Abstract This paper studies both $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM and CDM models under the über gravity theory, named ü $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM and üCDM respectively. We report bounds over their parameter phase-space using several cosmological data, in particular, the recent Pantheon+ sample. Based on the joint analysis, the best fit value of the über characteristic parameter is $$z_\oplus = 0.046^{+0.047}_{-0.032}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>z</mml:mi> <mml:mo>⊕</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>046</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.032</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.047</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> and $$z_\oplus = 1.382^{+0.020}_{-0.021}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>z</mml:mi> <mml:mo>⊕</mml:mo> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>382</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.021</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.020</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> at 68% confidence level for ü $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM and üCDM respectively. Although über gravity can successfully mimics the cosmological constant, we find that the $$\mathbb {H}0(z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> diagnostic suggests the $$H_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> tension is not alleviated. Finally, both models are statistically compared with $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM through the Akaike and Bayesian information criteria. Both über gravity models and $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM are equally preferred for most of the single samples, in particular, ü $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM is not rejected by the CMB data. However, there is strong evidence against them for the joint analysis. 

/pdf/constraining-uber-gravity-with-recent-observations-and-1arcyct3.pdf

Constraining über gravity with recent observations and studying the $$H_0$$ problem

From the mathematical expression relating the redshift parameter with time and the cosmological densities of matter, radiation and vacuum in the Lemaitre model, we have derived an equation for the age of the universe at present time taking into account the contribution of the radiation energy density (that generally is neglected in the calculations). Additionally we calculate the value of the redshift parameter in the transition age when matter and radiation decouple.

Edad del universo y la densidad de energía de la radiación

There are several nuclei (see Table 5.1) having excited states at energies in the vicinity of 511 keV. This circumstance permits conducting experiments aimed at observing resonant scattering on these nuclei that is experienced by photons originating from in matter. 


Table 5.1
Properties of the some nuclei having the levels with energy near 511 keV



	
Nucleus
	
Relative content in the natural mixture of isotopes (percent)
	
Energy of the excited state (keV)
	
Mean lifetime τ of nuclei in the excited state (s)


71Ga
	
39.8 [33]
	
511.5 ± 0.1 [33]
	
1.98 × 10−12 [34]
	

0.19 × 10−9 [33]
	

106Pd
	
27.33 [35]
	
511.76 ± 0.08 (averaging of data from [14, 17, 32, 36, 37, 38, 39, 40, 41]
	
(16.31 ± 0.87) × 10−12 [32]
	

165Ho
	
100 [35]
	
515, 472 [42]
	
(24.5 ± 4.3) × 10−12 [42]
	

177Hf
	
18.5 [35]
	
508.1 ± 0.1 [43]
		

187Re
	
62.93 [44]
	
511.65 ± 0.05 [45]
	
(23.1 ± 8.7) × 10−12 [45]
	

239Pu
		
511.8 [46]
		

511.84 [34]

Nuclear Resonant Scattering of Annihilation Photons

Positronium in a void in a high- T c superconductor

https://iopscience.iop.org/article/10.1070/PU1968v011n02ABEH003804/pdf

Annihilation of positrons in metals

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Annihilation of positrons in metals