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Peaks in the CMBR power spectrum: Physical interpretation for any cosmological scenario

Peaks in the CMBR power spectrum: Physical interpretation for any cosmological scenario. References : López- Corredoira & Gabrielli , 2013, Physica A , 392, 474 López- Corredoira , 2013, Int . J. Mod . Phys . D , 22(7), id. 1350032. Martín López- Corredoira

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Peaks in the CMBR power spectrum: Physical interpretation for any cosmological scenario

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  1. Peaks in the CMBR power spectrum: Physical interpretation for any cosmological scenario • References: • López-Corredoira & Gabrielli, 2013, Physica A, 392, 474 • López-Corredoira, 2013, Int. J. Mod. Phys. D, 22(7), id. 1350032 Martín López-Corredoira Instituto de Astrofísica de Canarias Tenerife, Spain

  2. Origin of the oscillations Two-point correlation function(Transform: Fourier/Legendre)Power spectrum

  3. Origin of the oscillations - If has some non-continuous derivative at some point, then Cl[or P(k)] presents oscillations.(see mathematical demonstration in López-Corredoira & Gabrielli 2013)- These kinds of discontinuities do not need to be abrupt in an infinitesimal range of angular distances but may also be smooth.- The positions, widths, amplitudes of the peaks are not independent, but they depend only on the position of the point with the abrupt transition in and its derivatives.

  4. ToyModel Howtogenerateabruptchanges in thecorrelationfunction? Filled disks of contant radius R=1owith a Poissoniandistribution

  5. ToyModel Howtogenerateabruptchanges in thecorrelationfunction? Filled disks of contant radius R=1owith a randomdistributionbut disks do notintersect

  6. ToyModel Howtogenerateabruptchanges in thecorrelationfunction? Filled disks of contant radius R=1owith a non-Poissoniandistribution

  7. ToyModel Howtogenerateabruptchanges in thecorrelationfunction? Filled disks of variable (finite) radiuswithanydistributioninside, and distribution of disks

  8. Physical interpretation A modeltogenerate CMBR powerspectrum • Disks may represent a projection of spherical regions in 3D space. • The standard cosmological model is a particular case in which the radius of the disk is constant representing the size of the acoustic horizon (diameter of the acoustic horizon region at recombination epoch: 1.2 degrees). Photon-baryon fluid compressed by gravitational attraction produced by local density fluctuations. • Non-standard cosmological models: any fluid with clouds of overdensities that emits/absorbs radiation or interact gravitationally with the photons. Different radii is possible when the 3D distribution projects clouds from different distances.

  9. Physical interpretation Caveats of analternativemodel of CMBR • Black body shape. • (Almost) Gaussian fluctuations. • Only 6 free parameters to fit the power spectrum.

  10. Howmany free Parameters? WMAP-7yr data Dip = anticorrelation of disks f6: set of polynomialfunctionswithcontinuousderivativewith 6 free parameters: χred2=3.0 f4: set of polynomialfunctionswithcontinuousderivativewith4 free parameters. g4: set of polynomial / logarithmicfunctionswith4 free parameters.

  11. Howmany free Parameters? WMAP-7yr + ATACAMA/ACT data f6,A: set of polynomialfunctionswithcontinuousderivativewith 6 free parameters: χred2=1.4

  12. Howmany free Parameters? Powerspectrum Peaks 3rd. and beyondare notfittedwiththe sets of polynomials(possiblybecausewehavenotusedѳ<0.2 deg.)

  13. Howmany free Parameters? Powerspectrum Narlikar et al. (2007): WMAP-3yr data. Solid line: QSSC and clusters of galaxieswith 6 parameters; Dashed line: standard model. Angus & Diaferio (2011): WMAP-7yr+ACT+ACBAR data. Blue line: MOND, withsterile neutrinos with 6 free parameters; Red line: standard model.

  14. Discussion Success of standard cosmologicalmodel? Wrongpredictionswhichwerecorrected ad hoc: Temperature TCMBR=50 K (Gamow 1961) or 30 K (Dicke et al. 1965) Amplitude of theanisotropies (ΔT/T ~10-2-10-3; Sachs & Wolfe 1967) Position of thefirstpeak at l≈200 (measuredforthefirst time in themiddle 90s [White et al. 1996] and contradictingthepreferredcosmologicalmodel at that time Ω=Ωm≈0.2) Amplitude of thesecondpeak as high as thefirstpeak (Bond & Efstathiou 1987) Etc. Succesfulpredictions: Isotropy Black bodyradiation Peaks in CMBR powerspectrum (Peebles & Yu 1970) Etc. Darkmatterad hoc Darkenergyad hoc

  15. Discussion Recipetocook CMBR in analternativecosmology General features of CMBR and itspowerspectrum/two-pointcorrelationfunction: Temperature TCMBR=3 K Isotropy Black bodyradiation Gaussianfluctuations Peaks in CMBR powerspectrum 6 free parametersshouldfitit Others (polarization,…) Explanationswhich do notrequirethe standard model: Severalideas (e.g., stellarradiation) Radiationcomingfromalldirections Thermalization of radiation? Notclearyet There are manyprocesses in NaturewhichgenerateGaussianfluctuations; but, theremay be non-Gaussianitytoo Abrupttransition of emission/absorptioninside and outsidesomeclouds/regions A simple set of polynomials produce a quite goodfit of the 2-point corr.func., butdo notexplain 3rd peak ≈ 2nd peakamplitude FURTHER RESEARCH IS NEEDED Pending Majorproblem References: López-Corredoira & Gabrielli, 2013, Physica A, 392, 474 López-Corredoira, 2013, Int. J. Mod. Phys. D, 22(7), id. 1350032

  16. Science is in decline. Facts and challenging ideas about the exhaustion of our culture in The Twilight of the Scientific Age Publisher: BrownWalker Press Year: 2013 Book available at: BrownWalker Press, Amazon, Barnes & Noble,…

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