Modeling of SN1a data with my theory
1University of Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
2Studienseminar Stade, Bahnhofstraße 5, 21682 Stade, Germany
3Gymnasium Athenaeum, Harsefelder Straße 40, 21680 Stade, Germany
April 25, 2021
1 Suggested and executed modeling
In a discussion with Prof. Marco Pereira, Rutgers University, he suggested that I model distance moduli
µas a function of the redshift zfor the case of the supernova SN1a data of the Union Sample, see Suzuki
et al. (2011). I did it with my theory, see1, without executing any ﬁt, fully based on quantum gravity
and the universal constants G,c,kBand h. My theoretical values µtheo(z) are in precise accordance with
the observed values µobs(z), see2. Additionally, I presented the code, see3.
Next Marco Pereira suggested that I model the Hubble constants H0corresponding to these supernovae
SN1a. I did it. For it I calculated for each observed distance modulus µobs the corresponding observed
Hubble constant H0,obs by application of the usual formula, see e. g. (Riess et al.,2018, eq. 1):
H0,obs =c·(1 + z)
with the luminosity distance dLand with
E(z) = H(z)
Hereby the luminosity distance is calculated from the observed distance modulus:
Again, I present the details of the derivation and of the calculation in my code, see4. Moreover I present
the essential results here.
Firstly, the standard deviation of H0is relatively large, see Fig. (1):
1Carmesin (2021), presented in https://www.researchgate.net/publication/350373240_Quanta_of_Spacetime_
We interpret that large standard deviation by using Eq. (3): The observed distance modulus is in the
exponent, so small errors of measurement can easily be magniﬁed.
Secondly, we see that the average is in precise accordance with my theory, see Fig. (1). Again, I do
not execute any ﬁt, instead I use the universal constants G,c,kBand hin my theory.
Thirdly, as a consequence of the large standard deviation in Eq. (4), the Union sample can hardly be
used in order to investigate the Hubble tension.
Fourthly, I used many other probes in order to analyze the Hubble tension, see (Riess et al.,2019,
Fig. 4) and Fig. (1). And my theory is in precise accordance with observation.
My theory is in precise accordance with the observations for both suggested modelings: the distance
modulus as a function of the redshift µ(z), and the Hubble constant H0as a function of the redshift
Indeed, supernovae are particularly interesting for the investigation of the Hubble tension, see Fig.
(1). Accordingly, observers are improving their results in this ﬁeld, at least since 20 years, see e. g. (Riess
et al.,2019, Fig. 5).
Acknowledgement: I thank Marco Pereira for the interesting and stimulating discussion.
strong lensing: ∆
weak lensing: full ∆
Hubble constant H0in km
Figure 1: H0as a function of the redshift zof the probe. Probes: distance ladder (full ,
from left to right: Riess et al. (2019), Scolnic et al. (2018), Suzuki et al. (2011), Riess et al.
(2018)), baryonic acoustic oscillations (o, Zaldarriaga et al. (2020), Weiland et al. (2018)),
weak gravitational lensing (full ∆, Lu and Haiman (2020)), strong gravitational lensing
(∆, Birrer et al. (2020)), gravitational wave (open , large error of measurement, Fishbach
et al. (2019)), CMB (pentagon, Collaboration (2020)). Semiclassical dark energy theory
(dotted) and quantum theory of dark energy (dashed). Both theories do not execute
any ﬁt, use as numerical input the universal constants G,c,kBand has well as two
reference values: The reference value H0marks the time after the Big Bang. The second
reference value provides information about matter, as matter is not modeled completely
in the present theory of dark energy. In particular, the reference value for matter is
the amplitude of matter ﬂuctuations σ8for the case of the semiclassical theory. And
that reference value is the density parameter Ωbfor baryonic matter for the case of the
quantum theory, as in my quantum theory the matter is modeled from the time of its
formation, see Carmesin (2021), Carmesin (2019).
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