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
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 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.

4. 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

5. 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

6. 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

7. 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

8. 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.

9. 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.

10. 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.

11. 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

12. 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.)

13. 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.

14. 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

15. 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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Year: 2013
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