ЯДЕРНАЯ ФИЗИКА, 2012, том 75, № 11, с. 1492-1499
= ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ CONFORMAL COSMOLOGICAL MODEL AND SNe Ia DATA
©2012 A. F. Zakharov1),2),3)*, V. N. Pervushin3)
Received October 13, 2011; in final form, May 2,2012
Now there is a huge scientific activity in astrophysical studies and cosmological ones in particular. Cosmology transforms from a pure theoretical branch of science into an observational one. All the cosmological models have to pass observational tests. The supernovae type Ia (SNe Ia) test is among the most important ones. If one applies the test to determine parameters of the standard Friedmann— Robertson—Walker cosmological model one can conclude that observations lead to the discovery of the dominance of the Л term and as a result to an acceleration of the Universe. However, there are big mysteries connected with an origin and an essence of dark matter (DM) and the Л term or dark energy (DE). Alternative theories of gravitation are treated as a possible solution of DM and DE puzzles. The conformal cosmological approach is one of possible alternatives to the standard ЛCDM model. As it was noted several years ago, in the framework of the conformal cosmological approach an introduction of a rigid matter can explain observational data without Л term (or dark energy). We confirm the claim with much larger set of observational data.
1. INTRODUCTION
In 2011 S. Perlmutter, A. Riess, and B. Schmidt have been awarded the Nobel prize in physics for their investigations [1, 2]4), connected with an evaluation of cosmological model parameters through observations of type Ia supernovae with high red-shifts. In these studies it was supposed that maximal luminosities do not appear on redshifts (distances) (however, maximal luminosities depend on time derivatives of luminosities according to the Pskovsky—Phillips law [3]), therefore the supernovae are used as so-called the standard candles. Practically the astronomers measured fluxes from the supernovae and redshifts z. Studying supernovae with high redshifts, observers found the stars are
!)National Astronomical Observatories of Chinese Academy of Sciences, Beijing.
2)Institute of Theoretical and Experimental Physics, Moscow, Russia.
3)Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.
E-mail: zakharov@itep.ru
4)It was a third Nobel prize awarded for observations connected with cosmology. In 1978 A. Penzias and R. Wilson were awarded the Nobel prize for physics for their discovery of the cosmic microwave background radiation, in 2006 G. Smoot and J. Mather were awarded the Nobel prize for physics for discoveries of an anisotropy and a black body spectrum of the cosmic microwave background radiation. A summary of preceding results of the Soviet Relikt-1 experiment and a chronology of COBE and Relikt-1 publications are given in A. F. Zakharov et al., AIP Conf. Proc. 966, 173 (2008); Proceedings of the 6th International Heidelberg Conference, Ed. by H. V. Klapdor-Kleingrothaus and G. Lewis (World Sci., 2008), p. 366.
fainter than predictions of Friedmann—RobertsonWalker with the vanishing A term. In particular, it was shown [1, 2] that Friedmann-RobertsonWalker cosmological models with a non-vanishing A term provide much better fit of observational data in comparison with the vanishing A-term models. In the case, if the A term is shifted from the left-hand side of Einstein equations into the right-hand side where the stress-energy tensor is written usually, the corresponding term can be interpreted as the stress-energy component corresponding to unusual equation of state p = wp (w < 0) and the value w = 1 corresponds to the ordinary A term. In this case one can speak about the so-called dark energy. There is a serious unsolved problem about an origin of matter with such properties. In article [2] the authors of the discovery compared results of their observations with conformal cosmological model interpretations [4, 5] where a rigid equation of state was introduced to explain observational data without the non-vanishing A term. According to the conformal cosmological approach [6], S. Perlmutter, A. Riess, and B. Schmidt discovered a physical vacuum of the Universe. Conformal cosmological models were used for the interpretation of a greater set of the supernovae data in paper [7], where it was shown that using a large data set of supernovae the conformal cosmological model fit provides a good fit and it provides practically the same quality interpretation as the Friedmann—Robertson—Walker model with the non-vanishing A term.
Now there is a great progress in observational and theoretical cosmology and even it is typically accepted that cosmology enters into an era of a precise science
(it means that a typical accuracy of standard parameter determination is about a few percent), despite, there are different approaches including alternative theories of gravity to fit observational data (see recent reviews [8] for references). Some classes of theories could be constrained by Solar system data [9] even if they passed cosmological tests. Thus, all the theories should pass all possible tests including cosmological ones.
Since the end of the last century distant supernovae data is a widespread test for all theoretical cos-mological models in spite of the fact the correctness of the hypothesis about SNe Ia as the perfect standard candles is still not proven [10]. However, the first observational conclusion about accelerating Universe and existence of non-vanishing A term was done with the cosmological SNe Ia data. Therefore, typically standard (and alternative) cosmological approaches are checked with the test.
First attempts to analyze SNe Ia data to evaluate parameters of Conformal Cosmological (CC) models were done [4], so it was used only 42 high-redshift-type Ia SNe [1], but after that it was analyzed with a slightly extended sample [5]. In spite of a small size of the samples used in previous attempts to fit CC model parameters, it was concluded that if Q„g is significant in respect to the critical density, CC models could fit SNe Ia observational data with a reasonable accuracy. After that a possibility to use CC models among other alternatives was seriously discussed by different authors [11].
Later on, in paper [7] we checked basic conclusions done in [4] using a more extended sample [12]. The Hubble Space Telescope (HST) cosmological SNe Ia team has corrected data of previous smaller samples as well and also considered possible non-cosmological but astronomical ways to fit observational ways and concluded that some of them, such as a replenishing dust (with Qm = 1, Qa = 0), could fit observational data pretty well even in respect to the best-fit cosmological model [12]. As it was found in [7], subsample of "gold" events gives more sustainable results in fitting cosmological models in contrast with a total sample of "silver" and "gold" events5). In paper [7] we checked our conclusions concerning best fits for CC models for "gold" events and we confirmed them with larger samples (around 200 "gold" supernovae) [13—15].
An aim of the paper is to check and clarify previous conclusions about possible bands for CC parameters with a more extended (and more accurate)
5)To express differences in quality of spectroscopic and photometric data the supernovae were separated into "high-confidence" ("gold") and "likely but not certain" ("silver") subsets [12].
sample [16] used commonly to check standard and alternative cosmological models.
The content of the paper is the following. In Section 2, the basic CC relations are reminded. In Section 3, a magnitude—redshift relation and a data analysis for distant SNe are described. In Section 4, results of fitting procedure for CC models with the sample are given. In Section 5 we use SNLS data to evaluate parameters of CC models. Conclusions are presented in Section 6.
2. CONFORMAL COSMOLOGY RELATIONS
We will remind basic relations for CC-model parameters (see papers [4, 6] for details) considering the General Relativity with an additional scalar field Q, as usually people did to introduce quintessence [17] (earlier, the approach was used for conformal cosmology, see, for example, paper [18] and references therein)
s = ÄDirac + J (Рхл/^д
dßQdßQ - V(Q)
here we used the natural units
^Planck
= h = c = l,
(1)
(2)
therefore, we have the following expressions for density and pressure of the scalar field (pq and pQ, respectively) [ 17]
■PQ{i) = \Q2 + V{Q), PQ(t) = \Q2~V(Q),
(3)
and equation of state (EOS) such as pq = wqpq, where
wq
¡Q2 - V(Q) kQ2 + V(Q)
(4)
( —1 < wq < 1, for "natural" potentials V(Q) > 0). In contrast to quintessence model where one uses typically Q2 < V(Q), below for CC model we will use an approximation Q2 » V(Q) (for a standard representation of the potential V(Q) = \rriQ2, where m is a mass of the field, the approximation corresponds to a massless field model) and we have
iQ2 1
WQ = W '
(5)
or in other words, a rigid EOS for the scalar field Pq = Pq (Prig = Prig, since for our future needs an
i
ц = m - M 46
44
42 40 38 36 34 32
1.5
z
Fig. 1. Observational data (the Hubble diagram) without theoretical fits. The updated supernova Union2.1 compilation of 580 SNe [16].
origin of the EOS is not important, hereafter, we will call the component as the rigid matter).
Defining, as usual, the Standard Cosmological (SC) luminosity-distance is such that
de 1 ~chdt = 4^fL (6)
one finds the SC luminosity-distance—redshift relation
is (z) = (1 + z)2rs = (1 + z)r(z). (7)
The CC luminosity-distance—redshift relation can be obtained
4(z) = (1 + z)is(z) = (1 + z)2r(z) (8)
because all measurable lengths in CC and SC differ, and all observable lengths in CC contain an additional factor (1 + z).
3. MAGNITUDE-REDSHIFT RELATION
Typically to test cosmological theories one should check a relation between an apparent magnitude an
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