Ref HAL: hal-02464734_v1
Ref Arxiv: 2001.11670
DOI: 10.1103/PhysRevD.101.074009
WoS: 000525109000003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We reconsider our former determination of the chiral quark condensate $\langle \bar q q \rangle$ from the related QCD spectral density of the Euclidean Dirac operator, using our Renormalization Group Optimized Perturbation (RGOPT) approach. Thanks to the recently available {\em complete} five-loop QCD RG coefficients, and some other related four-loop results, we can extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to $N^5LO$ (six-loops), the latter within a well-defined approximation accounting for all six-loop contents exactly predictable from five-loops RG properties. The RGOPT results overall show a very good stability and convergence, giving primarily the RG invariant condensate, $\langle \bar q q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \bar\Lambda_0 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) \bar\Lambda_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) \bar\Lambda_3 $, where $\bar\Lambda_{n_f}$ is the basic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and the range spanned is our rather conservative estimated theoretical error. This leads {\it e.g.} to $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(273^{+7}_{-4}\pm 13)$ MeV, using the latest $\bar\Lambda_3$ values giving the second uncertainties. We compare our results with some other recent determinations. As a by-product of our analysis we also provide complete five-loop and partial six-loop expressions of the perturbative QCD spectral density, that may be useful for other purposes.

Ref HAL: hal-02423733_v1
Ref Arxiv: 1912.06958
Ref INSPIRE: 1770954
DOI: 10.1103/PhysRevD.101.103501
WoS: 000529824500006
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé:

We analyze the global behavior of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold nonrelativistic matter and dark energy (DE) with an arbitrary equation of state. Using a dynamical system approach, we find the critical points of the system. That unique trajectory for which the growth index γ is finite from the asymptotic past to the asymptotic future is identified as the so-called heteroclinic orbit connecting the critical points (Ωm=0,γ∞) in the future and (Ωm=1,γ-∞) in the past. The first is an attractor while the second is a saddle point, confirming our earlier results. Further, in the case when a fraction of matter (or DE tracking matter) ϵΩmtot remains unclustered, we find that the limit of the growth index in the past γ-∞ϵ does not depend on the equation of state of DE, in sharp contrast with the case ϵ=0 (for which γ-∞ is obtained). We show indeed that there is a mathematical discontinuity: one cannot obtain γ-∞ by taking limϵ→0γ-∞ϵ (i.e., the limits ϵ→0 and Ωmtot→1 do not commute). We recover in our analysis that the value γ-∞ϵ corresponds to tracking DE in the asymptotic past with constant γ=γ-∞ϵ found earlier.

Ref HAL: hal-02178711_v1
Ref Arxiv: 1906.05991
Ref INSPIRE: 1739993
DOI: 10.1093/mnras/staa633
WoS: 000535885900062
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
10 Citations
Résumé:

Using redshift space distortion data, we perform model-independent reconstructions of the growth history of matter inhomogeneity in the expanding Universe using two methods: crossing statistics and Gaussian processes. We then reconstruct the corresponding history of the Universe background expansion and fit it to Type Ia supernovae data, putting constraints on (Ω_m, 0, σ_8, 0). The results obtained are consistent with the concordance flat-ΛCDM model and General Relativity as the gravity theory given the current quality of the inhomogeneity growth data.