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001513376 001__ 1513376
001513376 003__ SzGeCERN
001513376 005__ 20210715024757.0
001513376 0247_ $$2DOI$$a10.1088/1475-7516/2013/06/002
001513376 0248_ $$aoai:cds.cern.ch:1513376$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
001513376 035__ $$9arXiv$$aoai:arXiv.org:1302.0740
001513376 035__ $$9Inspire$$a1217517
001513376 037__ $$9arXiv$$aarXiv:1302.0740$$castro-ph.CO
001513376 037__ $$aDESY-13-011
001513376 037__ $$aCERN-PH-TH-2012-362
001513376 037__ $$aBA-TH-666-12
001513376 037__ $$aLPTENS-13-01
001513376 041__ $$aeng
001513376 088__ $$aCERN-PH-TH-2012-362
001513376 084__ $$2CERN Library$$aTH-2012-362
001513376 100__ $$aBen-Dayan, I.$$uDESY
001513376 245__ $$aAverage and dispersion of the luminosity-redshift relation in the concordance model
001513376 269__ $$c05 Feb 2013
001513376 260__ $$c2013
001513376 300__ $$a27 p
001513376 500__ $$aComments: 27 pages, 8 figures
001513376 500__ $$9arXiv$$a28 pages, 8 figures. Comments and references added. Paper published in JCAP
001513376 520__ $$aStarting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined light-cone and ensemble average of various functions of the luminosity distance, and on their variance, as functions of redshift. We apply a gauge-invariant light-cone averaging prescription which is free from infrared and ultraviolet divergences, making our results robust with respect to changes of the corresponding cutoffs. Our main conclusions, in part already anticipated in a recent letter for the case of a perturbation spectrum computed in the linear regime, are that such inhomogeneities not only cannot avoid the need for dark energy, but also cannot prevent, in principle, the determination of its parameters down to an accuracy of order $10^{-3}-10^{-5}$, depending on the averaged observable and on the regime considered for the power spectrum. However, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision. The predicted dispersion appears to be in good agreement with current observational estimates of the distance-modulus variance due to Doppler and lensing effects (at low and high redshifts, respectively), and represents a challenge for future precision measurements.
001513376 520__ $$9IOP$$aStarting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined light-cone and ensemble average of various functions of the luminosity distance, and on their variance, as functions of redshift. We apply a gauge-invariant light-cone averaging prescription which is free from infrared and ultraviolet divergences, making our results robust with respect to changes of the corresponding cutoffs. Our main conclusions, in part already anticipated in a recent letter for the case of a perturbation spectrum computed in the linear regime, are that such inhomogeneities not only cannot avoid the need for dark energy, but also cannot prevent, in principle, the determination of its parameters down to an accuracy of order 10−3−10−5, depending on the averaged observable and on the regime considered for the power spectrum. However, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision. The predicted dispersion appears to be in good agreement with current observational estimates of the distance-modulus variance due to Doppler and lensing effects (at low and high redshifts, respectively), and represents a challenge for future precision measurements.
001513376 520__ $$9arXiv$$aStarting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined light-cone and ensemble average of various functions of the luminosity distance, and on their variance, as functions of redshift. We apply a gauge-invariant light-cone averaging prescription which is free from infrared and ultraviolet divergences, making our results robust with respect to changes of the corresponding cutoffs. Our main conclusions, in part already anticipated in a recent letter for the case of a perturbation spectrum computed in the linear regime, are that such inhomogeneities not only cannot avoid the need for dark energy, but also cannot prevent, in principle, the determination of its parameters down to an accuracy of order $10^{-3}-10^{-5}$, depending on the averaged observable and on the regime considered for the power spectrum. However, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision. The predicted dispersion appears to be in good agreement with current observational estimates of the distance-modulus variance due to Doppler and lensing effects (at low and high redshifts, respectively), and represents a challenge for future precision measurements.
001513376 540__ $$3Preprint$$aCC-BY-3.0
001513376 542__ $$3Preprint$$dCERN$$g2012
001513376 595__ $$aLANL EDS
001513376 595__ $$aCERN-TH
001513376 65017 $$2arXiv$$aAstrophysics and Astronomy
001513376 65027 $$2arXiv$$aParticle Physics - Theory
001513376 65027 $$2arXiv$$bGeneral Relativity and Cosmology
001513376 695__ $$9LANL EDS$$aastro-ph.CO
001513376 695__ $$9LANL EDS$$agr-qc
001513376 695__ $$9LANL EDS$$ahep-th
001513376 690C_ $$aARTICLE
001513376 690C_ $$aCERN
001513376 700__ $$aGasperini, M.$$uINFN, Bari$$uU. Bari (main)
001513376 700__ $$aMarozzi, G.$$uGeneva U., CAP$$uGeneva U., Dept. Theor. Phys.$$uCollege de France
001513376 700__ $$aNugier, F.$$uEcole Normale Superieure
001513376 700__ $$aVeneziano, G.$$uNew York U., CCPP$$uCERN$$uCollege de France
001513376 773__ $$c002$$pJCAP$$v06$$y2013
001513376 8564_ $$uhttp://arxiv.org/pdf/1302.0740.pdf$$yPreprint
001513376 8564_ $$81297795$$s1151325$$uhttps://cds.cern.ch/record/1513376/files/arXiv:1302.0740.pdf
001513376 8564_ $$81297793$$s7410$$uhttps://cds.cern.ch/record/1513376/files/f3a.png$$y00003 The fractional correction to the flux $f_\Phi$ of Eq. (\ref{7a}) (thin curves) is plotted together with the fractional correction to the luminosity distance $f_d$ of Eq. (\ref{13}) (thick curves), for a $\La$CDM model with $\Om_{\La 0}=0.73$. We have used two different cutoff values: $k_{UV}=0.1 {\rm Mpc}^{-1}$ (dashed curves) and $k_{UV}=1 {\rm Mpc}^{-1}$ (solid curves). The left panel shows the results obtained with a linear spectrum without baryon contributions. The right panel illustrates the effects of including baryons (we have used, in particular, $\Omega_{b0}=0.046$).
001513376 8564_ $$81297794$$s7351$$uhttps://cds.cern.ch/record/1513376/files/f3b.png$$y00004 The fractional correction to the flux $f_\Phi$ of Eq. (\ref{7a}) (thin curves) is plotted together with the fractional correction to the luminosity distance $f_d$ of Eq. (\ref{13}) (thick curves), for a $\La$CDM model with $\Om_{\La 0}=0.73$. We have used two different cutoff values: $k_{UV}=0.1 {\rm Mpc}^{-1}$ (dashed curves) and $k_{UV}=1 {\rm Mpc}^{-1}$ (solid curves). The left panel shows the results obtained with a linear spectrum without baryon contributions. The right panel illustrates the effects of including baryons (we have used, in particular, $\Omega_{b0}=0.046$).
001513376 8564_ $$81297796$$s23305$$uhttps://cds.cern.ch/record/1513376/files/f5.png$$y00007 The linear spectrum $\Pcal_\psi^{\rm{L}}$ (dotted curves) and the non-linear spectrum $\Pcal_\psi^{\rm{NL}}$ for the HaloFit model of \cite{Smith:2002dz} (dashed curves) and of \cite{Takahashi} (solid curves). In all three cases the spectrum is multiplied by $k^2$ (for graphical convenience) and is given for $z=0$ (thin curves) and $z=1.5$ (thick curves). We have included  baryons with $\Om_{b0}=0.046$.
001513376 8564_ $$81297797$$s9651$$uhttps://cds.cern.ch/record/1513376/files/f6.png$$y00008 The fractional correction to the flux ($f_\Phi$, thin curves) and to the luminosity distance ($f_d$, thick curves), for a perturbed $\La$CDM model with $\Omega_{\Lambda 0}=0.73$. Unlike in Fig. \ref{Fig3}, we have taken into account the non-linear contributions to the power spectrum given by the HaloFit model of \cite{Takahashi} (including baryons), and we have used the following cutoff values: $k_{UV}=10 h \,{\rm Mpc}^{-1}$ (dashed curves) and $k_{UV}=30 h \,{\rm Mpc}^{-1}$ (solid  curves).
001513376 8564_ $$81297798$$s6536$$uhttps://cds.cern.ch/record/1513376/files/f1.png$$y00001 The fractional correction $f_\Phi$ of Eq. (\ref{9}) (solid curve), compared with the same quantity given to leading order by Eq. (\ref{10}) (dashed curve), in the context of an inhomogeneous CDM model. We have used for the spectrum the one defined in Eq. (\ref{PsiP}).  The plotted curves refer, as an illustrative example, to an UV cutoff $k_{UV}=1 {\rm Mpc}^{-1}$.
001513376 8564_ $$81297799$$s2972$$uhttps://cds.cern.ch/record/1513376/files/f8.png$$y00011 The $z$-dependence of the total dispersion $\sg_\mu$ is illustrated by the thick solid curve, and it is separated into its ``Doppler" part (dashed curve dominant at low $z$)  and ``lensing" part (dashed curve dominant at large $z$). The slope of the dispersion in the lensing-dominated regime is compared with the experimental estimates of  Kronborg \etal \cite{Kronborg} (dark shaded area), and  of J\"onsson \etal \cite{Jonsson} (light shaded area).
001513376 8564_ $$81297800$$s3859$$uhttps://cds.cern.ch/record/1513376/files/f7a.png$$y00009 The averaged  distance modulus $ \overline{\langle \mu \rangle} -\mu^M$ of Eq. (\ref{14}) (thick solid curve), and its dispersion of Eq. (\ref{15}) (shaded region), for a perturbed $\La$CDM model with $\Omega_{\Lambda 0}=0.73$. Unlike Fig. \ref{Fig4}, we have taken into account the non-linear contributions to the power spectrum given by the HaloFit model of \cite{Takahashi} (including baryons), and used the cut-off  $k_{UV}=30 h \,{\rm Mpc}^{-1}$. The averaged results are compared with the homogeneous values of $\mu$ predicted by  unperturbed $\La$CDM models with  (from bottom to top) $\Omega_{\Lambda 0}= 0.68$, $0.69$ $0.71$, $0.73$, $0.75$, $0.77$, $0.78$ (dashed curves). The right panel simply provides a zoom of the same curves, plotted in the smaller redshift range $0.5 \leq z \leq 2$.
001513376 8564_ $$81297801$$s3062$$uhttps://cds.cern.ch/record/1513376/files/f7b.png$$y00010 The averaged  distance modulus $ \overline{\langle \mu \rangle} -\mu^M$ of Eq. (\ref{14}) (thick solid curve), and its dispersion of Eq. (\ref{15}) (shaded region), for a perturbed $\La$CDM model with $\Omega_{\Lambda 0}=0.73$. Unlike Fig. \ref{Fig4}, we have taken into account the non-linear contributions to the power spectrum given by the HaloFit model of \cite{Takahashi} (including baryons), and used the cut-off  $k_{UV}=30 h \,{\rm Mpc}^{-1}$. The averaged results are compared with the homogeneous values of $\mu$ predicted by  unperturbed $\La$CDM models with  (from bottom to top) $\Omega_{\Lambda 0}= 0.68$, $0.69$ $0.71$, $0.73$, $0.75$, $0.77$, $0.78$ (dashed curves). The right panel simply provides a zoom of the same curves, plotted in the smaller redshift range $0.5 \leq z \leq 2$.
001513376 8564_ $$81297802$$s4016$$uhttps://cds.cern.ch/record/1513376/files/f4a.png$$y00005 The averaged distance modulus $ \overline{\langle \mu \rangle} -\mu^M$ of Eq. (\ref{14}) (thick solid curve), and its dispersion of Eq. (\ref{15}) (shaded region) are computed for $\Om_{\La 0}=0.73$ and compared with the homogeneous value for the unperturbed $\La$CDM models with, from bottom to top, $ \Om_{\La 0}= 0.69$, $0.71$, $0.73$, $0.75$, $0.77$ (dashed curves). We have used $k_{UV}=1\,\rm{Mpc}^{-1}$. The left panel shows the results obtained with a linear spectrum without baryon contributions. The right panel illustrates the effects of including baryons, with $\Omega_{b0}=0.046$.
001513376 8564_ $$81297803$$s3927$$uhttps://cds.cern.ch/record/1513376/files/f4b.png$$y00006 The averaged distance modulus $ \overline{\langle \mu \rangle} -\mu^M$ of Eq. (\ref{14}) (thick solid curve), and its dispersion of Eq. (\ref{15}) (shaded region) are computed for $\Om_{\La 0}=0.73$ and compared with the homogeneous value for the unperturbed $\La$CDM models with, from bottom to top, $ \Om_{\La 0}= 0.69$, $0.71$, $0.73$, $0.75$, $0.77$ (dashed curves). We have used $k_{UV}=1\,\rm{Mpc}^{-1}$. The left panel shows the results obtained with a linear spectrum without baryon contributions. The right panel illustrates the effects of including baryons, with $\Omega_{b0}=0.046$.
001513376 8564_ $$81297804$$s15956$$uhttps://cds.cern.ch/record/1513376/files/f2.png$$y00002 A comparison of the primordial inflationary spectrum (long-dashed curve) with the spectrum of the CDM model neglecting baryons (thick solid curve) and of a $\Lambda$CDM model (thin solid curves), at various values of $z$. The dotted curves for the  $\La$CDM case describe the spectrum obtained by neglecting the baryon contribution (hence without taking into account the Silk-damping effect).
001513376 8564_ $$82306609$$s9563$$uhttps://cds.cern.ch/record/1513376/files/fig00000.png$$y00000 noimgThe spectral coefficients $\Ccal_{\Tcal^{(1)}_i}$ for the  $\overline{\lla {\Tcal^{(1)}_i} \rra \lla {\Tcal^{(1)}_j} \rra}$ terms.
001513376 916__ $$sn$$w201305
001513376 960__ $$a13
001513376 980__ $$aARTICLE