Research Article The Energy Conservation in Our Universe and the Pressureless Dark Energy

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1 Gravity Volume 2015, Article ID , 4 pages Research Article The Energy Conservation in Our Universe an the Pressureless Dark Energy Man Ho Chan Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong Corresponence shoul be aresse to Man Ho Chan; mhchan@phy.cuhk.eu.hk Receive 5 May 2015; Revise 25 June 2015; Accepte 25 June 2015 Acaemic Eitor: Kazuharu Bamba Copyright 2015 Man Ho Chan. This is an open access article istribute uner the Creative Commons Attribution License, which permits unrestricte use, istribution, an reprouction in any meium, provie the original work is properly cite. Recent observations confirm that a certain amount of unknown ark energy exists in our universe so that the current expansion of our universe is accelerating. It is commonly believe that the pressure of the ark energy is negative an the ensity of the ark energy is almost a constant throughout the universe expansion. In this paper, we show that the law of energy conservation in our universe has to be moifie because more vacuum energy is gaine ue to the universe expansion. As a result, the pressure of ark energy woul be zero if the total energy of our universe is increasing. This pressureless ark energy moel basically agrees with the current observational results. 1. Introuction In the past ecaes, the ata from supernovae confirme the accelerating expansion of our universe [1, 2]. This acceleration can be explaine by assuming the existence of a cosmological constant Λ in the Einstein fiel equation. Usually, this constant is regare as a kin of energy calle ark energy that exists in our universe. The ΛCDM moel, which is the most robust scenario nowaays to escribe the evolution of our universe, suggests that the ark energy ensity ρ Λ is a constant throughout the evolution of our universe. This moel provies goo fits for the ata on the large-scale structure of theuniverseanthecosmicmicrowavebackgroun[3, 4]. Besies this major moel, there are some other ark energy moels which can also satisfy the current observational constraints [5 9]. In fact, quantum physics shows that vacuum is not really nothing but contains energy. The iscovery of the Casimir effect inicates that some nonzero energy exists in vacuum, which is calle the vacuum energy [10]. Therefore, many cosmologists believe that ark energy is inee the vacuum energy [11 13]. However, theoretical calculations show that the preicte value of vacuum energy is nearly 120 orers of magnitue larger than the observe value in our universe [11]. Although there are some theoretical suggestions which can alleviate the problem, no satisfactory explanation is obtaine [14 17]. Moreover, the iea of vacuum energy suffere from the coincience problem [13]. It states that the ratio of ark energy ensity to matter energy ensity is extremely very small at the very beginning of universe expansion while the current value of ark energy ensity is so close to the present matter ensity [18]. Therefore, some suggest invoking a timeepenent ark energy, which is now known as the quintessence moel, to solve the coincience problem [19 21]. Although the iea of vacuum energy has two major problems, recent observations show that the ark energy ensity is really very close to a constant value [22 24]. If ρ Λ is a constant, the parameter of the ark energy equation of state shoul be w= 1, where the pressure of ark energy is given by P Λ =wρ Λ c 2. The most recent observational constraint is w = 0.99 ± 0.06 [25]. Therefore, it seems that it may not be necessary to invoke the iea of quintessence, which suggests that w is not exactly equal to 1. Furthermore, most of the quintessence moels involve some free parameters an arbitrary scalar potential functions which make the moel much more complicate than the vacuum energy moel. Therefore, base on the observations an the simplicity of moel, vacuum energy moel is still a better one that can explain the require ark energy in our universe. Since positive pressure an energy woul prouce attractive gravitational effect on our universe expansion, the negative pressure in ark energy is usually interprete as

2 2 Gravity the effect of antigravity. It is very strange because we o not know anything that is positive in energy but prouces negative pressure. However, the result of the negative pressure of ark energy is solely base on the assumption of energy conservation. What woul be the equation of state of the ark energy if the total energy of our universe is increasing? In this paper, we show that ark energy can be pressureless if we assume that the total energy of our universe is increasing when the universe is expaning. We first review the essential equations that govern the evolution of our universe in the stanar picture. Then we iscuss the effect of the equations after allowing that our universe s total energy is increasing. 2. The Evolution of Our Universe in the Stanar Picture The original Friemann equation with ark energy term in a flat universe is given by a 2 = 8πG 3 ρa2, (1) where a is the cosmic scale factor, G is the universal constant for gravitation, an ρ=ρ r +ρ m +ρ Λ with ρ m an ρ r being the energy ensity of matter an raiation, respectively. On the other han, if the total energy of our universe remains constant, the law of energy conservation gives t (ρa3 )= P c 2 t (a3 ), (2) where P=P m +P r +P Λ is the total pressure with P m an P r being the matter an raiation pressure, respectively, an c is the spee of light. By ifferentiating (1),weget a 4πGρ a 3 a 8πG ρ=0. (3) 3 From (2),weget ρ=( 3ρ 3P c 2 ) a a. (4) By substituting (4) to (3) an P Λ =wρ Λ c 2,weget a = 4πG 3 [( 3w 1) ρ Λ ρ m 3P m c 2 3P r ]. (5) c2 The above equation is the stanar equation to escribe our universe expansion. Since the effects of P m an P r are negligibleinthematteranarkenergyominateuniverse,the accelerating universe expansion requires w 1/3; that is, ark energy shoul have negative pressure. For the stanar ΛCDM moel, ρ Λ is a constant an w= 1. Our universe is accelerating now since ρ Λ >ρ m. 3. The Increasing Energy in Our Universe However, the above calculations are base on the assumption of the constant total energy (2). Ifarkenergyisreallythe vacuum energy, the total energy of our universe is increasing when the universe is expaning. The more the space is involve in our universe, the more the energy woul be containe in our universe [26]. In other wors, some extra energy is flowing into our universe. If this is the case, (2) shoul be rewritten as t (ρa3 ) = P c 2 t (a3 ) + E, (6) where E istherateofenergy flowing intoouruniverse. Since our universe is expaning, the actual volume of our universe is also increasing. Therefore the amount of ark energy (vacuum energy) in our universe is increasing ue to the increasing vacuum volume. Since the ensity of vacuum energy is a constant an the cube of the scale factor a 3 is irectly proportional to the total vacuum volume, we shoul have E =ρ Λ t (a3 ). (7) Therefore, by using (6) an (7),weget ρ=(3ρ Λ 3ρ 3P c 2 ) a a. (8) By putting (8) into (3), the aitional term E finally rewrites the acceleration equation as a = 4πG 3 [(2 3w) ρ Λ ρ m 3P m c 2 3P r ]. (9) c2 Obviously, the expansion of our universe can be accelerating even if w=0. From the traitional moel (our universe as a close system), observations inicate that w 1[25]. Surprisingly, by comparing (5) with (9), this is equivalent to w 0inthenewmoel(thetotalenergyofouruniverseisincreasing). This shows that ark energy is pressureless if we rewrite the energy conservation law. 4. Discussion The traitional cosmological moel consiers the total energy of our universe being constant so that ark energy must provie negative pressure in our universe. However, if we assume that ark energy is inee the vacuum energy, more energy woul be containe in our universe as the universe is expaning. In other wors, the total energy in our universe shoul be increasing. If we inclue the increasing energy term in the flui equation, we nee not require the ark energy to have negative pressure. Recent observations suggest that w 1 in the traitional moel is actually equivalent to w 0 in our moel. This inicates that ark energy is pressureless. Therefore, our moel is consistent an compatible with the observational evience about a negative w. Basically, the iea of negative pressure in ark energy servesasthe antigravity tobalancethegravityeffectfrom matter. If ark energy is pressureless, how can it balance the

3 Gravity 3 attractive gravitational force? The above result tells us that the Einstein fiel equation can intrinsically give acceleration of universe expansion if the total energy of universe is increasing. In the traitional moel, the increase vacuum energy ue to universe expansion is use to o negative work so that the total energy remains unchange. However, we have no clear iea why the ark energy has to o negative work to issipate the energy gaine by itself ue to expansion. If ark energy is pressureless, no work has to be one by the ark energy. All the energy gaine uring universe expansion is vacuum energy. Since the term ρ Λ in (6) woul be cancelle by (7), the scale epenence of matter an raiation woul notbeaffectebytheamountofvacuumenergyifw=0. In fact, assuming that the total energy of our universe is increasing an the ark energy is pressureless is mathematically equivalent to the view that the total energy of our universe remains constant with negative pressure ark energy. However, the physical interpretations are ifferent from each other. The former view is a better interpretation because we nee not assume some new form of energy which has negative pressure. In fact, the Casimir effect just shows us that vacuum energy exists, but not the existence of negative pressure. Also, no work has to be one by the ark energy when the universe is expaning. The only rawback is that we nee to assume that the total energy of our universe is not always constant, whichhasneverbeenproventobeastrictlawinastrophysics. Nevertheless, law of energy conservation can still be applie in general situations as the effect of vacuum energy is negligible. This woul not be true only if we consier our entire universe as an object. Inourmoel,wearenotsayingthattheuniverseis expaning in a greater space with increasing its size an volume in a backgroun space an proceeing in the environment. Base on general relativity, the new volume in ouruniverseiscreatebytheexpansionoftheuniverse. Accoring to quantum mechanics, this simultaneously creates the new vacuum energy because the vacuum energy (ark energy) is associate with the volume. Therefore, the increasing energy in our universe is a irect consequence of the theories of general relativity an quantum mechanics. Although our moel can give a new interpretation of the nature of ark energy, it cannot offer a satisfactory explanation to the cosmological constant problem. Some new mechanisms are require to cancel out the large amount of vacuum energy. Also, this moel cannot account for the scalar fiel that is responsible for inflation. 5. Conclusion If the total energy of our universe is increasing uring the universe expansion, the ark energy coul be regare as pressureless. This interpretation oes not violate any observational results in cosmology. Conflict of Interests The author eclares that there is no conflict of interests regaring the publication of this paper. References [1] A. G. Riess, A. V. Filippenko, P. 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