Weyl R2 inflation with an emergent Planck scale

Ghilencea, D. M.

doi:10.1007/jhep10(2019)209

Cited by 49 publications

(48 citation statements)

References 102 publications

(157 reference statements)

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“…Nonmetricity effects are then strongly suppressed by a large M (their current lower bound seems low [77,78]). Hence, the long-held criticisms that have implicitly assumed v μ be massless are actually avoided and Weyl gravity is then viable [26][27][28]. As outlined, in this work we obtain similar results in EP quadratic gravity, up to different non-metricity effects.…”

Section: Introductionsupporting

confidence: 74%

“…Another theory where the connection is not determined by the metric itself is the original Weyl quadratic gravity of gauged scale invariance [22][23][24] (also [25]). With hindsight, it is then not too surprising that the above results are similar to those in [26][27][28] for Weyl theory. This theory came under early criticism from Einstein [22] for its non-metricity implying e.g.…”

Section: Introductionsupporting

confidence: 53%

“…Inflation in EP quadratic gravity has a specific prediction for the tensor-to-scalar ratio 0.007 ≤ r ≤ 0.010 for the current spectral index n s at 95% CL. This range of r is distinct from that predicted by inflation in Weyl gravity [28,47] and will soon be reached by CMB experiments [79][80][81]. The conclusions are presented in Sect.…”

Section: Introductionmentioning

confidence: 78%

“…With the Planck scale a simple phase transition scale in our theory, field values above M are natural. Interestingly, the inflaton potential is similar to that in Weyl quadratic gravity [28], up to couplings and field redefinitions (due to a different nonmetricity of the theory). Inflation in EP quadratic gravity has a specific prediction for the tensor-to-scalar ratio 0.007 ≤ r ≤ 0.010 for the current spectral index n s at 95% CL.…”

Section: Introductionmentioning

confidence: 88%

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Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

Ghilencea

2020

Eur. Phys. J. C

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We study quadratic gravity $$R^2+R_{[\mu \nu ]}^2$$ R 2 + R [ μ ν ] 2 in the Palatini formalism where the connection and the metric are independent. This action has a gauged scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $$v_\mu = (\tilde{\Gamma }_\mu -\Gamma _\mu )/2$$ v μ = ( Γ ~ μ - Γ μ ) / 2 , with $$\tilde{\Gamma }_\mu $$ Γ ~ μ ($$\Gamma _\mu $$ Γ μ ) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $$R_{[\mu \nu ]}^2$$ R [ μ ν ] 2 term acting as a gauge kinetic term for $$v_\mu $$ v μ . We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($$\phi $$ ϕ ) is not added ad-hoc to this purpose but is “extracted” from the $$R^2$$ R 2 term. The gauge field becomes massive by absorbing the derivative term $$\partial _\mu \ln \phi $$ ∂ μ ln ϕ of the Stueckelberg field (“dilaton”). In the broken phase one finds the Einstein–Proca action of $$v_\mu $$ v μ of mass proportional to the Planck scale $$M\sim \langle \phi \rangle $$ M ∼ ⟨ ϕ ⟩ , and a positive cosmological constant. Below this scale $$v_\mu $$ v μ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $$0.007\le r\le 0.01$$ 0.007 ≤ r ≤ 0.01 for current spectral index $$n_s$$ n s (at $$95\%$$ 95 % CL) and $$N=60$$ N = 60 efolds. This value of r is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.

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Section: Introductionsupporting

confidence: 74%

Section: Introductionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 88%

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Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

Ghilencea

2020

Eur. Phys. J. C

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“…But unlike in [29] where no Stueckelberg mechanism takes place since there is no gauge kinetic term, here there is no flat direction left -this was "absorbed" by the gauge field which became massive. This issue and inflation are discussed in detail elsewhere [30].…”

Section: Canonical Action More Scalar Fields and Sm In Weyl Geometrymentioning

confidence: 99%

Stueckelberg breaking of Weyl conformal geometry and applications to gravity

Ghilencea

2020

Phys. Rev. D

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Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a particular Weyl gauge transformation (of "gauge fixing") while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number (n df ). The Weyl gauge field (ω µ ) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dynamic origin, corresponding to a transition from Weyl to Riemannian geometry. We show that a "gauge fixing" symmetry transformation of the original Weyl's quadratic gravity action in its Weyl geometry formulation, immediately gives the Einstein-Proca action for the Weyl gauge field and a positive cosmological constant, plus matter action (if present). As a result, the Planck scale is an emergent scale, where Weyl gauge symmetry is spontaneously broken and Einstein action is the broken phase of Weyl action. This is in contrast to local scale invariant models (no gauging) where a negative kinetic term (ghost dilaton) remains present and n df is not conserved when this symmetry is broken. The mass of ω µ , setting the non-metricity scale, can be much smaller than M Planck , for ultraweak values of the coupling (q), with implications for phenomenology. If matter is present, a positive contribution to the Planck scale from a scalar field (φ 1 ) vev induces a negative (mass) 2 term for φ 1 and spontaneous breaking of the symmetry under which it is charged. These results are immediate when using a Weyl geometry formulation of an action instead of its Riemannian picture. Briefly, Weyl gauge symmetry is physically relevant and its role in high scale physics should be reconsidered. *

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Spontaneous scale symmetry breaking at high temperature

Lalak

Michalak

2023

J. High Energ. Phys.

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We consider a scale symmetric extension of the Standard Model Higgs scalar sector. The new sector, dilaton, is responsible for the generation of mass scales and may have geometric origin in the Weyl gravity $$ {\overset{\sim }{R}}^2 $$ R ~ 2 term. We show how temperature as a mass scale breaks scale symmetry explicitly and through a nonvanishing thermal vev. In addition we demonstrate that cosmological evolution of the dilaton-Higgs system can lead to late time mass scales, which agree with the Standard Model.

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Weyl R2 inflation with an emergent Planck scale

Cited by 49 publications

References 102 publications

Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

Stueckelberg breaking of Weyl conformal geometry and applications to gravity

Spontaneous scale symmetry breaking at high temperature

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