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How Inflation Might Explain Large-Scale Anisotropy
General Relativity and Quantum Cosmology · Submitted 20 Aug 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation.
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The abstract, sentence by sentence
Several recent observational analyses have suggested the possible existence of a large-scale anisotropy in our Universe. It is often thought that this would contradict the inflationary picture of the earliest times. We show that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation. This is seen most clearly if one uses a ``$1\,+\,3\,$'' analysis of a torsional spacetime, leading naturally to concepts of intrinsic torsion and extrinsic torsion. An anisotropic quantum fluctuation of the inflaton leads to an extrinsic torsion field which is anisotropic and which grows throughout the inflationary era, even though the intrinsic geometry of the spatial sections is isotropised in the conventional manner. The competition between the intrinsic torsion (which does inflate away) and the extrinsic torsion leads to a short interval, early in the inflationary era, during which there is a torsion-induced energy flux, which leaves an anisotropic signal in superhorizon modes and thus ultimately at large scales in the present Universe.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Several recent observational analyses have suggested the possible existence of a large-scale anisotropy in our Universe. | background 1.00 | 0.04 | 0.02 | hedged possibility 1.00 |
| s1 | It is often thought that this would contradict the inflationary picture of the earliest times. | background 0.99 | 0.03 | 0.02 | hedged possibility 0.67 |
| s2 | We show that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation. | result 0.55 | 0.93 | 0.92 | asserted 1.00 |
| s3 | This is seen most clearly if one uses a ``$1\,+\,3\,$'' analysis of a torsional spacetime, leading naturally to concepts of intrinsic torsion and extrinsic torsion. | method 0.98 | 0.58 | 0.05 | asserted 0.97 |
| s4 | An anisotropic quantum fluctuation of the inflaton leads to an extrinsic torsion field which is anisotropic and which grows throughout the inflationary era, even though the intrinsic geometry of the spatial sections is isotropised in the conventional manner. | result 0.95 | 0.80 | 0.16 | asserted 1.00 |
| s5 | The competition between the intrinsic torsion (which does inflate away) and the extrinsic torsion leads to a short interval, early in the inflationary era, during which there is a torsion-induced energy flux, which leaves an anisotropic signal in superhorizon modes and thus ultimately at large scales in the present Universe. | result 0.80 | 0.82 | 0.50 | asserted 1.00 |
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The paper
Original abstract
Several recent observational analyses have suggested the possible existence of anisotropy in our Universe. It is often thought that this would contradict the inflationary picture. We have argued that this is not the case: if we relax the artificial restriction that spacetime torsion must be zero, then such anisotropies arise naturally, indeed almost inevitably, in a theory of torsional Inflation. This is seen most clearly if one uses a ``$1\,+\,3\,$'' analysis of a torsional spacetime, leading naturally to concepts of intrinsic torsion and extrinsic torsion. An anisotropic quantum fluctuation of the inflaton leads to an extrinsic torsion field which is anisotropic and which grows throughout the inflationary era, even though the intrinsic geometry of the spatial sections is isotropised in the conventional manner. This leads to an anisotropic Hubble field at the \emph{end} of Inflation. The anisotropy takes a very specific and characteristic form, which in principle could be observable on relatively short cosmic scales. On the other hand, an unusual feature of torsional geometry leads to a short interval, \emph{early} in the inflationary era, during which there is a torsion-induced energy flux, which leaves an anisotropic signal in superhorizon modes and thus ultimately at very large scales in the present Universe. Thus in principle torsion can explain anisotropies both on relatively short cosmic scales and also at the largest scales.
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What it cites · 89 sentences without a confident label
Builds on 3 papers
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Since the initial energy density is large and positive, then, from the usual Friedmann equation and the vanishing of the extrinsic curvature, the intrinsic curvature of the initial hypersurface must have a large positive value[Arguments in favour of the positivity of the spatial curvature (when the torsion is zero) at early times have recently been advanced in [ref] ; here, we apply this to creation-from-nothing cosmologies, and not to the (however, closely related) bouncing cosmologies considered there.
Open case for a closed universe · Section · 0.92
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Since the initial energy density is large and positive, then, from the usual Friedmann equation and the vanishing of the extrinsic curvature, the intrinsic curvature of the initial hypersurface must have a large positive value[Arguments in favour of the positivity of the spatial curvature (when the torsion is zero) at early times have recently been advanced in [ref] ; here, we apply this to creation-from-nothing cosmologies, and not to the (however, closely related) bouncing cosmologies considered there.
Geodesically Complete Curvature-Bounce Inflation · Section · 0.92
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Since the initial energy density is large and positive, then, from the usual Friedmann equation and the vanishing of the extrinsic curvature, the intrinsic curvature of the initial hypersurface must have a large positive value[Arguments in favour of the positivity of the spatial curvature (when the torsion is zero) at early times have recently been advanced in [ref] ; here, we apply this to creation-from-nothing cosmologies, and not to the (however, closely related) bouncing cosmologies considered there.
Affine ANEC selects the closed FRW branch for geodesically complete cosmology · Section · 0.92
Cites as support 1 paper
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It turns out [ref] that $κ$ also directly parametrises the anisotropy of the vector field describing the rates of change of positions of (fictitious) point particles imagined to be embedded in the inflaton, pictured as a “fluid”.
Reconciling Inflation with Anisotropies at Small Scales · Section · 0.98
Cites as background 19 papers
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For much more complete discussions of torsional cosmology, see for example [ref] , and particularly [ref] .
Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis · Section · 1.00
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For much more complete discussions of torsional cosmology, see for example [ref] , and particularly [ref] .
Torsional pseudo-inflation beyond Einstein-Cartan · Section · 1.00
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For much more complete discussions of torsional cosmology, see for example [ref] , and particularly [ref] .
Einstein-Cartan pseudoscalaron inflation · Section · 1.00
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