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Constraints on alternative theories of gravity and cosmology

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ong>Constraintsong> on alternative theories of gravity and cosmologyAlexander F. Zakharov 1,2 , Victor N. Pervushin 2 , Francesco De Paolis 3 ,Gabriele Ingrosso 3 and Achille A. Nucita 41 Institute of Theoretical and Experimental Physics,B. Cheremushkinskaya, 25, 117259, Moscow, Russia,email: zakharov@itep.ru2 Bogoliubov Laboratory for Theoretical Physics,Joint Institute for Nuclear Research, 141980 Dubna, Russia3 Department of Physics and INFN,University of Salento, CP 193, I-73100, Lecce, Italy4 XMM-Newton Science Operations Centre, ESAC, ESA,PO Box 50727, 28080 Madrid, SpainAbstractOne could call 2006 as the year of cosmology since in the year two US scientists were awarded bythe Nobel prize for their studies of Cosmic Microwave Background (CMB) spectrum and anisotropy.Studies of CMB anisotropy done with the Soviet spacecraft Prognoz-9 by the Relikt-1 team arereminded. Problems of modern cosmology are outlined. We discuss conformal cosmology parametersfrom supernovae data in brief. Two approaches to solve the basic problems of cosmology,such as dark matter and dark energy, are discussed, the first (standard) possibility is to introducenew particles, fields etc, the second possibility is to try to change a gravity law to fit observationaldata. We discuss advantages and disadvantages of the second choice.Keywords: General Relativity and Gravitation; Cosmology; Observational Cosmology; Cosmologicaltests; Supernovae; Cosmic Microwave Background Radiation.1 IntroductionFor a scientific community 2005 was the World year of physics due to publications of the famousEinstein’s papers and the birth of modern (contemporary) physics in 1905. The next year (2006) wasalso remarkable for a physical community (it was the year of astrophysics and cosmology) since in 2006the Nobel prize for CMB studies was presented to J. Mather and G. Smoot, moreover J. Mather andthe COBE (COsmic Background Explorer) team was awarded by the Peter Gruber prize on cosmologyin the same year at the General Assembly of the International Astronomical Union in Prague. Nodoubt, 2007 will be recognized as the very important year for astrophysical (or probably for scientificin general) community since a number of of discoveries were done even at present date. For Russianspace science 2007 is the jubilee year since the first artificial satellite (Sputnik) was launched fifty yearsago on October 4, 1957.A structure of the paper is the following. In section 2 we remind results of CMB anisotropystudies done with the Soviet Relikt-1 mission. In section 3 we outline a current status of cosmologicalstudies and parameters of conformal cosmological models in brief. In section 4 we discuss a success ofalternative way to solve DM and DE problem (so-called, a geometrical approach or f(R)-models), wherea gravity law is substituting with changing classical Lagrangian for gravity and severe constraints onparameters of so-called R n theory from Solar system data will be given. Conclusions will be presentedin section 5.2 CMB anisotropy studies, Relikt-1 & COBECosmic microwave background (CMB) existence was predicted in the framework of the the so called BigBang cosmological model [1, 2, 3, 4], however, first estimates CMB temperature T CMB ∼ 50 0 K were1


ather rough since it was assumed that the age of the Universe is about 2–3×10 9 years (because of theHubble constant estimate was very high H = 500 km/(s·Mpc) due to errors in distance measurementsat the time), but later Gamow re-estimated the temperature T CMB ∼ 6 0 K [5]. The CMB radiationwas discovered by A. Penzias and R. Wilson [6] in an unexpected way (and they awarded by the Nobelprize for the discovery in 1978). The physical meaning the discovery was explained in the introductorypaper [7] published in the same issue of the Astrophysical Journal as the paper [6] with a descriptionof the discovery.Because the Earth moves in respect to the CMB, a dipole temperature anisotropy of the level of isexpected. A dipole temperature anisotropy of the level of ∆T/T = 10 −3 was observed, it corresponds toa peculiar velocity 380 km/s of the Earth towards the constellation Virgo (first measurements of dipoleanisotropy were not very precise [8], but later the accuracy was significantly improved [10, 11, 12]).Moreover, based on results of balloon measurements it was claimed several times about features ofquadrupole anisotropy [12, 13], however, the quadrupole term is too high in these experiments asfurther studies had indicated, or reversely the realistic level of quadrupole anisotropy is to low to bedetected in the balloon experiments.In 1983, in the Soviet Union the Relikt-1 experiment 1 was conducted aboard the Prognoz-9 spacecraft2 in order to investigate CMB radiation from space for the first time in history. As many otherPrognoz missions, the scientific payload was prepared by the Space Research Institute of the SovietAcademy of Sciences. Dr. Igor Strukov was the principal investigator.The spacecraft Prognoz-9, had an 8 mm band radiometer with an extremely high sensitivity of35 µK per second and it was launched into a high apogee orbit with a 400,000 km semi-axis. The highorbit was a great advantage of the mission since it allows to reduce of geomagnetic field impact onmeasurements. A disadvantage of the experiment was that the observations were conducted only inone spectral band, therefore, it was a freedom for a theoretical interpretation of the results, in contrast,multi-band measurements provide very small room for alternative explanations of anisotropy.The radiometer scanned the entire celestial sphere for six months. Computer facilities (and therefore,data analyzing) were relatively slow in the time. Preliminary analysis of anisotropy studiesindicate upper limits on anisotropy [15], but in this case even the negative results (upper limits) wereextremely important to evaluate a sensitivity to design detectors for next missions (including COBE).In 1986, at the Space Research Institute it was decided to prepare a next generation of spaceexperiments to study the anisotropy of CMB, and start to develop the Relikt-2 project. The sensitivityof the detectors was planned to be in 20 times better than the Relikt-1 sensitivity. The Libris satellitewas scheduled to carry the Relikt-2 payload and the spacecraft was planned to be located near theLagrangian point L 2 (in the Sun – Earth system). 3 Originally, it was a plan to launch the Librisspacecraft in 1993–1994, however, the project has not been realized, basically due to a lack of funds.To prepare Relikt-2, the team members re-analyzed Relikt-1 data and finally in beginning of 1991 theydiscovered signatures of the quadrupole anisotropy, but I. Strukov required to check the conclusionsagain and again. The discovery of anisotropy by the Relikt-1 spacecraft was first reported officially inJanuary 1992 at the Moscow astrophysical seminar and the Relikt-1 team submitted papers in SovietAstronomy Letters [16] and Monthly Notices of Royal Astronomical Society [17] (soon after the paperswere published). Relikt-1 results are described in an adequate way at the at the official NASA web-sitehttp://lambda.gsfc.nasa.gov/product/relikt/ 4 ”... The Relikt Experiment Prognoz 9, launched on 1July 1983 into a high-apogee (700,000 km) orbit, included the Relikt-1 experiment to investigate theanisotropy of the CMB at 37 GHz, using a Dicke-type modulation radiometer. During 1983 and 1984some 15 million individual measurements were made (with 10% near the galactic plane providing some5000 measurements per point). The entire sky was observed in 6 months. The angular resolution was5.5 degrees, with a temperature resolution of 0.6 mK. The galactic microwave flux was measured andthe CMB dipole observed. A quadrupole moment was found between 17 and 95 microKelvin rms, with1 In Russian literature CMB radiation is called as a relic radiation, therefore the name Relic (”Relikt” in Russian)was chosen.2 In Russian ”Prognoz” means ”forecast”. Prognoz spacecrafts were designed originally for studies of Solar activity(Solar flares in particular) and its impact on geophysics, geomagnetic fields and space weather [14]. The spacecrafts werelaunched at high elliptical orbits with apogee about 200 000 km.3 The trajectories near the L 2 point are suitable for different space experiments, for example, the orbit was selectedfor the WMAP spacecraft (it is one of the most successful mission to study the CMB anisotropy and such an orbit wasplanned to be used for the future Millimetron cryogenic telescope (it scheduled to be launched around 2016)).4 See, also, an article ”Cosmic microwave background radiation” in Wikipedia, the free encyclopedia(http://en.wikipedia.org/wiki/Main Page).2


90% confidence level. A map of most of the sky at 37 GHz is available...” (also, references [16, 17],given at the NASA web-site).The Nobel Prize in Physics for 2006 was awarded to John Mather and George Smoot. The RoyalSwedish Academy of Sciences had issued the Press Release, dated on 3 October 2006, on The NobelPrize in Physics 2006. 5 The Royal Swedish Academy of Sciences has decided to award the Nobel Prizein Physics for 2006 jointly to John C. Mather (NASA Goddard Space Flight Center, Greenbelt, MD,USA), and George F. Smoot (University of California, Berkeley, CA, USA) ”for their discovery of theblackbody form and anisotropy of the cosmic microwave background radiation”. Really, J. Mather wasthe project scientist of the COBE mission and was responsible for measurements of CMB spectrum (hewas the PI of the Far InfraRed Absolute Spectrometer (FIRAS) experiment) and measurements of CMBspectrum were rather successful. G. Smoot did a great contribution into measurements of the dipoleanisotropy [11] and the quadrupole one [18], since he was PI of the differential microwave radiometer(DMR) aboard the COBE satellite and found the quadrupole anisotropy with these facilities, but bothanisotropies were discovered earlier by other people.The discovery of anisotropy by the Relikt-1 spacecraft was first reported officially in January 1992at the Moscow astrophysical seminar. Relikt-1 team submitted their paper in Soviet Astronomy Lettersand Monthly Notices of Royal Astronomical Society on January 19, 1992 and on February 3, 1992,respectively.On April 21, 1992, G. Smoot (the head of DMR experiment aboard the COBE mission) and his coauthorssubmitted a paper in Astrophysical Journal (Letters) [18]. On April 22, 1992, Smoot reportedat a press conference about the discovery of the CMB anisotropy with the COBE satellite. After thatmass media reported this results as the main science success. In 1992, COBE results about discoveryof the CMB anisotropy were reported elsewhere. However, no doubt, the COBE collaboration knewresults of Relikt-1 team and even quoted their upper limit on the quadrupole anisotropy published atthe paper.[15] Sometimes, results of both (COBE and Relikt-1) collaborations were presented at thesame scientific meetings. In particular, in June 1992, at the conference on Particle Astrophysics in Blois(France) results on discoveries of CMB anisotropy were presented at a plenary session by representativesof both teams (Relikt-1 and COBE), namely M. V. Sazhin and G. Smoot. The Smoot’s paper waspublished in the conference proceedings [19], but unfortunately, eventually, Sazhin’s contribution wasnot published there.However, summarizing, one could say that since papers of the Relikt-1 team were submitted onJanuary 19, 1992 and February 3, 1992 in Soviet Astronomy and Monthly Notices of Royal AstronomySociety respectively, but COBE paper was submitted on April 21, 1992, one would conclude that thediscovery one quadrupole anisotropy was done by the Relikt-1 team and published in papers [16, 17].3 Precise cosmology & Conformal Cosmological ModelsSince 1998 people claimed that cosmology started to be a precise science. Really, if the standard cosmologicalparadigm was chosen, now we can evaluate cosmological with a precision about 10 % (typicallyonly statistical errors are indicated and it is assumed that systematical errors are negligible). However,even in the framework of the standard paradigm of the Big Bang cosmology, our understanding thebest fit for cosmological model is changing. For example, in the beginning of 1998 it was found thatthe Universe is opened and Ω m ∼ 0.2 − 0.4 (based on observations of galactic clusters [20] (immediately,mass media had reported that eventually scientists proved that the Universe would be expandingforever), but at the end of 1998, it was concluded that the Universe is flat Ω m = 0.3, Ω Λ = 0.7 [21, 22](assuming that the SNeIa are standard candles).We will remind basic relations for CC model parameters (see papers [23, 24] for details) consideringthe General Relativity with an additional scalar field Q, as usually people did to introduce quinessence[25, 26, 27, 28] (earlier, the approach was used for inflationary cosmology, see for example, paper [29]and references therein)∫S CR =d 4 x √ [−g − 1 6 R(g) + 1 ]2 ∂ µQ∂ µ Q − V (Q) , (1)5 Information from the Nobel prize committee web-site http://www.kva.se.3


where we used the natural units√3M Planck = = c = 1, (2)8πtherefore, we have the following expressions for density and pressure of the scalar field, p Q and ρ Q ,respectively [25, 26, 27, 28],p Q (t) = 1 2 ˙Q 2 + V (Q),and equation of state (EOS) such as p Q = w Q ρ Q , whereρ Q (t) = 1 2 ˙Q 2 − V (Q), (3)w Q =12 ˙Q 2 − V (Q)12 ˙Q 2 + V (Q) , (4)(−1 ≤ w Q ≤ 1, for ”natural” potentials V (Q) ≥ 0). In contrast with quintessence model where one usestypically ˙Q 2 ≪ V (Q), below for CC model we will use an approximation ˙Q 2 ≫ V (Q) (for a standardrepresentation of the potential V (Q) = 1 2 mQ2 , where m is a mass of the field, the approximationcorresponds to a massless field model) and we havew Q =1 ˙Q 2212˙Q2= 1, (5)or on the other words, a rigid EOS for the scalar field p Q = ρ Q (p rig = ρ rig , since for our future needsan origin of the EOS is not important, hereafter, we will call the component such as the rigid matter).We suppose that a measurable interval is defined by the Weyl-like ratiods 2 meas = ds2 Einsteinds 2 units=g µν dx µ dx ν[g µν dx µ dx ν ] units(6)of two Einstein intervalsds 2 Einstein = g µν dx µ dx ν (7)one of which ds 2 units plays a role of measurement units determined by one of masses. The Weyl definitionmeans that there is no device measuring the absolute value of any length. Nevertheless, this definitiongives us a possibility to fit also the units of observations as two choices of observable variables. Thesechoices correspond to two different cosmological models: the Standard Cosmology with observablemasses m sc = m and Einstein’s intervals in homogeneous approximationand the Conformal Cosmology, where all massesare scaled by the factor a and measurable intervalsds 2 sc = dt 2 − a 2 (dx k ) 2 = a 2 (η)[(dη) 2 − (dx k ) 2 ] (8)do not depend on the cosmological scale factor a.In general case, both SC and CC are described by equationwherem cc = ma(η) (9)ds 2 cc = (dη) 2 − (dx k ) 2 (10)ρ(a) = ρ 0(a ′ ) 2 = ρ(a), (11)∑J=−2,0,1,4Ω J a J (12)is the conformal energy density connected with the SC one by the transformationρ(a) = a 4 ρ SC (a) , (13)4


factor a 4 = a 3 a arises due to differences of length and mass units in SC and CC, Ω J is partial energydensity marked by index J running a set of values J = −2 (rigid), J = 0 (radiation), J = 1 (mass),∑and J = 4 (Λ-term) in correspondence with a type of matter field contributions; here Ω J = 1is assumed.In terms of the standard cosmological definitions of the redshiftthe density parameter Ω c (z) =∑J=−2,0,1,4Ω c (z) = Ω rig (1 + z) 2 + Ω rad +where Ω rig = Ω −2 , Ω rad = Ω 0 , Ω m = Ω 1 , Ω Λ = Ω 2 .Then the equation (11) takes the formJ=−2,0,1,41 + z ≡ 1a(η) . (14)Ω J a J in Eq. (12) takes the formΩ m(1 + z) + Ω Λ(1 + z) 4 , (15)H 0dηdz = 1(1 + z) 2 1√Ωc (z) , (16)and determines the dependence of the conformal time on the redshift factor. This equation is valid alsofor the conformal time - redshift relation in the SC where this conformal time is used for descriptionof a light ray.A light ray traces a null geodesic, i.e. a path for which the conformal interval (ds L ) 2 = 0 thussatisfying the equation dr/dη = 1. As a result we obtain for the coordinate distance as a function ofthe redshiftH 0 r(z) =∫ z0dz ′(1 + z ′ ) 2 1√Ωc (z ′ ) . (17)The equation (17) coincides with the similar relation between coordinate distance and redshift in SC.In the comparison with the stationary space in SC and stationary masses in CC, a part of photonsis lost. To restore the full luminosity in both SC and CC we should multiply the coordinate distanceby the factor (1 + z) 2 . This factor comes from the evolution of the angular size of the light cone ofemitted photons in SC, and from the increase of the angular size of the light cone of absorbed photonsin CC. However, an observable length in SC contains an additional factor (1 + z) −1in comparison with measurable distances in CC∫ dtl SC = aa = r1 + z . (18)l CC =∫ dta = r1 + z . (19)(that coincide with the coordinate ones).Thus, we obtain the relations for observable lengths in SC and CC, respectivelyl SC (z) = (1 + z)r(z) , (20)l CC (z) = (1 + z) 2 r(z) , (21)simply because of l SC (z) = al CC (z). It means that the observational data are described by differentmanners in SC and CC, since functions H 0 l(z) have different representations in SC and CC modelstherefore, observational data can be fitted with different parameters of the functions as we willdemonstrate below.5


CC optimalSC optimalCC rigidCC matterCC lambdaCC radFigure 1: µ(z)-dependence for cosmological models in SC and CC. The data points include 186 SN Ia(the ”gold” and ”silver” sample) used by the cosmological supernova HST team [30]. For a referencewe use the best fit for the flat standard cosmology model with Ω m = 0.27, Ω Λ = 0.73 (the thick dashedline), the best fit for CC is shown with the thick solid line. For this CC model we assume Ω m ≥ 0.3.1 Magnitude-Redshift RelationTypically to test cosmological theories one should check a relation between an apparent magnitudeand a redshift. In both SC and CC models it should be valid the effective magnitude-redshift relation:µ(z) ≡ m(z) − M = 5 log [H 0 l(z)] + M, (22)where m(z) is an observed magnitude, M is the absolute magnitude, M is a constant with recentexperimental data for distant SNe. Values of µ i , z i and σ i could be taken from observations ofa detected supernova with index i (σ 2 i is a dispersion for the µ i evaluation). Since we deal withobservational data we should choose model parameters to satisfy an array of relations (22) by thebest way because usually, a number of relations is much more than a number of model parametersand there are errors in both theory and observations (as usual we introduce indices for the relationscorresponding to all objects). Typically, χ 2 -criterium is used to solve the problem, namely, we calculateχ 2 = ∑ i(µ theori − µ i ) 2, (23)σ 2 iwhere µ theori are calculated for given z i with the assumed theoretical model and after that we canevaluate the best fit model parameters minimizing χ 2 -function.However, in principle, other alternatives for cosmology are not completely ruled out, for example,a conformal cosmological model was discussed in papers [23, 24]. Using ”gold” and ”silver” 186 SNeIa [30] we confirm in general and clarify previous conclusions about CC model parameters [31], doneearlier with analysis of smaller sample of SNe Ia data [23, 24] that the pure flat rigid CC model couldfit the data relatively well since ∆χ 2 ≈ 44.3 (or less than 20 %) in respect of the standard cosmologyflat model with Ω m = 0.28. Other pure flat CC models should be ruled out since their χ 2 values aretoo high. For the total sample, if we consider CC models with a ”realistic” constraint 0.2 Ω m 0.3based on other astronomical or cosmological arguments except SNe Ia data, we conclude that thestandard cosmology flat model with Ω m = 0.28 is still preferable in respect to the fits for the CCmodels but the preference is not very high (about 5 % in relative units of χ 2 value), so the CC modelscould be adopted as acceptable ones taking into account possible sources of errors in the sample andsystematics.6


Figure 2: The parameter β as a function of n for fourth order gravity.that the standard general relativity plus DM and DE may be distinguished from R n approaches withgravitational microlensing [40], but Solar system data (planetary orbital periods, in particular) putsevere constraints on parameters of the the theories [41].4.1 Planetary ong>Constraintsong>We now discuss some observational consequences of fourth order gravity which, after fixing the coreradius r c ≃ 1 A.U., still depends on the parameter β in the weak field approximation.A constraint on the fourth order gravity theory can be obtained from the motion of the solar systemplanets. Let us consider as a toy model a planet moving on circular orbit (of radius r) around the Sun.From Eq. (25), the planet acceleration a = −∂Φ(r)/∂r is given by[a = − Gm ( ) β ( ) ] β r r2r 2 1 + − β . (27)r c r cAccordingly, the planetary circular velocity v can be evaluated and, in turn, the orbital period P isgiven byP = P K√2[1 +( rr c) β− β( rr c) β] −1/2, (28)where P K = [4π 2 r 3 /(Gm)] 1/2 is the usual Keplerian period. In order to compare the orbital periodpredicted by the fourth order theory with the Solar System observations, let us define the quantity∆P= |P − P K|= |f(β, r c ) − 1| (29)P K P K8


eing f(β, r c ) the factor appearing on the right hand side of equation (28) and multiplying the usualKeplerian period.There is a question about a possibility to satisfy the planetary period condition – vanishing theEq. (29) – with β parameter which is significantly different from zero. Vanishing the right hand sideof Eq. (29) we obtain the relationln (1 − β)ln r = ln r c − , (30)βso that Eq. (30) should be satisfied for all the planetary radii. This is obviously impossible since thefourth order theory defines β as a parameter, while the specific system under consideration (the Solarsystem in our case) allows us to specify the r c parameter. Hence the right hand side of Eq. (30) isfixed for the Solar system, implying that it is impossible to satisfy Eq. (30) even with two (or more)different planetary radii.Just for illustration we presented the function f(β, r c ) as a dependence on β parameter for fixed r cand planetary radii r (see Figs. in paper [41]). As one can see from Eq. (30) (and Figs. in paper [41]as well) for each planetary radius r > r c there is β ∈ (0, 1) satisfying Eq. (30), but the β value dependson fixed r c and r, so that they are different for a fixed r c and different r. Moreover, if we have at leastone radius r ≤ r c , there is no solution of Eq. (30). Both cases imply that the β parameter should bearound zero.As one can note, only for β approaching zero it is expected to recover the value of the Keplerianperiod. In the above mentioned figure, the calculation has been performed for the Earth orbit (i.e.r = 1 A.U.).Current observations allow also to evaluate the distances between the Sun and the planets of theSolar System with a great accuracy. In particular, differences in the heliocentric distances do notexceed 10 km for Jupiter and amount to 180, 410, 1200 and 14000 km for Saturn, Uranus, Neptuneand Pluto, respectively [42]. Errors in the semi-major axes of the inner planets are even smaller(see e.g. Table 2 in the paper [43]) so that the relative error in the orbital period determination isextremely low. As an example, the orbital period of Earth is T = 365.256363051 days with an errorof ∆T = 5.0 × 10 −10 days, corresponding to a relative error of ∆T/T less than 10 −12 . These valuescan be used in order to constrain the possible values of both the parameters β and r c introduced bythe fourth order gravity theory. This can be done by requiring that ∆P/P K ∆T/T so that, in thecase of Earth, |f(β, r c ) − 1| 10 −12 which can be solved with respect to β once the r c parameter hasbeen fixed to some value. For r c = 1 AU and r c = 10 4 AU (i.e. the two limiting cases considered inthe paper [40]) we find the allowed upper limits on the β parameter to be 4.0 × 10 −12 and 3.9 × 10 −13 ,respectively (since ∆P/P K = ∆β[−1 + ln (r/r c )]/4).A more precise analysis which takes into account the planetary semi-major axes and eccentricitiesleads to variations of at most a few percent, since the planetary orbits are nearly circular. Therefore,in spite of the fact that orbital periods of planets are not generally used to test alternative theoriesof gravity (since it is taken for granted that the weak field approximation of these theories gives theNewtonian limit), we found that these data are important to constrain parameters of the fourth ordergravity theory.4.2 DiscussionGR and Newtonian theory (as its weak field limit) were verified by a very precise way at different scales.There are observational data which constrain parameters of alternative theories as well. As a result,the parameter β of fourth order gravity should be very close to zero (it means that the gravitationaltheory should be very close to GR). In particular, the β parameter values considered for microlensing[40], for rotation curves [34] and cosmological SN type Ia [35] are ruled out by solar system data.No doubt that one could also derive further constraints on the fourth order gravity theory byanalyzing other physical phenomena such as Shapiro time delay, frequency shift of radio photons [44],laser ranging for distant objects in the solar system, deviations of trajectories of celestial bodies fromellipses, parabolas and hyperbolas and so on. But our aim was only to show that only β ≃ 0 valuesare not in contradiction with solar system data in spite of the fact that there are a lot of speculationsto fit observational data with β values significantly different from zero.9


5 ConclusionsIn conclusion we note that, unfortunately, even well-informed Russian (and other) authors did not citeRelikt-1 results in papers on cosmology, where the COBE anisotropy result was quoted as the onlyexperiment discovered the phenomenon. It means the Nobel prize winner (1978) P. L. Kapitza 6 wrotequite correctly about this kind of problems in 1946: ”... Our main national defect is an underestimationof our powers and overestimation of foreign ones. So, an extra modesty is much more defective thanan extra self-confidence... Very often a cause of unused innovations is that usually we underestimateour own discoveries and overestimate foreign ones...”For CC model fits calculated with SNe Ia data, in some sense, a rigid equation of state couldsubstitute the Λ-term (or quintessence) in the Universe content. The rigid matter can be formed by afree massless scalar field [31].Solar system data put severe limits on parameters of alternative theories of gravity [41], thus,the Solar system limits a gravity law not only at scales about several A.U., but also at cosmologicaldistances, in this class of alternative theories of gravity.Acknowledgement. AFZ acknowledges GAS@BS-2007 conference organizers, especially prof.P. Fiziev, for the hospitality and a financial support.References[1] Gamow, G. (1946) Expanding Universe and Orgin of Elements, Phys. Rev. 70, 572–573.[2] Gamow, G. (1948) The Origin of Elements and the Separation of Galaxies, Phys. Rev. 74, 505–506.[3] Gamow, G. (1948) Evolution of the Universe, Nature 162, 680.[4] Alpher, R. A. (1948) A Neutron – Capture Theory of the Formation and Relative Abundance of Elements,Phys. Rev. 74, 1577–1589.[5] Gamow, G. (1956) The physics of the expanding universe, Vistas in Astronomy 2, 1726–1732.[6] Penzias, A. A., Wilson, R. W. (1965) A Measurement of Excess Antenna Temperature at 4080 Mc/s,Astrophys. J. 142, 419–420.[7] Dicke, R.H., Peebles, P. J. E., Roll, P. G., Wilkinson, D. T. (1965) Cosmic Black-Body Radiation,Astrophys. J. 142, 414–419.[8] Conklin, E.-K. (1969) Velocity of the Earth with Respect to the Cosmic Background Radiation, Nature,222, 971–972.[9] Henry, P.S. (1971) Isotropy of the 3 K Background, Nature, 231, 516–518.[10] Corey, B.E., Wilkinson, D. T. (1976) A Measurement of the Cosmic Mirowave Background Anisotropy at19 GHz Bull. Amer. Astron. Soc., 8, 351.[11] Smoot, G.F., Gorenstein, M.V., Muller, R. A. (1977) Detection of Anisotropy in the Cosmic BlackbodyRadiation, Phys. Rev. Lett., 39, 898–891.[12] Fabbri, R., Giudi, I., Melchiorri, F., Natale, V. (1980) Measurement of the Cosmic-Background Large-Scale Anisotropy in the Millimetric Region, Phys. Rev. Lett., 44, 1563–1566.[13] Boughn, S.P., Cheng, E. S., Wilkinson, D. T., (1981) Dipole and quadrupole anisotropy of the 2.7 Kradiation Astrophys. J., 243, L113–L117.[14] Vernov, S. N. et al. (eds.) (1977) Problems of Solar activity and space system ”Prognoz” Nauka, Moscow,in Russian).[15] Klypin, A. A., Sazhin, M. V., Strukov, I. A., Skulachev, D.P. (1987), Limits on Microwave BackgroundAnisotropies - the Relikt Experiment, Sov. Astron. Lett. 13, 104–107.6 He was awarded by the Nobel prize for his experimental discovery of superfluidity and received the prize in the sameyear as Penzias and Wilson got. He was the favorite Rutherford’s student and worked for a long time in UK, therefore,he knew Western and Russian mentalities very well.10


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