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

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

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.

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

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

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

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

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.

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.

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.

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

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.)

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.

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 ~10-2-10-3; 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

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. 1350032

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