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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Finite, symmetry-reduced model of loop quantum gravity</div> <p><b>Loop <a href="/wiki/Quantum_cosmology" title="Quantum cosmology">quantum cosmology</a></b> (LQC)<sup id="cite_ref-url[1612.01236]_Loop_Quantum_Cosmology:_A_brief_review_1-0" class="reference"><a href="#cite_note-url[1612.01236]_Loop_Quantum_Cosmology:_A_brief_review-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-url[2002.05703]_Critical_evaluation_of_common_claims_in_loop_quantum_cosmology_2-0" class="reference"><a href="#cite_note-url[2002.05703]_Critical_evaluation_of_common_claims_in_loop_quantum_cosmology-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-url[1612.04551]_Testing_loop_quantum_cosmology_3-0" class="reference"><a href="#cite_note-url[1612.04551]_Testing_loop_quantum_cosmology-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-url[1703.10274]_Loop_quantum_cosmology_and_singularities_4-0" class="reference"><a href="#cite_note-url[1703.10274]_Loop_quantum_cosmology_and_singularities-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-url[1906.01501]_Effective_Field_Theory_of_Loop_Quantum_Cosmology_5-0" class="reference"><a href="#cite_note-url[1906.01501]_Effective_Field_Theory_of_Loop_Quantum_Cosmology-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> is a <a href="https://en.wiktionary.org/wiki/finite" class="extiw" title="wikt:finite">finite</a>, <a href="/wiki/Symmetry_(physics)" title="Symmetry (physics)">symmetry</a>-reduced model of <a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">loop quantum gravity</a> (<a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">LQG</a>) that predicts a "quantum bridge" between contracting and expanding <a href="/wiki/Cosmology" title="Cosmology">cosmological</a> branches. </p><p>The distinguishing feature of LQC is the prominent role played by the <a href="/wiki/Quantum_geometry" title="Quantum geometry">quantum geometry</a> effects of loop quantum gravity (LQG). In particular, <a href="/wiki/Quantum_geometry" title="Quantum geometry">quantum geometry</a> creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck regime</a>, overwhelming the classical gravitational attraction and thereby resolving <a href="/wiki/General_relativity#Singularities" title="General relativity">singularities of general relativity</a>. Once singularities are resolved, the conceptual paradigm of <a href="/wiki/Cosmology" title="Cosmology">cosmology</a> changes and one has to revisit many of the standard issues—e.g., the "<a href="/wiki/Horizon_problem" title="Horizon problem">horizon problem</a>"—from a new perspective. </p><p>Since LQG is based on a specific quantum theory of <a href="/wiki/Riemannian_geometry" title="Riemannian geometry">Riemannian geometry</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-MartinLQC_7-0" class="reference"><a href="#cite_note-MartinLQC-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> geometric observables display a fundamental discreteness that play a key role in <a href="/wiki/Quantum_dynamics" title="Quantum dynamics">quantum dynamics</a>: While predictions of LQC are very close to those of quantum <a href="/wiki/Geometrodynamics" title="Geometrodynamics">geometrodynamics</a> (QGD) away from the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck regime</a>, there is a dramatic difference once densities and curvatures enter the <a href="/wiki/Planck_scale" class="mw-redirect" title="Planck scale">Planck scale</a>. In LQC the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> is replaced by a <a href="/wiki/Quantum_bounce" class="mw-redirect" title="Quantum bounce">quantum bounce</a>. </p><p>Study of LQC has led to many successes, including the emergence of a possible mechanism for <a href="/wiki/Cosmic_inflation" title="Cosmic inflation">cosmic inflation</a>, resolution of <a href="/wiki/Gravitational_singularities" class="mw-redirect" title="Gravitational singularities">gravitational singularities</a>, as well as the development of effective semi-classical <a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonians</a>. </p><p>This subfield originated in 1999 by <a href="/wiki/Martin_Bojowald" title="Martin Bojowald">Martin Bojowald</a>, and further developed in particular by <a href="/wiki/Abhay_Ashtekar" title="Abhay Ashtekar">Abhay Ashtekar</a> and <a href="/wiki/Jerzy_Lewandowski" title="Jerzy Lewandowski">Jerzy Lewandowski</a>, as well as <a href="/w/index.php?title=Tomasz_Paw%C5%82owski&action=edit&redlink=1" class="new" title="Tomasz Pawłowski (page does not exist)">Tomasz Pawłowski</a> and <a href="/w/index.php?title=Parampreet_Singh&action=edit&redlink=1" class="new" title="Parampreet Singh (page does not exist)">Parampreet Singh</a>, et al. In late 2012 LQC represented a very active field in <a href="/wiki/Physics" title="Physics">physics</a>, with about three hundred papers on the subject published in the literature. There has also recently been work by <a href="/wiki/Carlo_Rovelli" title="Carlo Rovelli">Carlo Rovelli</a>, et al. on relating LQC to <a href="/wiki/Spinfoam" class="mw-redirect" title="Spinfoam">spinfoam</a> cosmology. </p><p>However, the results obtained in LQC are subject to the usual restriction that a truncated classical theory, then quantized, might not display the true behaviour of the full theory due to artificial suppression of degrees of freedom that might have large quantum fluctuations in the full theory. It has been argued that singularity avoidance in LQC is by mechanisms only available in these restrictive models and that singularity avoidance in the full theory can still be obtained but by a more subtle feature of LQG.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Big_bounce_in_loop_quantum_cosmology">Big bounce in loop quantum cosmology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loop_quantum_cosmology&action=edit&section=1" title="Edit section: Big bounce in loop quantum cosmology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Big_Bounce.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/Big_Bounce.jpg/220px-Big_Bounce.jpg" decoding="async" width="220" height="123" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/8/86/Big_Bounce.jpg 1.5x" data-file-width="268" data-file-height="150" /></a><figcaption>Illustration of big bounce universe</figcaption></figure> <p>Due to the quantum geometry, the Big Bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. An important feature of loop quantum cosmology is the effective <a href="/wiki/Space-time" class="mw-redirect" title="Space-time">space-time</a> description of the underlying quantum evolution.<sup id="cite_ref-PSLoopQuantumCosmology_10-0" class="reference"><a href="#cite_note-PSLoopQuantumCosmology-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The effective dynamics approach has been extensively used in loop quantum cosmology to describe physics at the Planck scale and the very early universe. Rigorous numerical simulations have confirmed the validity of the effective dynamics, which provides an excellent approximation to the full loop quantum dynamics.<sup id="cite_ref-PSLoopQuantumCosmology_10-1" class="reference"><a href="#cite_note-PSLoopQuantumCosmology-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> It has been shown that only when the states have very large quantum fluctuations at late times, which means that they do not lead to macroscopic universes as described by general relativity, that the effective dynamics has departures from the quantum dynamics near bounce and the subsequent evolution. In such a case, the effective dynamics overestimates the density at the bounce, but still captures the qualitative aspects extremely well.<sup id="cite_ref-PSLoopQuantumCosmology_10-2" class="reference"><a href="#cite_note-PSLoopQuantumCosmology-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Scale-invariant_loop_quantum_cosmology">Scale-invariant loop quantum cosmology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loop_quantum_cosmology&action=edit&section=2" title="Edit section: Scale-invariant loop quantum cosmology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the underlying spacetime geometry with matter has a <a href="/wiki/Scale_invariance" title="Scale invariance">scale invariance</a>, which has been proposed to resolve the <a href="/wiki/Problem_of_time" title="Problem of time">problem of time</a>, <a href="/wiki/Immirzi_parameter" title="Immirzi parameter">Immirzi ambiguity</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and hierarchy problem of fundamental couplings,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> then the resulting loop quantum geometry has no definitive discrete gaps or a minimum size.<sup id="cite_ref-:0_13-0" class="reference"><a href="#cite_note-:0-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Consequently, in scale-invariant LQC, the Big Bang is shown not to be replaced by a quantum bounce.<sup id="cite_ref-:0_13-1" class="reference"><a href="#cite_note-:0-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loop_quantum_cosmology&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Big_Bounce" title="Big Bounce">Big Bounce</a> – Model for the origin of the universe</li> <li><a href="/wiki/Loop_quantum_gravity" title="Loop quantum gravity">Loop quantum gravity</a> – Theory of quantum gravity, merging quantum mechanics and general relativity</li> <li><a href="/wiki/Cyclic_model" title="Cyclic model">Cyclic model</a> – Cosmological models involving indefinite, self-sustaining cycles</li> <li><a href="/wiki/Canonical_quantum_gravity" title="Canonical quantum gravity">Canonical quantum gravity</a></li> <li><a href="/wiki/Dilaton" title="Dilaton">Dilaton</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Loop_quantum_cosmology&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-url[1612.01236]_Loop_Quantum_Cosmology:_A_brief_review-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-url[1612.01236]_Loop_Quantum_Cosmology:_A_brief_review_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free 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