  • May combine two claims. 54
  • Classified as probably not a substantial claim. 22
  • The quote only partly states this claim. 2

  • May combine two claims.

    Premisecitation

    When a trapped null surface forms in a black hole, the region within this surface is causally connected and mathematically equivalent to a new, closed universe.

    “When a trapped null surface forms in a black hole (Hochberg & Visser 1998), the region within this surface is causally connected and mathematically equivalent to a new, closed universe (Berger et al. 1998;Garfinkle 2004;Popławski 2010cPopławski , 2011a).”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites Hochberg & Visser 1998 source

      Section 4.1.1 (p. 14) associates trapped surfaces with gravitational collapse and black-hole physics, supporting the general connection in the clause cited to Hochberg and Visser. It does not state that a trapped null surface forms in a black hole. The sentence cites other works for the separate claim about a new, closed universe. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
    • cites Berger et al. 1998 source

      The discussion on p. 4 says that spatial points causally decouple as the singularity is approached, contrary to the claimed causal connection. The paper studies the local approach to a singularity; it does not establish that the region inside a trapped surface is mathematically equivalent to a new, closed universe. (LLM, conf=0.78)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
    • cites Popławski 2010c source

      The Discussion (section 7; page unavailable) says that, after an event horizon forms, contraction inside it looks like that of a closed universe and that this universe is initially causally connected. It does not establish mathematical equivalence, and the Horizon problem section (section 6; page unavailable) says causal connection does not persist throughout expansion. (LLM, conf=0.84)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    Numerical analysis of generic gravitational collapse in general relativity shows that spatial derivatives of the metric and curvature tensors become negligible in the dynamics, and each spatial point in the interior of a black hole locally evolves toward the singularity as an independent, spatially homogeneous universe.

    “Numerical analysis of generic gravitational collapse in general relativity shows that spatial derivatives of the metric and curvature tensors become negligible in the dynamics, and each spatial point in the interior of a black hole locally evolves toward the singularity as an independent, spatially homogeneous universe (Berger et al. 1998;Garfinkle 2004).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Berger et al. 1998 source

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

      Experimental — accuracy not yet measured
    • cites Garfinkle 2004 source

  • May combine two claims.

    Premisecitation

    The singular big bang is replaced by a nonsingular big bounce, before which the universe was contracting.

    “Accordingly, the singular big bang is replaced by a nonsingular big bounce, before which the universe was contracting (Kuchowicz 1978;Garcia de Andrade 2001;Popławski 2010cPopławski , 2011a)).”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Kuchowicz 1978 source
    • cites Garcia de Andrade 2001

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

    • cites Popławski 2010c source

  • May combine two claims.

    Premisecitation

    Cosmic inflation solves the flatness and horizon problems but requires additional matter fields with specific conditions and does not address the big bang singularity.

    “Cosmic inflation, which is supported by the measurements of the inhomogeneities of the cosmic microwave background radiation (Rich 2001), also solves the flatness and horizon problems, but it requires additional matter fields with specific conditions on their form and does not address the big bang singularity (Kazanas 1980;Guth 1981;Linde 1982).”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Kazanas 1980 source
    • cites Guth 1981 source

      Guth says the inflationary scenario could eliminate the horizon and flatness problems and discusses it in grand unified models involving Higgs fields and conditions on their potential (Secs. IV and VI; page unavailable). The Introduction describes a singularity in the standard hot-big-bang model and begins its analysis below the Planck scale, but it does not explicitly establish that inflation leaves the big-bang singularity unresolved. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • cites Linde 1982 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The ECSK theory may solve the problem of divergent integrals in quantum field theory by providing fermions with spatial extension and thus introducing an effective ultraviolet cutoff for their propagators.

    “The ECSK theory may also solve the problem of divergent integrals in quantum field theory by providing fermions with spatial extension and thus introducing an effective ultraviolet cutoff for their propagators (Popławski 2010b(Popławski , 2013c)).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Popławski 2010b source

      The opening passage (p. 1) says that Dirac particles have spatial extension and that their Cartan radius is expected to introduce an effective ultraviolet cutoff for fermions in quantum field theory. Section IV (p. 6) repeats the cutoff expectation. Our copy does not specifically say that the cutoff acts on fermion propagators or that it solves divergent integrals. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites Popławski 2013c source

  • May combine two claims.

    Interpretationcitation

    This value solves both the flatness and horizon problems.

    “This value solves both the flatness and horizon problems (Popławski 2010c(Popławski , 2011a)).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Popławski 2010c source
    • cites Popławski 2011a source

  • May combine two claims.

    Interpretationcitation

    This scenario could also explain the arrow of time and the black hole information paradox.

    “This scenario could also explain the arrow of time and the black hole information paradox (Popławski 2010c(Popławski , 2011a(Popławski , 2014)).”
    Quote in the paperNot a substantial claim2 of 3 sources checked
    • cites Popławski 2010c source

      The Discussion (section 7; page unavailable) says the proposed scenario may explain the arrow of time through the one-way motion of matter across a black-hole horizon. Our copy does not address the black hole information paradox, so it supports only the first part of the attributed claim. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites Popławski 2011a source
    • cites Popławski 2014 source

  • May combine two claims.

    Interpretationcitation

    If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging, and the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with effective energy density and pressure.

    “If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging.Thus, the Einstein-Cartan equations for such a spin fluid are equivalent to the Einstein equations for a perfect fluid with the effective energy density  k s 4 2 and the effective pressure k p s 4 2 (Hehl et al. 1974;Kuchowicz 1978;Gasperini 1986;Bre”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites Hehl et al. 1974 source
    • cites Kuchowicz 1978 source
    • cites Popławski 2010c source
    • The authors state this as an assumption: The spin orientation of particles in the spin fluid is random.

  • Classified as probably not a substantial claim.

    Findingcitation

    If we define x = a/a_min and choose t = 0 at a = a_min, then integrating Equation (23) gives Equation (24).

    “If we define x=a/a min and choose t=0 at a=a min , then integrating Equation (23) gives (Popławski 2010c, 2011a)”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Popławski 2010c source
    • cites Popławski 2011a source

  • May combine two claims.

    Premisecitation

    Standard inflation, which assumes the existence of a fundamental scalar field with a specific potential, requires fine-tuning and is geodesically incomplete in the past.

    “Standard inflation, which assumes the existence of a fundamental scalar field with a specific potential, requires fine-tuning and is geodesically incomplete in the past (Borde et al. 2003).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Borde et al. 2003 source

      The Discussion states that null and timelike geodesics in inflationary models are generally past-incomplete when the averaged expansion condition holds. The paper mentions a potential energy function, but the passages do not establish that standard inflation requires a fundamental scalar field with a specific potential or that it requires fine-tuning. Page numbers are not available in our copy. (LLM, conf=0.88)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Interpretationcitation

    This scenario simultaneously can explain the future of black hole interiors and the origin of the universe.

    “This scenario simultaneously can explain the future of black hole interiors and the origin of the universe (Popławski 2010c(Popławski , 2011a)).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Popławski 2010c source
    • cites Popławski 2011a source

  • May combine two claims.

    Study design and conductcitation

    Numerical analysis of this scenario showed that the dynamics of the universe is insensitive to the value of a_i, and thus to that of a_min, and effectively depends on the particle production coefficient β only.

    “Numerical analysis of this scenario (Desai & Popławski 2016) showed that the dynamics of the universe is insensitive to the value of a i , and thus to that of a min , and effectively depends on the particle production coefficient β only.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Desai & Popławski 2016 source

  • May combine two claims.

    Premisecitation

    High-energy observations of photons originating from gamma-ray bursts indicate that spacetime is continuous at the Planck temperature, which is on the order of the temperature near a bounce.

    “Finally, we note that the high-energy observations of photons originating from gamma-ray bursts indicate that specatime is continuous at the Planck temperature (Vasileiou et al. 2015), which is on the order of the temperature near a bounce.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Vasileiou et al. 2015 source

      The Abstract (page unavailable) reports that high-energy photons from GRB090510 place a Planck-scale limit on a model of stochastic photon-speed variation. It does not conclude that spacetime is continuous at the Planck temperature; it discusses Planck energy and length, not temperature. The comparison with a bounce is likewise not addressed in the cited paper. (LLM, conf=0.87)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationcitation

    The observed matter-antimatter asymmetry in the universe may be caused by the nonlinearity of the Dirac equation in the presence of torsion.

    “The observed matter-antimatter asymmetry in the universe may be caused by the nonlinearity of the Dirac equation in the presence of torsion (Popławski 2011b).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Popławski 2011b source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    The presented scenario predicts phenomena that are similar to those in some other cosmological models such as inflationary bubbles in the multiverse, cyclic universe, or holographic world.

    “The presented scenario predicts phenomena that are similar to those in some other cosmological models such as inflationary bubbles in the multiverse (Kazanas 1980;Guth 1981;Linde 1982), cyclic universe (Steinhardt & Turok 2002), or holographic world (Susskind 1995).”
    Quote in the paperNot a substantial claim1 of 3 sources checked
    • cites Kazanas 1980 source
    • cites Guth 1981 source

      Guth’s discussion of bubble formation in an inflationary universe supports citing this paper as an example of an inflationary bubble model. The passage on bubble formation describes bubbles within a Robertson–Walker universe, not bubbles in a multiverse. The cyclic-universe and holographic-world examples are attributed to other citations, not Guth. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites Linde 1982 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    A similar spin-spin interaction was analyzed in Khriplovich & Rudenko (2013), obtaining the same dynamics, but the cusp-like bounce was not noted; instead, it was assumed that the compression would not be followed by the expansion.

    “A similar spin-spin interaction was analyzed in Khriplovich & Rudenko (2013), obtaining the same dynamics, but the cusplike bounce was not noted; instead, it was assumed that the compression would not be followed by the expansion.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Khriplovich & Rudenko 2013 source

  • May combine two claims.

    Premisecitation

    We showed in Popławski (2012a) that a semiclassical spin-spin interaction, generated by the minimal coupling between the torsion tensor and Dirac spinors, averts the unphysical big bang singularity and replaces it with a cusp-like big bounce at a finite minimum scale factor, before which the universe was contracting.

    “We showed in Popławski (2012a) that a semiclassical spin-spin interaction, generated by the minimal coupling between the torsion tensor and Dirac spinors, averts the unphysical big bang singularity and replaces it with a cusp-like big bounce at a finite minimum scale factor, before which the universe was contracting.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Popławski 2012a source

  • May combine two claims. The quote only partly states this claim.

    Findingreasoning

    If the universe begins to contract when a = a_i and a_dot = 0, then Equation (10) gives a_i = (3/κρ)^{1/2} and the initial temperature is given by Equation (16).

    “If we assume that the universe begins to contract when a=a i and = a 0 ˙, where  a  n f 2 , then Equation (10) gives /  k = a 3 1 i 2 .Accordingly, the initial temperature is given by”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The universe begins to contract when a = a_i and a_dot = 0.

  • May combine two claims.

    Findingreasoning

    At a bounce, neglecting k, Equation (10) gives ρ - α n_f^2 = 0, and the maximum temperature is given by Equation (20).

    “At a bounce, where we can neglect k, Equation (10) gives  a -= n 0 f 2 .Accordingly, the maximum temperature is given by”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    For g_b = 28 and g_f = 90, T_max = 1.15×10^32 K, t_max = 4.75×10^-45 s, t_min = 8.1×10^-43 s, Ω_min - 1 = 5.7×10^-36, and N_max = 10^52.

    “For these values, we find t = ´= ´ = ´W -= ´ » ---T H N 1.15 10 K, 4.75 10 s, 8.1 10 s , 1 5.7 10 , 10 .28 max 32 45 max 43 1 min 36 max 52 | | ( )”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    The universe is accelerating if a_ddot > 0, which is equivalent, using Equation (19), to T > T_max/2 (a < a_min/2).

    “The universe is accelerating if > a ¨0, which is equivalent, using Equation (19), to > T T 2 max ( < a a 2 min ).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    Without particle production, a_i = a_i~; with particle production, a_i > a_i~.

    “Without particle production, = a a i i ˜.With particle production, > a a i i ˜.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims. The quote only partly states this claim.

    Findingreasoning

    The dynamics of the new universe is described by Equations (15) and (10), which can be written as Equations (17) or (18).

    “The dynamics of the new universe is described by Equations ( 15) and (10), which can be written as”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: No particles are produced in the oscillatory universe without particle production.

  • May combine two claims.

    Findingnone given

    The cosmological constant does not change the Cartan equations but adds a term to the Einstein Equations (2).

    “The cosmological constant does not change the Cartan equations but adds a term to the Einstein Equations (2):”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Findingnone given

    At matter-radiation equality, the energy density of nonrelativistic matter exceeds the energy density of radiation and the universe enters the matter-dominated era.

    “At the matter-radiation equality, the energy density of nonrelativistic matter exceeds the energy density of radiation and the universe enters the matter-dominated era.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    For a typical stellar black hole with Schwarzschild radius a_i = 10^4 m, T_i = 1.38×10^12 K and a_min = 1.19×10^16 m.

    “For this value, we find = ´= ´-T a 1.38 10 K, 1.19 10 m. 29 i 12 min 16”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    The value of T_eq depends on the number ratio of photons to massive particles and on the masses of the particles.

    “The value of T eq depends on the number ratio of photons to massive particles and on the masses of the particles.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    The torsion-dominated phase of the expansion lasts on the order of the Planck time and depends only on the numbers of thermal degrees of freedom.

    “the torsion-dominated phase of the expansion.This time is on the order of the Planck time t P and depends only on the numbers of thermal degrees of freedom.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Findingnone given

    For the FLRW metric, the Weyl tensor vanishes and the two independent invariants of dimension m^-4 constructed from the Riemann and metric tensors are P^2 and P_ik P^ik.

    “For the FLRW metric, the Weyl tensor vanishes and the two independent invariants of dimension m -4 constructed from the Riemann and metric tensors are P 2 and P P ik ik .”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: The universe is isotropic and described by the FLRW metric.

  • Classified as probably not a substantial claim. May combine two claims.

    Findingreasoning

    Relation (42) generalizes Equation (14) and describes, together with Equation (17), the dynamics of the universe.

    “Relation (42) generalizes Equation ( 14) and describes, together with Equation (17), the dynamics of the universe.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    As β increases, the number of cycles decreases and the accelerated expansion of the universe in each cycle is closer to exponential.

    “As β increases, the number of cycles decreases and the accelerated expansion of the universe in each cycle is closer to exponential.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    At this temperature, Equation (47) gives T ̇ ≈ -T a ̇/2a in a contracting phase and T ̇ ≈ 0 in an expanding phase.

    “At this temperature, Equation (47) therefore gives » -T T a a 2 52 ˙˙( ) in a contracting phase and » T 0 5 3 ˙( ) in an expanding phase.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    An exponential expansion lasts until the term in Equation (51) decreases significantly below 1 and T continues to decrease.

    “An exponential expansion lasts until the term in Equation (51) decreases significantly below 1 and T continues to decrease.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    For g_b1 = 9, β_cr ≈ 1/929, which is on the order of 1/288 in Equation (39).

    “For this value, we find b » 1 929 , 5 0 cr ( ) which is on the order of p 1 288 ( ) in Equation (39).”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationcitation

    Such a contraction could correspond to gravitational collapse of matter inside a newly formed black hole existing in another universe.

    “Such a contraction could correspond to gravitational collapse of matter inside a newly formed black hole existing in another universe (Novikov 1966;Pathria 1972;Frolov et al. 1989Frolov et al. , 1990;;Smolin 1992;Stuckey 1994;Easson & Brandenberger 2001;Smoller & Temple 2003;Popławski 2010aPopławski , 2010cPopławski , 2011a)).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Novikov 1966

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

    • cites Pathria 1972 source
    • cites Smolin 1992 source

  • Classified as probably not a substantial claim.

    Premisecitation

    Each spatial point in the interior of a black hole locally evolves toward the singularity as an independent, spatially homogeneous, and isotropic universe.

    “Accordingly, each spatial point in the interior of a black hole locally evolves toward the singularity as an independent, spatially homogeneous, and isotropic universe (Landau & Lifshitz 1975;Lord 1976).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Landau & Lifshitz 1975

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

    • cites Lord 1976

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

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationnone given

    The contraction of the universe before the big bounce must be caused by a physical initial condition.

    “The contraction of the universe before the big bounce must be caused by a physical initial condition.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    The ECSK theory passes all tests of general relativity because at nuclear densities the torsion contribution to the Einstein equations is negligibly small and both theories give indistinguishable predictions.

    “The ECSK theory also passes all tests of general relativity, because even at nuclear densities the contribution from torsion to the Einstein equations is negligibly small and both theories give indistinguishable predictions at these densities.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Cosmic inflation is supported by measurements of the inhomogeneities of the cosmic microwave background radiation.

    “Cosmic inflation, which is supported by the measurements of the inhomogeneities of the cosmic microwave background radiation (Rich 2001), also solves the flatness and horizon problems, but it requires additional matter fields with specific conditions on their form and does not address the big bang singularity (Kazanas 1980;Guth 1981;Linde 1982).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Rich 2001 source

  • Classified as probably not a substantial claim.

    Premisecitation

    A closed, homogeneous, and isotropic universe is described by the FLRW metric.

    “A closed, homogeneous, and isotropic universe is described by the Friedmann-Lemai ̂tre-Robertson-Walker (FLRW) metric, which, in the isotropic spherical coordinates, is given by”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Landau & Lifshitz 1975

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

    • cites Lord 1976

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

  • May combine two claims.

    Interpretationreasoning

    In the ECSK theory, each spatial point is expected to evolve toward a state of extremely high but finite density and curvature, where local contraction ends, matter bounces, and local expansion begins.

    “In the ECSK theory, we expect that each spatial point evolves toward a state of an extremely high but finite density and curvature.At such a state, the local contraction ends, the matter undergoes a bounce, and the local expansion begins.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The spin-torsion contribution to the energy density is negative and generates gravitational repulsion, which becomes stronger as T increases.

    “The spin-torsion contribution to the energy density is negative and generates gravitational repulsion, which becomes stronger as T increases.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    In a black hole, fermions composing the spin fluid have energies much greater than their rest energies, so they are described by an ultrarelativistic barotropic equation of state p = ρ/3.

    “In a black hole, fermions composing the spin fluid have energies much greater than their rest energies.These particles are thus described by an ultrarelativistic barotropic equation of state, p=ò/3, as for radiation.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation

    When the universe in a black hole creates sufficient amounts of mass, it reaches the size at which the cosmological constant becomes dominant and the expansion proceeds to infinity.

    “When the universe in a black hole creates sufficient amounts of mass, it reaches the size at which the cosmological constant becomes dominant and the expansion proceeds to infinity (Lord 1976).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Lord 1976

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

  • May combine two claims.

    Interpretationreasoning

    The universe continues to expand with a_ddot < 0 until it reaches its maximum scale factor (a crunch) at a = a_i, after which another contraction begins.

    “The universe continues to expands with < a ¨0 until it reaches its maximum scale factor (a crunch) at a=a i , after which another contraction begins.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The universe in a black hole would contract until it reaches a minimum radius and maximum density, undergoes a bounce, and expands again.

    “The universe in a black hole would then contract until it reaches a minimum radius and maximum density, undergoes a bounce, and expands again.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Our universe may be the interior of a black hole existing in another universe and a part of a multiverse.

    “Accordingly, our universe may be the interior of a black hole existing in another universe and a part of a multiverse.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Since the spin-torsion contribution scales with T faster (∼T^6) than ρ∼T^4, a_dot eventually reaches zero and the universe undergoes a nonsingular bounce.

    “Since this contribution scales with T faster (∼ T 6 ) than ò∼T 4 , a ˙eventually reaches zero and the universe undergoes a nonsingular bounce.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    For a = a_i, the term with k in Equation (23) can be neglected.

    “For  a a i , the term with k in Equation (23) can be neglected.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The characteristic time of the torsion-dominated phase of the expansion is on the order of the Planck time and depends only on the numbers of thermal degrees of freedom.

    “This time is on the order of the Planck time t P and depends only on the numbers of thermal degrees of”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisereasoning

    Below the Cartan density, the predictions of the ECSK theory do not differ from the predictions of metric general relativity and reduce to them in vacuum, where torsion vanishes.

    “Below this density, the predictions of the ECSK theory do not differ from the predictions of the metric general relativity and reduce to them in vacuum, where torsion vanishes.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The universe begins to decelerate and enters the radiation-dominated era.

    “The universe begins to decelerate and enters the radiation-dominated era.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    To identify our universe with a universe in a black hole, quantum effects in curved spacetime must be included; these are responsible for particle production by the gravitational field.

    “To identify our universe with a universe in a black hole, we must include quantum effects in curved spacetime, which are responsible for particle production by the gravitational field (Parker 1968(Parker , 1969;;Zel'dovich 1970;Parker 1971aParker , 1971b;;Zel'dovich & Starobinskii 1977).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites Parker 1968 source
    • cites Zel'dovich 1970

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

    • cites Parker 1971a source

  • May combine two claims.

    Premisereasoning

    The energy density of particles in kinetic equilibrium scales like a^-4, and their number density scales like a^-3.

    “The energy density of particles in kinetic equilibrium scales like ò∼a -4 , and their number density scales like n∼a -3 .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    This arrow is also entropic: although black holes are states of maximum entropy in the frame of reference of outside observers, new universes expanding inside black holes continue to increase entropy.

    “This arrow is also entropic: although black holes are states of maximum entropy in the frame of reference of outside observers, new universes expanding inside black holes continue to increase entropy.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    After such a universe is formed, spin and torsion provide the mechanism to avoid a singularity and to bounce (when the universe reaches T_max), and particle production provides the mechanism to generate inflation in the subsequent expansion.

    “After such a universe is formed, spin and torsion provide the mechanism to avoid a singularity and to bounce (when the universe reaches T max ), and particle production provides the mechanism to generate inflation in the subsequent expansion.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The exponential expansion of space in the early universe, known as cosmic inflation, also solves the flatness and horizon problems.

    “The exponential expansion of space in the early universe, known as cosmic inflation, also solves the flatness and horizon problems (Kazanas 1980;Guth 1981;Linde 1982).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Kazanas 1980 source
    • cites Guth 1981 source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites Linde 1982 source

  • May combine two claims.

    Interpretationnone given

    Moreover, it naturally solves the flatness and horizon problems and can generate an inflationary phase that lasts for a finite amount of time without requiring finely tuned scalar fields, replacing R in the gravitational Lagrangian density by more complicated functions, or adding other hypothetical objects.

    “Moreover, it naturally solves the flatness and horizon problems and can generate an inflationary phase that lasts for a finite amount of time without requiring finely tuned scalar fields, replacing R in the gravitational Lagrangian density by more complicated functions, or adding other hypothetical objects.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    The motion of matter through the event horizon is unidirectional, and thus it defines the arrow of time in the universe in a black hole.

    “The motion of matter through the event horizon is unidirectional, and thus it defines the arrow of time in the universe in a black hole.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: The motion of matter through the event horizon is unidirectional.

  • May combine two claims.

    Interpretationreasoning

    When T ≈ T_max/2, the term in Equation (51) is nearly 1 and the universe begins to expand exponentially at a nearly constant T (inflation).

    “When » T T 2 max , the term in Equation (51) is nearly 1 and the universe begins to expand exponentially at a nearly constant T (inflation).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationcitation

    Particle production by quantum effects in strong gravitational fields may also be affected by torsion.

    “Particle production by quantum effects in strong gravitational fields may also be affected by torsion (Rumpf 1979a(Rumpf , 1979b(Rumpf , 1979c)).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Rumpf 1979a source
    • cites Rumpf 1979b source
    • cites Rumpf 1979c source

  • May combine two claims.

    Interpretationreasoning

    If this new value satisfies Equation (33), then the universe expands to infinity; if not, the universe has another cycle of contraction and expansion.

    “If this new value satisfies Equation (33), then the universe expands to infinity.If not, the universe has another cycle of contraction and expansion.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    After a finite number of cycles, D satisfies Equation (33) and the universe expands indefinitely.

    “After a finite number of cycles, D satisfies Equation (33) and the universe expands indefinitely.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Inflation predicts the observed spectrum of primordial density fluctuations.

    “In addition, inflation predicts the observed spectrum of primordial density fluctuations (Bardeen 1980;Mukhanov et al. 1992).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Bardeen 1980 source
    • cites Mukhanov et al. 1992 source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    Including the torsion tensor can give other forms for K.

    “Including the torsion tensor can give other forms for K.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The universe then starts expanding according to Equation (42) and moves from the torsion-dominated era to the radiation-dominated era.

    “The universe then starts expanding according to Equation (42) and moves from the torsion-dominated era to the radiation-dominated era.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    Contrary to the other models, this scenario does not need new, hypothetical fields.

    “However, contrary to the other models, this scenario does not need new, hypothetical fields.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Our universe could be a stable part of the multiverse and may contain inflating regions of spacetime (new universes) only in black holes.

    “Our universe could be a stable part of the multiverse and may contain inflating regions of spacetime (new universes) only in black holes.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationnone given

    The nature of dark matter and dark energy should be related to later epochs in the universe.

    “The nature of dark matter and dark energy should be related to later epochs in the universe.”
    Quote in the paperNot a substantial claim
69 of 69

  • The authors state this as an assumption.

    The universe in a black hole is already homogeneous and isotropic.

    “We will also assume, for simplicity, that such a universe is already homogeneous and isotropic (Hochberg & Visser 1998).”

  • The authors state this as an assumption.

    The universe begins to contract when a = a_i and a_dot = 0.

    “If we assume that the universe begins to contract when a=a i and = a 0 ˙, where  a  n f 2 , then Equation (10) gives /  k = a 3 1 i 2 .”

  • The authors state this as an assumption.

    No particles are produced in the oscillatory universe without particle production.

    “If no particles are produced, then we can use Equation ( 14).”

  • The authors state this as an assumption.

    The spin orientation of particles in the spin fluid is random.

    “If the spin orientation of particles in a spin fluid is random, then the last term on the right-hand side of Equation (6) vanishes after averaging.”

  • The authors state this as an assumption.

    The cosmological constant is negligible in the early universe.

    “(the cosmological constant is negligible in the early universe; Kuchowicz 1978;Gasperini 1986;Brechet et al. 2008;Popławski 2010cPopławski , 2011a))”

  • The authors state this as an assumption.

    The effective numbers of thermal degrees of freedom g_b and g_f are constant in the range of T where torsion is significant.

    “since g b and g f are constant in the range of T where torsion is significant.”

  • The authors state this as an assumption.

    The wormholes eventually merge into one wormhole and the outermost trapped surface can be regarded as the event horizon.

    “we conjecture that eventually the wormholes will merge into one wormhole and the outermost trapped surface can be regarded as the event horizon.”

  • The authors state this as an assumption.

    Equation (10) is satisfied.

    “If we assume that Equation (10) is satisfied, then Equation (11) must be modified.”

  • The paper relies on this without support.

    The universe is isotropic and described by the FLRW metric.

    “In an isotropic universe, described by the FLRW metric, an alternating gravitational field causes production of particleantiparticle pairs (Beilin et al. 1980).”

  • The paper relies on this without support.

    The motion of matter through the event horizon is unidirectional.

    “The motion of matter through the event horizon is unidirectional, and thus it defines the arrow of time in the universe in a black hole.”
10 of 10

Cites

Flagged first, then by citations

Research works printed but not linked: 9

  1. Beilin, 1980, JETP, 51, 1045
  2. Chrobok, 2002, Tech. Mech., 22, 1
  3. Garcia de Andrade, 2001, NCimB, 116, 1107
  4. Mathisson, 1937, AcPP, 6, 167
  5. Novikov, 1966, JETPL, 3, 142
  6. Rumpf, 1979b, GReGr, 10, 525, 10.1007/bf00756901 · DOI · Paper page
  7. Rumpf, 1979c, GReGr, 10, 647, 10.1007/bf00756901 · DOI · Paper page
  8. Zel’dovich, 1970, JETPL, 12, 307
  9. Zel’dovich, 1977, JETPL, 26, 252

Cited by

Sorted by citations

Related

Authors
Popławski, N.
Affiliations
University of New Haven (US)
Corresponding author
Popławski, Nikodem
ORCID
Popławski, Nikodem
Venue
The Astrophysical Journal
Publisher
American Astronomical Society
Published
2016-11-21
Volume
832
Issue
2
Pages
96
ISSN
  • 0004-637X (ISSN-L)
  • 1538-4357
DOI
10.3847/0004-637x/832/2/96
OpenAlex
W1794764097
Cited by
91
References
71
Citations by year
2026: 2 · 2025: 21 · 2024: 19 · 2023: 5 · 2022: 7 · 2021: 7 · 2020: 8 · 2019: 8 · 2018: 10 · 2017: 3 · 2015: 1
FWCI
3.35
Type
journal article
Language
en
Open access
Licence
Locations
  • The Astrophysical Journal (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
Einstein-Cartan theory, torsion, black hole singularity resolution, non-singular bounce, spin fluid, fermionic matter, angular momentum conservation, primordial inflation, Big Bang, closed universe, cosmic acceleration, cosmological constant, entropy production

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-30.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-30.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

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