Dark Side of Weyl Gravity
We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [<i>Phys. Rev. D</i><b>2020</b>, <i>101</i>, 044050], where we found a non-t...
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MDPI AG
2020-08-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/6/8/123 |
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| author | Petr Jizba Lesław Rachwał Stefano G. Giaccari Jaroslav Kňap |
| author_facet | Petr Jizba Lesław Rachwał Stefano G. Giaccari Jaroslav Kňap |
| author_sort | Petr Jizba |
| collection | DOAJ |
| description | We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [<i>Phys. Rev. D</i><b>2020</b>, <i>101</i>, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-functions related to three couplings associated with <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>2</mn></msup></semantics></math></inline-formula> (Weyl square), <inline-formula><math display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula> (Gauss–Bonnet), and <inline-formula><math display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed. |
| first_indexed | 2024-03-10T17:34:41Z |
| format | Article |
| id | doaj.art-e9470e46c40346b2843c593f23184cf6 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T17:34:41Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-e9470e46c40346b2843c593f23184cf62023-11-20T09:54:57ZengMDPI AGUniverse2218-19972020-08-016812310.3390/universe6080123Dark Side of Weyl GravityPetr Jizba0Lesław Rachwał1Stefano G. Giaccari2Jaroslav Kňap3FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech RepublicFNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech RepublicDepartment of Sciences, Holon Institute of Technology (HIT), 52 Golomb St., Holon 5810201, IsraelFNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech RepublicWe address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [<i>Phys. Rev. D</i><b>2020</b>, <i>101</i>, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-functions related to three couplings associated with <inline-formula><math display="inline"><semantics><msup><mi>C</mi><mn>2</mn></msup></semantics></math></inline-formula> (Weyl square), <inline-formula><math display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula> (Gauss–Bonnet), and <inline-formula><math display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky <inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed.https://www.mdpi.com/2218-1997/6/8/123Weyl gravityrenormalization groupinflationdark energy |
| spellingShingle | Petr Jizba Lesław Rachwał Stefano G. Giaccari Jaroslav Kňap Dark Side of Weyl Gravity Universe Weyl gravity renormalization group inflation dark energy |
| title | Dark Side of Weyl Gravity |
| title_full | Dark Side of Weyl Gravity |
| title_fullStr | Dark Side of Weyl Gravity |
| title_full_unstemmed | Dark Side of Weyl Gravity |
| title_short | Dark Side of Weyl Gravity |
| title_sort | dark side of weyl gravity |
| topic | Weyl gravity renormalization group inflation dark energy |
| url | https://www.mdpi.com/2218-1997/6/8/123 |
| work_keys_str_mv | AT petrjizba darksideofweylgravity AT lesławrachwał darksideofweylgravity AT stefanoggiaccari darksideofweylgravity AT jaroslavknap darksideofweylgravity |