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**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 Martín López-Corredoira Instituto de Astrofísica de Canarias Tenerife, Spain

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

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Origin of the oscillations - If 𝐶 𝜃 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 𝐶 𝜃 and its derivatives.

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**How to generate abrupt changes in the correlation function?**

Toy Model How to generate abrupt changes in the correlation function? Filled disks of contant radius R=1o with a Poissonian distribution

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**How to generate abrupt changes in the correlation function?**

Toy Model How to generate abrupt changes in the correlation function? Filled disks of contant radius R=1o with a random distribution but disks do not intersect

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**How to generate abrupt changes in the correlation function?**

Toy Model How to generate abrupt changes in the correlation function? Filled disks of contant radius R=1o with a non-Poissonian distribution

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**How to generate abrupt changes in the correlation function?**

Toy Model How to generate abrupt changes in the correlation function? Filled disks of variable (finite) radius with any distribution inside, and distribution of disks

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**A model to generate CMBR power spectrum**

Physical interpretation A model to generate CMBR power spectrum 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.

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**Caveats of an alternative model of CMBR**

Physical interpretation Caveats of an alternative model of CMBR Black body shape. (Almost) Gaussian fluctuations. Only 6 free parameters to fit the power spectrum.

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**WMAP-7yr data How many free Parameters? Dip = anticorrelation of disks**

f6: set of polynomial functions with continuous derivative with 6 free parameters: χred2=3.0 f4: set of polynomial functions with continuous derivative with 4 free parameters. g4: set of polynomial / logarithmic functions with 4 free parameters.

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**WMAP-7yr + ATACAMA/ACT data**

How many free Parameters? WMAP-7yr + ATACAMA/ACT data f6,A: set of polynomial functions with continuous derivative with 6 free parameters: χred2=1.4

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**Power spectrum How many free Parameters?**

Peaks 3rd. and beyond are not fitted with the sets of polynomials (possibly because we have not used ѳ<0.2 deg.)

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**Power spectrum How many free Parameters?**

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

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**Success of standard cosmological model?**

Discussion Success of standard cosmological model? Wrong predictions which were corrected ad hoc: Temperature TCMBR=50 K (Gamow 1961) or 30 K (Dicke et al. 1965) Amplitude of the anisotropies (ΔT/T ~ ; Sachs & Wolfe 1967) Position of the first peak at l≈200 (measured for the first time in the middle 90s [White et al. 1996] and contradicting the preferred cosmological model at that time Ω=Ωm≈0.2) Amplitude of the second peak as high as the first peak (Bond & Efstathiou 1987) Etc. Succesful predictions: Isotropy Black body radiation Peaks in CMBR power spectrum (Peebles & Yu 1970) Etc. Dark matter ad hoc Dark energy ad hoc

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**FURTHER RESEARCH IS NEEDED**

Discussion Recipe to cook CMBR in an alternative cosmology General features of CMBR and its power spectrum/two-point correlation function: Temperature TCMBR=3 K Isotropy Black body radiation Gaussian fluctuations Peaks in CMBR power spectrum 6 free parameters should fit it Others (polarization,…) Explanations which do not require the standard model: Several ideas (e.g., stellar radiation) Radiation coming from all directions Thermalization of radiation? Not clear yet There are many processes in Nature which generate Gaussian fluctuations; but, there may be non-Gaussianity too Abrupt transition of emission/absorption inside and outside some clouds/regions A simple set of polynomials produce a quite good fit of the 2-point corr.func., but do not explain 3rd peak ≈ 2nd peak amplitude FURTHER RESEARCH IS NEEDED Pending Major problem References: López-Corredoira & Gabrielli, 2013, Physica A, 392, 474 López-Corredoira, 2013, Int. J. Mod. Phys. D, 22(7), id

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