Horizon, homogeneity and flatness problems -- do their resolutions really depend upon inflation?

asingal@prl.res.in; COS3, Poster, CICAHEP15.169. 1 In textbooks and reviewarticles on modern cosmology [1, 2, 3, 4, 5, 6] one almost invariably comesacross a section devoted to the subject of observed homogeneity and near-flatness of the universe, where it is argued that to explain these observationsinflation is almost a must. In fact that was the prime motive of Guth [7] topropose inflation in the first place. We show that the arguments offered thereinare not proper. The horizon problem, which leads to the causality arguments,arises only in the world models where homogeneity and isotropy (cosmologicalprinciple) is presumed to begin with. We do not know whether the horizon problemwould still arise in non-homogeneous world models. Therefore as long as we areinvestigating consequences of the cosmological models based on Robertson-Walkerline element, there is no homogeneity issue. We also show that the flatnessproblem, as it is posed, is not even falsifiable. The usual argument used inliterature is that the present density of the universe is very close (within anorder of magnitude) to the critical density value. From this one infers that theuniverse must be flat since otherwise in past at 10 −35 second (near the epochof inflation) there will be extremely low departures of density from thecritical density value (i.e., differing from unity by a fraction of order ∼ 10−53), requiring a sort of fine tuning. Actually we show that even if the presentvalue of the density parameter (in terms of the critical density value) werevery different, still at 10 −35 second it would in any case differ from unity bya fraction of order ∼ 10 −53. For instance, even if had an almost emptyuniverse, with say, ρ o ∼ 10 −56 gm/cc or so (with density parameter Ω o ∼ 10−28 , having a mass equivalent to that of Earth alone to fill the wholeuniverse), we still get the same numbers for the density parameter at the epochof inflation. So such a fine-tuning does not discriminate between various worldmodels and a use of fine tuning argument amounts to a priori rejection of allmodels with k = 0, because inflation or no inflation, the density parameter inall Friedmann-Robertson-Walker (FRW) world models gets arbitrarily close tounity as we approach the epoch of the big bang. That way, without even botheringto measure the actual density, we could use any sufficiently early epoch and use" extreme fine-tuning " arguments to rule out all non-flat models. Thus withoutcasting any whatsoever aspersions on the inflationary theories, we point outthat one cannot use these type of arguments, viz. homogeneity and flatness, insupport of inflation. 1. Horizon and homogeneity problem Horizon in thecosmological context implies a maximum distance yonder which we as observershave not yet seen the universe due to a finite speed of light as well as afinite age of the universe. In other words these are the farthest regions of theuniverse (redshift z → ∞) from which the light signals have just reached us.However when we look at the universe we find that distant regions in oppositedirections seen by us have similar cosmic microwave background radiation (CMBR)temperatures. The object horizon problem in standard cosmological big bang modelis that these different regions of the universe have not ever communicated witheach other, but nevertheless they seem to have the same temperature, as shown bythe CMBR which shows almost a uniform temperature (2.73 • K) across the sky,irrespective of the direction. How can this be possible, considering that anyexchange of information (say, through photons or any other means) can occur, atmost, at the speed of light. How can such two causally disconnected regions haveone and same temperature, unless one makes a somewhat " contrived " presumptionthat the universe was homogeneous and isotropic to begin with when it came intoexistence [1]? One can illustrate the object horizon problem using a simple,though somewhat naive, argument in the following way. According to the big bangmodel the universe has only a finite age, say t o. Then light (or information)from regions at a cosmological distance ct o from us would have reached us justnow, and could not have crossed over to similar distant regions on the otherside of us. Then how two far-off regions on two opposite sides of us havemanaged to achieve the homogeneity so that we see them having same properties.Though the argument does contain an element of truth, but it could not be alwaystrue and its naive nature can be seen from the simplest of FRW models, namelyempty universe of Milne (ρ = 0, q o = 0), where even the most distant (z → ∞)observable 94