Theseus–BTA Cosmological Crucial Tests Using Multimessenger Gamma-Ray Bursts Observations

Abstract—Modern Multimessenger Astronomy is a powerful instrument for performing crucial tests of the Standard Cosmological Model in the wide redshift interval up to z ∼ 10. This testing is principally important for discussion related to discrepancies between local and global measurements of cosmological parameters. We present a review of multimessenger gamma-ray burst observations currently performed and planed for THESEUS–BTA cooperative program. Such observations provide a unique opportunity to test the fundamental foundations of cosmological models: gravitation theory, cosmological principle of homogeneity and isotropy of large-scale distribution of matter, and space expansion paradigm. Important role of various selection effects leading to systematic distortions of true cosmological relations is discussed.

Keywords: gamma-ray bursts

Recent discussion of the standard Lambda Cold non-baryonic Dark Matter (ΛCDM) model uncovered "possible crisis for cosmology" (Baryshev 2015; Di Valentino et al., 2020a, b; Handley, 2019; Lin et al., 2019; Riess et al., 2020; Verde et al., 2019), which demonstrated that the large-scale cosmological physics contains several fundamental uncertainties. Among them: the absence of crucial decision on closed-flat-open geometry of the Universe (curvature parameter k = +1, 0, −1) (Di Valentino et al., 2020a, b; Handley, 2019), the nature and value of the totally dominating dark energy and nonbaryonic dark matter (Ωde, w, and Ωm) (Colin et al., 2019; Demianski et al., 2019; Di Valentino et al., 2020a; Makarov and Karachentsev, 2011), the difference between local and global values for the Hubble constant H0 (Lin et al., 2019; Riess et al., 2018, 2020; Tully et al., 2016; Verde et al., 2019) are especially worrying problems. The currently observed discordances may indicate the need for new physics and possibly point to drastic changes in the ΛCDM scenario (Di Valentino et al., 2020a, b; Lin et al., 2019; Riess et al., 2020; Verde et al., 2019).

This new situation in cosmology stimulates deep testing of the fundamental physical laws at micro and macro scales simultaneously. Modern physics uses the observable Universe as a part of physical laboratory, where the fundamental physical laws must be tested. Such basic theoretical assumptions as constancy of the fundamental constants c, G, mp, and me, the Lorentz invariance, the equivalence principle, and the quantum principles of the gravity theory are now being investigated by modern theoretical physics (de Rham 2014; Rubakov and Tinyakov, 2008; Uzan, 2003) and by contemporary astrophysical observations (Cardoso and Pani, 2019; Clifton et al., 2012; De Rham et al., 2017; Giddings, 2017; Ishak, 2018; Uzan, 2010).

Modern theoretical and experimental physics also tests foundations of the Standard Cosmological Model (SCM). In particular, the modified theories of gravity change the study of cosmic structure formation (Bartelmann et al., 2019; Clifton et al., 2012; Ishak, 2018; Slosar et al., 2019) (the review by Ishak (2018) contains 900 references).

In fact, in the beginning of the 21st century a New Cosmology emerges and a new set of questions arises. In particular, the famous Turner's list of new cosmological problems contains the following puzzles: What is the physics of underlying inflation? How was the baryon asymmetry produced? What is the nature of the non-baryonic dark matter particles? Why is the composition of our Universe so "absurd" relatively to the lab physics? What is the nature of the dark energy? Answering these questions will reveal deep connections between fundamental physics and cosmology: "There may even be some big surprises—time variation of the constants or a new theory of gravity that eliminates the need for dark matter and dark energy" (Turner, 2002).

The visible matter of the Universe as part, which we can actually observe, is a surprisingly small (about 0.5%) piece of the predicted matter content and this looks like an "Absurd Universe" (Turner, 2003). What is more, about 95% of the cosmological matter density that determine the dynamics of the whole Universe has an unknown physical nature. Turner emphasized that: "modern SCM predicts with high precision the values for dark energy and non-baryonic cold dark matter, but we have to make sense to all this" (Turner, 2002).

Current multimessenger astronomy, including observations of gamma-ray bursts(GRBs), offers new capabilities for cosmological tests, especially in view of the forthcoming mission Transient High Energy Sky and Early Universe Surveyor (THESEUS) (Amati et al., 2018; Strata et al., 2018). Preceding reviews of the GRB cosmology were given by Petrosian et al. (2009); Wang et al. (2015). We show that an important contribution to GRB cosmology belongs to cooperative optical observations using the 6-m SAO BTA telescope facilities (Vlasyuk, 2018).

In our paper we adopt the Sandage's "practical cosmology" approach (Sandage, 1995, 1997), started by Hubble (1937); Hubble and Tolman (1935). According to it one should test the initial principles of cosmological models by using new astronomical facilities. We review application of GRB multimessenger observations to classical cosmological tests described by Baryshev and Teerikorpi (2012). Tests that can probe the underlying basic principles of SCM are in the focus. In particular, we consider GRB multimessenger data for testing a gravity theory, Cosmological Principle and space expansion paradigm.

In Section 2 we list the SCM basic principles to be tested by THESEUS–BTA facilities. Such tests can strengthen the validity of the SCM foundations or point to limitation of its application. Gravity theory in strong field regime and its testing with GRB observations is considered in Section 3. Section 4 describes GRBs in application to the Cosmological Principle testing. In Section 5 we discuss GRB studies as an instrument for testing the space expansion paradigm, the Hubble Diagram and Wilson's time delay test. Conclusions are given in Section 6.

The success of the SCM in explaining the main cosmologically important observations is generally recognized (Baryshev and Teerikorpi, 2012; Peacock, 1999; Peebles, 1993). Fundamental physical basis of the SCM contains the following theoretical assumptions:

—General Relativity Theory—all gravity phenomena can be described by the metric tensor gik of the Riemannian space R.

—Einstein's Cosmological Principle—the strict mathematical homogeneity for the dynamically important matter, i.e. , , (on all scales r the matter density ρ, the total pressure p and the space metric are functions of time only).

—Expanding space paradigm—time dependent distances between galaxies r(t) = S(t)χ, where S(t) is the scale factor and χ is the comoving distance—according to which the observed cosmological redshift is interpreted as the Lemaître effect of the space stretching (not the Doppler effect).

At the beginning of the 21st century professional cosmological community began to discuss the validity and possibilities for testing these three conceptual "pillars" of the SCM (Baryshev, 2015).

Modern achievements of theoretical physics, especially different modifications of general relativity and quantum aspects of gravitation theory, require wider observational testing of the basic SCM principles.

Nowadays physicists consider the observable Universe as a part of "cosmic laboratory", where main physical fundamental laws must be tested in wider redshift interval and with increasing accuracy. GRB observations by THESEUS (Amati et al., 2018; Strata et al., 2018) will provide such an opportunity for redshifts up to z ~ 10. The abilities of gamma-ray, X-ray, IR instrumentation onboard THESEUS accompanying with GRB studies at the 6-m BTA SAO RAS (Sokolov et al., 2018b; Vlasyuk, 2018) and other optical ground-based telescopes can play a crucial role.

In particular, the Cosmological Principle, the general relativity and its modifications, as well as the space expansion paradigm, must be tested by new observations.

We consider the following strategy:

—gamma-to-IR observations of the massive core collapse supernovae (long GRBs) and the merging of binary neutron stars (Short GRBs) to test the gravity theory;

—testing the Cosmological Principle of homogeneity and isotropy in studies of the spatial distribution of GRBs host galaxies and sight-line distribution of galaxies towards GRB;

—constructing the high-redshift GRB Hubble diagram and comparison of time dilation in GRB pulses, GRB afterglow and core-collapse SN light curves to test the expanding space paradigm.

These tests are of the fundamental importance for developing an adequate cosmological model that includes modern multimessenger observations of GRBs.

The most important basic assumption of ΛCDM is the general relativity theory (GRT). It has been successfully tested in the weak gravity conditions. But nowadays theoretical physics suggests various new possibilities for its modification (see Cardoso and Pani, 2019; Giddings, 2017; Ishak, 2018). For this reason, crucial cosmological tests, including the modern alternative gravitation theories in strong gravity regime, are needed.

The cosmological model is a solution of the gravitational field equations for the case of a cosmologically large-scale distribution of matter.

Being a prototype of the geometrical approach to gravitation GRT is a non-quantum theory, so it does not obey the quantum principles of modern physics. The most challenging problem for modern theoretical physicists is to construct the quantum theory of gravitation which is united with other fundamental quantum interactions—strong, weak, electromagnetic (Amelino-Camelia, 2000; Giddings, 2017; Hawking, 2014; Wilczek, 2015).

In general, there are two alternative approaches for inclusion of gravitation to unified theory: (1) modification of existing theories of fundamental interactions to include them into curved geometry (Rovelli, 2004), or (2) development of a quantum field gravity theory of gravity based on the general principles with other fundamental physical interaction (Minkowski space-time, positive localizable field energy density, energy-momentum conservation, uncertainty principle, quanta of gravity field energy).

It is expected that the future "Core Theory" of physics will unify all fundamental forces (electromagnetic, weak, strong and gravitational) and also deliver unification of forces (bosons) and substances (fermions) via transformations of supersymmetry (Wilczek, 2015).

Feynman et al. (1995) considered the construction of quantum field theory of gravity as the symmetric second rank tensor field in Minkowski space, based on common principles with other fundamental forces. A development of Feynman's approach was done in Baryshev (2017); Baryshev and Teerikorpi (2012); Baryshev and Oschepkov (2019); Sokolov (2015, 2016, 2019); Sokolov and Baryshev (1980), where new predictions were considered for structure of the relativistic compact objects (RCO) and for cosmological solution of the gravity field equations.

Both modified geometrical and quantum field approaches should be studied more carefully and tested by observations of RCOs and cosmological processes.

To get important restrictions on possible gravitation theories the space and ground-based multimessenger GRB studies can be used.

We initiate an international observational program on monitoring of GRBs detected by Swift, Fermi, INTEGRAL, Lomonosov and other space missions. The program aims at searching for optical/electromagnetic counterparts connected with GRBs, neutrino sources and gravitational wave (GW) events detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo experiment. In collaboration with these studies we develop the future THESEUS space mission project, aiming at fully exploiting the unique capabilities of GRBs for cosmology and multi-messenger astrophysics.

In frames of the program optical observations with the 6-m BTA telescope of SAO RAS (Sokolov et al., 2018b; Vlasyuk, 2018) are conducted. We look for fast variability of optical flux of GRB afterglows both in imaging and spectroscopic modes. Using the BTA MANIA fast photometry facility one can detect very short optical variability (τ = R/c). Thus these observations are especially important for testing strong gravity, because it determines the size of a RCO. Observed polarization and possible RCO surface effects (magnetic field, hot spots) can deliver crucial information on the RCO nature.

In particular, general relativity predicts black holes of a mass of for RCO, while in the quantum field approach to gravitation a critical mass of for a quark RCO (Sokolov, 2015, 2016, 2019). Figure 1 presents an "unexplained" observed mass gap – between neutron stars and black hole candidates (Ozel et al., 2012). The nature of the RCO with a mass of is the laboratory for crucial testing for the gravity theory.

Graph: Fig. 1. The inferred mass distributions for the different populations of neutron stars (left) and black hole candidates (right) discussed in the Ozel et al. (2012). The dashed lines correspond to the most likely values of the parameters. For the recycled neutron star populations the peak is and . For the case of black hole candidates the peak is and a scale of . The solid lines represent the weighted mass distributions for each population.

Up to now, GW 170817/GRB 170817A is the only observation of gravitational waves originating from the merging of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to probe the internal structure of neutron stars directly (Abbott et al., 2017). These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short GRB170817A.

Future THESEUS–BTA observations of GRBs will essentially increase statistics of such crucial events and hence make crucial contribution to testing gravitation theory as the basis of cosmological models.

The sources of GRBs are massive supernovae explosions and merging of binary relativistic compact objects (Sokolov et al., 2018b). They mark their host galaxies up to high redshifts, hence their observations can probe the spatial large-scale distribution of visible matter.

Modern progress in spectral and photometric redshift surveys for wide-angle (e.g., 2dF, SDSS, BOSS) and deep fields (e.g., COSMOS) leads to the discovery of very large structures at all observed redshifts. Direct observations of the spatial distribution of visible matter (galaxies) do reveal inhomogeneity on scales much larger than the standard Peebles's correlation length r0 ∼ 5 Mpc.

Nowadays the observationally established scales of inhomogeneity reach several hundreds Mpc. The Laniakea supercluster of galaxies (Tully et al., 2014) and the Dipole Repeller with the Shapley Attractor (Hoffman et al., 2017) in the Local Universe reach a size of ~200 Mpc. The Sloan Great Wall has a size of ~100 Mpc at a distance of about 200 Mpc (Einasto et al., 2016; Gott III et al., 2005). The SDSS/CMASS survey discovered the BOSS Great Wall with a size approximately 300 Mpc at a distance of d ~ 2000 Mpc (Lietzen et al., 2016). In the ultra deep galactic field (UDHF) the photometric redshift survey COSMOS revealed evidence for Super Large Clusters with sizes of about 1000 Mpc at z ~ 1 (Nabokov and Baryshev, 2010b; Shirokov et al., 2016).

Studies of spatial distribution of GRBs with known redshifts also revealed very large inhomogeneous structures, though with large uncertainty. A giant ring of GRBs with a diameter of 1720 Mpc at redshifts of 0.78 < z < 0.86 has been found in Balazs et al. (2015). The probability of observing such a ring-shape structure by chance is 2 × 10–6.

The spatial distribution of 244 GRBs has been analyzed as part of the Swift mission using the Peebles ξ‑function method by Li and Lin (2015). They obtained the correlation length r0 ≈ 388 h–1 Mpc, and γ = 1.57 ± 0.65 (at the 1σ level), and the uniformity scale r ≈ 7700h–1.

These facts require reconsideration of the basic ΛCDM principles of homogeneity and isotropy distribution of matter and its evolution with cosmic time.

In general physics fractal structures naturally originate in phase transitions, dynamical chaos, strange attractors and other physical phenomena. Fractals are characterized by the power-law correlations in a wide range of scales.

The fractal model of spatial distribution of galaxies with the fractal dimension close to the critical value D = 2 finely describes the data of many redshift surveys (Baryshev and Teerikorpi, 2012; Gabrielli et al., 2005).

As it was demonstrated by Gabrielli et al. (2005) and Baryshev and Teerikorpi (2012) the Peebles's reduced correlation function (Peebles, 1993) ξ(r) is strongly distorted by the borders of real samples. To get robust statistical characteristics of the spatial distribution of galaxies one should use the complete correlation function, called also the conditional density function Γ(r). In particular, for a fractal spatial distribution the slope of power-law Γ(r) ∝ r−γ gives the robust estimation of the fractal dimension D = 3 − γ (for the homogeneous distribution γ = 0 and D = 3).

The conditional density and pairwise distances as methods of fractal analysis were proposed by Grassberger (1983a, b). Conditional density analysis of main galaxy samples was developed by Gabrielli et al. (2005), Baryshev and Teerikorpi (2012) and Sylos Labini et al. (2014). The pairwise method was developed in Raikov and Orlov (2011); Shirokov et al. (2017).

In papers Gerasim et al. (2015); Raikov et al. (2010) the fractal dimension of a GRB sample was estimated by the method of pairwise distances. They derived values of the fractal dimensions in the interval D = [2.2; 2.7], but only on scales up to 50 Mpc.

In our paper Shirokov et al. (2017) the new modified methods of conditional density and pairwise distances were presented, which allow one to estimate the fractal dimension at the full interval of scales for a given sample. The normalized distributions of the conditional density and pairwise distances for real GRB sample and for fractal model catalogs give values of the fractal dimension D ≈ 2.0 and D ≈ 2.5 respectively. For the case of a full celestial sphere, the conditional density method gives the fractal dimension of distribution of GRB sources equal to D = 2.6 ± 0.12 at r = [1.5; 2.5] Gpc and D = 2.6 ± 0.06 for r = [1.5; 5.5] Gpc. The pairwise distances method gives a stable power law dependence with D = 2.6 ± 0.06 and does not change essentially for the interval of linear scales l = [1.5; 5.5]. Thus, on scales of about [1.5; 5] Gpc, both methods of GRB spatial structure analysis give a similar exponent of the power law correlation. However the number of GRBs with measured redshifts in analyzed samples is still too small (N < 300), and the above estimations are preliminary results.

Isotropy of the distribution of GRBs in the celestial sphere by the Fermi, BATSE and Swift data was analyzed in paper Ripa and Shafieloo (2018). Authors considered the observed properties of GRBs and made the conclusion: "...the results are consistent with isotropy confirming."

However, anisotropy of sky distribution of GRBs was detected in a number of papers (Balazs et al., 2015; Gerasim et al., 2015; Raikov et al.2010; Shirokov et al., 2017). Thus, for example, a spatially isolated group of five GRBs was detected with the coordinates 23h50m< α < 0h50m and 5° < δ < 25° at redshift of 0.81 < z < 0.97 and also they found GRB groups in several directions on the sky.

It should be emphasized that homogeneity and isotropy of spatial distribution are different properties of the large-scale structure (Baryshev and Teerikorpi, 2012; Gabrielli et al., 2005; Sylos Labini et al., 2014). For example the fractal distribution of matter can have statistical isotropy and simultaneously be strongly inhomogeneous and the Copernican Principle is fulfilled (Sylos Labini and Baryshev, 2010). Our above mentioned results on fractal dimension D being close to its critical value Dcrit = 2 on a very large interval of scales demonstrate that such a situation may be realized in the spatial distribution of GRBs.

Future THESEUS–BTA observations will essentially increase the number of GRBs with known redshifts and hence allow one to get strong restrictions on Cosmological Principle of homogeneity and isotropy of visible and dark spatial (and sight-line) distribution of matter.

An important goal of cosmology is to set an observational limit on the sizes of the largest structures in visible distribution of galaxies. Recent deep spectral and multi-band photometric surveys of galaxies, deliver a new possibility to estimate a homogeneity scale on which the distribution of luminous matter becomes uniform.

Statistical analysis of the number density fluctuation for the various pencil-beam deep galaxy surveys (COSMOS, HUDF, ALHAMBRA) was considered in Nabokov and Baryshev (2010a, b); Shirokov et al. (2016).

Observational "cosmic tomography" test on the reality of the super-large structures (having large angular size on the sky) was suggested in Nabokov and Baryshev (2010b). It can be made possible by a lot of narrow angle (of several arcminutes) very deep multiband photometric beam-surveys in the grid nodes covering the sky (the cells are a several degrees and more). Then, increasing the number of nodes of the grid one can probe the extension of the super-large structure in tangential direction. An advantage of this method is that the very deep faint galaxy surveys allow one to achieve the very wide angular extensions needed for observations of super-large structures.

Important application of this method is to consider the directions to GRBs as nodes. In this case, deep field observations, which are needed for observations of the GRB host galaxies, play the role of nodes of the grid (Baryshev et al., 2010; Sokolov et al., 2016).

As a result of such observational program one can construct the 3D map of "super-structures" by performing correlation between neighboring radial redshift distributions, i.e. to perform the "cosmic tomography" of the observable Universe.

An example of such a node of a possible future grid is the BTA deep field of GRB021004. In Fig. 2 the direct BTA image centered on the GRB021004 host galaxy is shown (Baryshev et al., 2010; Sokolov et al., 2018a, 2016). The photometric redshift is measured for each faint galaxy in the field and the number of galaxies dN(z) in the redshift bin dz is presented in Fig. 3. The smoothed peaks correspond to the galaxy clusters along the GRB sight line.

Graph: Fig. 2. The objects detected in four filters (the galaxies are enclosed by the squares, the star-shaped objects are marked by crosses). The black arrow points to the host galaxy of GRB021004.

Graph: Fig. 3. The photometric redshift distribution for 246 objects with the peak at z ≈ 0.56 based on the BTA BV RI data.

The observed distribution of galaxies along the sight-line gives information about inhomogeneous distribution of visible matter in the fixed direction in the sky. Statistical analysis of a grid of such fields will allow one to perform a tomography of the large-scale distribution of galaxies on largest optically available scales (Nabokov and Baryshev, 2010b; Shirokov et al., 2016; Sokolov et al., 2016, 2018a).

This test may be executed step by step by deep BTA observations of neighboring GRB host galaxies, close to an initial GRB direction.

In a sense, in the beginning of the 20th century, using the largest at that time telescopes, Edwin Hubble opened the door into the "realm of galaxies", and now, in the beginning of the 21st century, by operating with multimessenger gamma–optical facilities, we have an opportunity of the observational studying the "realm of metagalaxies".

The most important cosmological observational fact discovered by Hubble (1929) is the linear (for small distances) relation between observed redshift z of the spectral lines and the distance r to a galaxy, i.e. the observed Hubble Law (redshift–distance relation):

Graph

where H0 is the Hubble constant at present time, Mpc is the Hubble radius, is the apparent spectroscopic radial velocity of a galaxy, c is the velocity of light, or

2

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given λobs is the observed photon wavelength at a telescope and λemit is the wavelength of emitted photon at the distance r in the observed galaxy.

To determine the distance r to a galaxy Hubble used the concept of the "standard candle", i.e. an object with an apriori known luminosity. Note that Hubble called the redshift "an apparent velocity" (in units of c) because he measured the distance r to a galaxy through the flux measure, and he did not measure the physical velocity of a galaxy as the change of distance with time.

The expanding space paradigm of the Standard Cosmological Model is the theoretical interpretation of the redshift as the Lemaître effect in the expanding Friedmann universe where the space expansion velocity is Vexp(r) ≡ Vapp(r).

Surprisingly, after almost hundred years after Lemaıtre's interpretation of cosmological redshifts as effect of the space expansion, the acute discussion again raised in professional cosmological literature about physical sense of the cosmological redshift and relation between mathematical geometrical concepts and measured astronomical quantities: Abramowicz (2009); Abramowicz et al. (2007); Baryshev (2015); Davis (2004, 2010); Francis et al. (2007); Harrison (1993, 1995, 2000); Kaiser (2014); Peacock (1999, 2008).

Cosmological Hubble Diagram (HD) incorporates the directly observed fluxes, luminosity distances and redshifts for a particular class of standard candles. This is why the HD can be used for observational testing the basic theoretical relations of cosmological models.

The expanding space paradigm states that the proper (internal) metric distance r to a galaxy, having fixed comoving coordinate χ from the observer, is given by the relation:

3

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and increases with time t as the scale factor S(t).

It is important to point out that the hypothesis of homogeneity and isotropy of space (Cosmological Principle) implies that for a given galaxy the recession velocity is proportional to distance via exact linear velocity–distance (Vexp vs r) relation for all Friedmann–Lemaître–Robertson–Walker metrics:

4

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where is the Hubble parameter and RH = c/H(t) is the Hubble distance at the time t. Note that from Eq. (4) one gets expansion velocity more than velocity of light Vexp(r) > c for r > RH (Baryshev and Teerikorpi, 2012; Harrison, 1993, 2000).

It should be emphasized that the cosmological expansion velocity Vexp(r) for an observed galaxy is conceptually different from the galaxy peculiar velocity Vpec, which can not be larger than the velocity of light. The cosmological redshift in expanding space is not the Doppler effect, but the Lemaître one defined as the ratio of scale factors:

5

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Instead of exact linear relation Eq. (4) for Vexp(r), the redshift-distance relation z(r) and expansion velocity–redshift relation Vexp(z) are non-linear:

6

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where .

When observed through the i filter an object with the absolute magnitude Mi has the apparent magnitude

7

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where Ci(z) = 25 + Mi + Ki(z) + Ai + Ei(z), and l(z) is the external metric distance (Baryshev and Teerikorpi, 2012): l(r) = S(t)Ik(r/S).

If the K-correction, extinction, and evolution corrections are known for a standard candle class, Eq. (7) can be used to derive the redshift-luminosity distance relation llum(z) = l(z)(1 + z). The "pure vacuum" flat model (Ω = ΩΛ = 1) has the linear relation l(z) = r(z) = RH0z, hence

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The luminosity and metric distances are related similarly as in the Friedmann flat models:

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Because in CSSM r(z) = RHz, the magnitude-redshift relation is

8

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In the framework of the fractal cosmological model (Baryshev, 2017; Baryshev and Teerikorpi, 2012; Baryshev, 2008) the Universe is isotropic and inhomogeneous with a fractal dimension D ≈ 2.0. Such a value of the fractal dimension guaranties the linear redshift-distance law, if the cosmological redshift is interpreted as the global gravitational redshift within the fractal structure.

In the fractal model, the luminosity and metric distances are related as rlum(z) = r(z)(1 + z). This result includes the lost energy of individual photons and their diminished arrival rate due to gravitational time dilation. The magnitude-redshift relation then becomes

9

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where function Y (z) is defined in Baryshev and Teerikorpi (2012); Baryshev (2008).

The Zwicky TL model can be used as a toy example, where cosmological time dilation effect is excluded. In the simplest tired light model with the Euclidean static space (for instance, La Violette (1986)) the magnitude of a standard candle depends on the redshift as follows:

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The Hubble Diagram (HD) is the directly observed relation between flux and redshift for a sample of standard candles. The Hubble Diagram test is expressed as the distance modulus versus redshift for "standard" GRBs, calibrated by means of the "Amati relation":

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where μ is the distance modulus and dL is luminosity distance. The latter is given by

12

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where Sbolo is GRB fluence and Eiso(Ep,i) is the isotropic energy calculated by the Amati relation (Amati et al., 2009). The cosmological rest-frame spectral peak energy

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The HD method is based on application of theoretical relations given by Eqs. (7), (8), (9), (10). Detailed analysis of the GRB Hubble Diagram as a high-redshift cosmological test is presented in Shirokov et al. (2020).

As an example of the modern HD testing of the basic cosmological relations z(r), F(z), we take the distance modulus of a sample of 193 long GRBs from Amati et al. (2018) and calculate the median distance modulus values in redshift bins.

Figure 4 shows that predictions of different models have several stellar magnitudes in the THESEUS redshift interval (up to z ∼ 10). So the future THESEUS observations will give essential extension and accuracy of the observed Hubble law and hence put strong new cosmological model restrictions.

Graph: Fig. 4. The Hubble Diagram for the SNe Ia Pantheon catalog from Scolnic et al. (2018) (purple points), the GRBs catalog from Amati et al. (2019) (gray point), the median values of GRB bins with Δz = 0.3 (black points), and the predictions of ΛCDM model (red curve) and two examples of other models (pure vacuum and no time dilation).

There are a lot of observational selection effects (e.g. limits on detector sensitivity, influence of interfering matter, gravitational lensing, beaming effect, evolution), which potentially distort the measured bolometric flux and fluence, and hence the derived distance to a GRB. Thus to construct the proper Hubble Diagram on should take into account the selection effects. However, a firm answer to this fundamental question is far from being settled until more GRB data with known redshifts are available.

The gravitational lensing of long GRBs by gravitating matter, located along the "source–observer" sight-line, produces apparent increase of flux and fluence Sbolo due to gravitational lens magnification, which does not change frequency (and Ep) of the lensed radiation. This can be misinterpreted as an evolution of GRB luminosity.

According to Ji et al. (2018), GRBs can be magnified by the gravitational lensing produced by different gravitating structures of the Universe (such as dark and luminous stellar mass objects, globular and dark stellar mass clusters, galaxies and dark galaxy mass objects). Hence the gravitational lensing can have a great impact on high-redshift long GRBs. For example, according to Kurt and Ougolnikov (2000); Ougolnikov (2001), in the BATSE catalog there are several GRBs which are lensed by the intergalactic globular clusters.

If we take into account that there is a threshold for detection in the burst apparent brightness, then, with gravitational lensing, bursts just below this threshold might be magnified in brightness and detected, whereas bursts just beyond this threshold might be reduced in brightness and excluded (the Malmquist bias).

As it is demonstrated in Shirokov et al. (2020), the combined gravitational lensing and Malmquist biases crucially influence on the observed Hubble Diagram. If one takes into account possible luminosity correction on high-redshift GRB HD, then the observed HD tends to be consistent with the ΛCDM having the vacuum density parameter ΩL → 0.9 and the dark matter density parameter Ωm → 0.1. This result is very important in view of recent discussion about the role of dark energy and dark matter (Colin et al.2019; Demianski et al., 2019; Di Valentino et al., 2020a; Makarov and Karachentsev, 2011).

So the crucially important fundamental question on the role of the gravitational lensing bias in high redshift long GRB data needs more observational and theoretical studies. In particular, the 6-m BTA observations (Sokolov et al., 2018a, 2016) of galaxies along the long GRB sight-line (Fig. 3) will be important for estimation of the lensing magnification probability of the long GRB fluxes and its influence on the high-redshift HD. Hence the THESEUS–BTA joint program will give crucial information on dark matter and dark energy.

One of the crucial cosmological tests on the nature of the cosmological redshift is the measurements of duration of known physical processes at high-redshift objects (cosmological time dilation).

Wilson (1939) suggested supernovae as a test of the nature of the cosmological redshift: in an expanding Universe the light-curve of a supernova occurring in a distant galaxy should appear to be expanded along the time axes in the ratio (1 + z) : 1 with respect to the standard local light-curve. This time delay test was also discussed by Rust (1974) and Teerikorpi (1981).

Recent observations of the Ia supernovae have finally given an opportunity to perform the test (Goldhaber et al., 2001; Leibundgut, 2001). The observed width τobs of the supernova light-curve can be written as

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where p = 1 for the local Doppler and gravitational effects, and also for Lemaître space expansion effect and de Sitter–Bondi global gravitational effects, while p = 0 for all models without cosmological time dilation.

Light curves for 35 Type Ia supernovae with redshifts up to z ≈ 1 were analyzed by Goldhaber et al. (2001). They derived the dilation parameter p = 1.0 ± 0.1. Another study by Blondin et al. (2008) measured the spectral ages in the supernova rest frame. Comparison with the observed time led again to the (1 + z)1 factor expected for expanding space and also gravitational nature of cosmological redshift.

Note that the time dilation test provides good evidence against the tired-light hypothesis, but it cannot distinguish between expanding space models and involving cosmological global gravitational redshift ones.

As an observational test of the time dilation effect one can consider the relation T90 ∝ (1 + z)α for GRB pulse pro files. Kocevski and Petrosian (2013) and Zhang et al. (2013) considered the dependence of GRB pulses duration on redshift and got the conclusion that the slope is about α ≈ 1. A similar result T ∝ (1 + z)1.4 ± 0.3 has been obtained for the radio-loud GRBs sample by Lloyd-Ronning et al. (2019).

The time dilation test can be made separately for long and short GRBs. The long GRBs are explosions of supernovas, while the short GRBs are mergers of binary systems. These events have the same physical nature as a result of relativistic gravitational collapse, but different light curves due to matter envelope (Dado and Dar, 2018; Sokolov et al., 2018b). GRBs are usually divided into long–soft (T90> 2 s) and short–hard (T90< 2 s), which are less than 10% in number, e.g., in the Swift sample (Shirokov et al., 2019).

In fact the observational selection effects can strongly influence the observed duration of GRBs at different redshifts. In particular, it strongly depends on instrumental time resolution and spectral sensitivity, and also on spectral features of sources (Castro-Tirado et al., 2018; Kocevski and Petrosian, 2013). Hence the time dilation test is hard to be performed by GRB pulses alone.

Time dilation of all physical processes observed at high-redshift is predicted by both cosmological models based on space expansion and on global gravitational redshift mechanisms. At small redshifts it is difficult to measure this effect because of other different competitive physical processes.

A new opportunity for Wilson cosmological test of the time dilation will appear when THESEUS observations of GRB gamma-ray pulses will be analyzed together with light curves of the same GRB afterglows observed at the 6-m BTA SAO telescope (Amati et al., 2018; Sokolov et al., 2018b; Vlasyuk, 2018).

Because long GRBs are related to core-collapse SN explosions, there is a possibility for cosmological test of the time dilation effect. One can consider simultaneously the shape of gamma-ray pulses and the shape of an afterglow in other wavelength bands. For example, the SN light curve can be visible in the GRB afterglow light curve. Hence time duration of different processes can be used for the same GRB, and their statistics in different channels and different redshifts will present the robust estimations of the time dilation effect. A cooperative THESEUS–BTA observations will be important for this cosmological test of the fundamental physics.

In the spirit of the Sandage's practical cosmology approach (Sandage, 1995, 1997), we have considered the current state of cosmology, which is characterized by general tendency to testing the fundamental principles lying in the basis of cosmological models. The especially important role belongs to the recent discovery of a discrepancy between Planck-2018 results on CMBR fluctuations analysis and the locally measured cosmological parameters of the SCM.

Such obstacles as the nature and value of dark energy and dark matter, the value of gravitational lensing by the large-scale structure and the value of the Hubble constant H0 for the Local Universe, are now discussed as a new crisis for cosmology (see references in Introduction).

The GRB observations in multimessenger astronomy epoch open new possibilities for testing the fundamental physics lying in the basis of the standard cosmological model: classical general relativity, cosmological principle of matter homogeneity, and the Lemaıtre space expansion nature of cosmological redshift.

Modern achievements of the theoretical physics, especially different modifications of general relativity and quantum aspects of gravitation theory, together with a number of conceptual problems of the SCM, also require a reanalysis and the wider observational testing of the initial principles of the SCM.

We have considered possible basic cosmological applications of GRBs multimessenger observations in the wide interval of cosmological redshifts up to z ∼ 10. THESEUS–BTA cosmological tests can probe strong-field regime of gravitation theory, spatial distribution of galaxies, Hubble Law and time dilation of physical processes at such redshifts. Perspectives for performing these cosmological tests in multimessenger astronomical observations of GRBs were considered and several new tests were proposed. The very important part of cosmological tests is related to careful taking into account different selection observational effects that distort the true cosmological relations.

Future THESEUS space observations of GRBs (Amati et al., 2018; Strata et al., 2018) and corresponding multimessenger ground-based studies, including large optical telescopes, such as BTA and GTC (and even 1-m class telescopes) (Castro-Tirado et al., 2018; Sokolov et al., 2016, 2018b; Vlasyuk, 2018), will bring crucial information for testing theoretical cosmological models.

Our analysis of possible application of observational cosmological tests for forthcoming THESEUS GRB mission have demonstrated its potentially fundamental contribution to cosmology, because GRBs are among the most distant astrophysical objects with measured spectral redshifts (see Fig. 4).

The promising cosmological tests of the SCM basis by forthcoming THESEUS and BTA observations of GRBs are:

—BTA identification and monitoring of fast optical counterparts for THESEUS GRBs, together with detections of neutrino and gravitational wave signals, allow one to test the strong regime of gravity theory as the basis of the standard cosmological model. The problem of transition of relativistic compact objects to neutron stars, quark stars or black holes can be solved and extended to cosmological solutions of the gravity field equations.

—large number of THESEUS GRBs and BTA optical observations of host galaxies make it possible to test the Cosmological Principle of homogeneity and isotropy on largest spatial scales up to r ~ 10 Gpc. The "cosmic tomography" of the large-scale structure can be studied by using BTA deep- field observations of sight-line distribution of galaxies in directions of GRBs.

—THESEUS high-redshift Hubble Diagram for long GRBs in collaboration with BTA sight-line observations provides means to test the flux-distance-redshift cosmological relations up to z ~ 10. The joint THESEUS–BTA observations of the gamma-X-ray-optical-IR light curves profiles will give an opportunity to perform a new form of the Wilson's time dilation test for high-redshift physical processes.

The joint THESEUS-BTA GRB project, together with other multimessenger observatiaons, will give decisive a new information on the fundamental cosmological physics.

The work was performed as part of the government contract of the SAO RAS approved by the Ministry of Science and Higher Education of the Russian Federation.

We are grateful to O.V. Verkhodanov, D.I. Nagirner, and A.J. Castro-Tirado for useful discussions and comments. We thank Tatyana Sokolova for editing corrections.

The authors declare no conflict of interest regarding this paper.